Programming in Scala, 2nd Edition


Programming in Scala artima Martin Odersky Lex Spoon Bill Venners A comprehensive step-by-step guide Second Edition Updated for Scala 2.8 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Praise for the first edition of Programming in Scala Programming in Scala is probably one of the best programming books I’ve ever read. I like the writing style, the brevity, and the thorough explana- tions. The book seems to answer every question as it enters my mind—it’s always one step ahead of me. The authors don’t just give you some code and take things for granted. They give you the meat so you really understand what’s going on. I really like that. - Ken Egervari, Chief Software Architect Programming in Scala is clearly written, thorough, and easy to follow. It has great examples and useful tips throughout. It has enabled our organi- zation to ramp up on the Scala language quickly and efficiently. This book is great for any programmer who is trying to wrap their head around the flexibility and elegance of the Scala language. - Larry Morroni, Owner, Morroni Technologies, Inc. The Programming in Scala book serves as an excellent tutorial to the Scala language. Working through the book, it flows well with each chapter building on concepts and examples described in earlier ones. The book takes care to explain the language constructs in depth, often providing examples of how the language differs from Java. As well as the main language, there is also some coverage of libraries such as containers and actors. I have found the book really easy to work through, and it is probably one of the better written technical books I have read recently. I really would recommend this book to any programmer wanting to find out more about the Scala language. - Matthew Todd Cover · Overview · Contents · Discuss · Suggest · Glossary · Index iii I am amazed by the effort undertaken by the authors of Programming in Scala. This book is an invaluable guide to what I like to call Scala the Plat- form: a vehicle to better coding, a constant inspiration for scalable software design and implementation. If only I had Scala in its present mature state and this book on my desk back in 2003, when co-designing and implement- ing parts of the Athens 2004 Olympic Games Portal infrastructure! To all readers: No matter what your programming background is, I feel you will find programming in Scala liberating and this book will be a loyal friend in the journey. - Christos KK Loverdos, Software Consultant, Researcher Programming in Scala is a superb in-depth introduction to Scala, and it’s also an excellent reference. I’d say that it occupies a prominent place on my bookshelf, except that I’m still carrying it around with me nearly everywhere I go. - Brian Clapper, President, ArdenTex, Inc. Great book, well written with thoughtful examples. I would recommend it to both seasoned programmers and newbies. - Howard Lovatt The book Programming in Scala is not only about how, but more im- portantly, why to develop programs in this new programming language. The book’s pragmatic approach in introducing the power of combining object- oriented and functional programming leaves the reader without any doubts as to what Scala really is. - Dr. Ervin Varga, CEO/founder, EXPRO I.T. Consulting This is a great introduction to functional programming for OO program- mers. Learning about FP was my main goal, but I also got acquainted with some nice Scala surprises like case classes and pattern matching. Scala is an intriguing language and this book covers it well. There’s always a fine line to walk in a language introduction book be- tween giving too much or not enough information. I find Programming in Scala to achieve a perfect balance. - Jeff Heon, Programmer Analyst Cover · Overview · Contents · Discuss · Suggest · Glossary · Index iv I bought an early electronic version of the Programming in Scala book, by Odersky, Spoon, and Venners, and I was immediately a fan. In addition to the fact that it contains the most comprehensive information about the language, there are a few key features of the electronic format that impressed me. I have never seen links used as well in a PDF, not just for bookmarks, but also providing active links from the table of contents and index. I don’t know why more authors don’t use this feature, because it’s really a joy for the reader. Another feature which I was impressed with was links to the forums (“Discuss”) and a way to send comments (“Suggest”) to the authors via email. The comments feature by itself isn’t all that uncommon, but the simple inclusion of a page number in what is generated to send to the authors is valuable for both the authors and readers. I contributed more comments than I would have if the process would have been more arduous. Read Programming in Scala for the content, but if you’re reading the electronic version, definitely take advantage of the digital features that the authors took the care to build in! - Dianne Marsh, Founder/Software Consultant, SRT Solutions Lucidity and technical completeness are hallmarks of any well-written book, and I congratulate Martin Odersky, Lex Spoon, and Bill Venners on a job indeed very well done! The Programming in Scala book starts by setting a strong foundation with the basic concepts and ramps up the user to an intermediate level & beyond. This book is certainly a must buy for anyone aspiring to learn Scala. - Jagan Nambi, Enterprise Architecture, GMAC Financial Services Programming in Scala is a pleasure to read. This is one of those well- written technical books that provide deep and comprehensive coverage of the subject in an exceptionally concise and elegant manner. The book is organized in a very natural and logical way. It is equally well suited for a curious technologist who just wants to stay on top of the current trends and a professional seeking deep understanding of the language core features and its design rationales. I highly recommend it to all interested in functional programming in general. For Scala developers, this book is unconditionally a must-read. - Igor Khlystov, Software Architect/Lead Programmer, Greystone Inc. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index v The book Programming in Scala outright oozes the huge amount of hard work that has gone into it. I’ve never read a tutorial-style book before that accomplishes to be introductory yet comprehensive: in their (misguided) at- tempt to be approachable and not “confuse” the reader, most tutorials silently ignore aspects of a subject that are too advanced for the current discussion. This leaves a very bad taste, as one can never be sure as to the understanding one has achieved. There is always some residual “magic” that hasn’t been explained and cannot be judged at all by the reader. This book never does that, it never takes anything for granted: every detail is either sufficiently explained or a reference to a later explanation is given. Indeed, the text is extensively cross-referenced and indexed, so that forming a complete picture of a complex topic is relatively easy. - Gerald Loeffler, Enterprise Java Architect Programming in Scala by Martin Odersky, Lex Spoon, and Bill Venners: in times where good programming books are rare, this excellent introduction for intermediate programmers really stands out. You’ll find everything here you need to learn this promising language. - Christian Neukirchen Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Programming in Scala Second Edition Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Programming in Scala Second Edition Martin Odersky, Lex Spoon, Bill Venners artima ARTIMA PRESS WALNUT CREEK,CALIFORNIA Cover · Overview · Contents · Discuss · Suggest · Glossary · Index viii Programming in Scala Second Edition Martin Odersky is the creator of the Scala language and a professor at EPFL in Lausanne, Switzerland. Lex Spoon worked on Scala for two years as a post-doc with Martin Odersky. Bill Venners is president of Artima, Inc. Artima Press is an imprint of Artima, Inc. P.O. Box 305, Walnut Creek, California 94597 Copyright © 2007-2010 Martin Odersky, Lex Spoon, and Bill Venners. All rights reserved. First edition published as PrePrint™ eBook 2007 First edition published 2008 Second edition published as PrePrint™ eBook 2010 Second edition published 2010 Build date of this impression December 13, 2010 Produced in the United States of America No part of this publication may be reproduced, modified, distributed, stored in a retrieval system, republished, displayed, or performed, for commercial or noncommercial purposes or for compensation of any kind without prior written permission from Artima, Inc. All information and materials in this book are provided "as is" and without warranty of any kind. The term “Artima” and the Artima logo are trademarks or registered trademarks of Artima, Inc. All other company and/or product names may be trademarks or registered trademarks of their owners. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index to Nastaran - M.O. to Fay - L.S. to Siew - B.V. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Overview Contents xi List of Figures xxii List of Tables xxiv List of Listings xxvi Foreword xxxiv Foreword to the First Edition xxxvi Acknowledgments xxxviii Introduction xli 1. A Scalable Language 49 2. First Steps in Scala 68 3. Next Steps in Scala 81 4. Classes and Objects 103 5. Basic Types and Operations 117 6. Functional Objects 139 7. Built-in Control Structures 159 8. Functions and Closures 184 9. Control Abstraction 207 10. Composition and Inheritance 222 11. Scala’s Hierarchy 250 12. Traits 258 13. Packages and Imports 277 14. Assertions and Unit Testing 295 15. Case Classes and Pattern Matching 309 16. Working with Lists 344 17. Collections 377 18. Stateful Objects 399 19. Type Parameterization 422 20. Abstract Members 447 21. Implicit Conversions and Parameters 479 22. Implementing Lists 503 23. For Expressions Revisited 516 24. The Scala Collections API 532 25. The Architecture of Scala Collections 607 26. Extractors 631 27. Annotations 647 28. Working with XML 655 29. Modular Programming Using Objects 669 30. Object Equality 684 31. Combining Scala and Java 710 32. Actors and Concurrency 724 33. Combinator Parsing 759 34. GUI Programming 788 35. The SCells Spreadsheet 800 A. Scala Scripts on Unix and Windows 825 Glossary 826 Bibliography 842 About the Authors 845 Index 846 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents Contents xi List of Figures xxii List of Tables xxiv List of Listings xxvi Foreword xxxiv Foreword to the First Edition xxxvi Acknowledgments xxxviii Introduction xli 1 A Scalable Language 49 1.1 A language that grows on you . . . . . . . . . . . . . . 50 1.2 What makes Scala scalable? . . . . . . . . . . . . . . . 55 1.3 Why Scala? ........................ 58 1.4 Scala’s roots ....................... 65 1.5 Conclusion ........................ 67 2 First Steps in Scala 68 Step 1. Learn to use the Scala interpreter . . . . . . . . . . . . 68 Step 2. Define some variables . . . . . . . . . . . . . . . . . 70 Step 3. Define some functions . . . . . . . . . . . . . . . . . 72 Step 4. Write some Scala scripts . . . . . . . . . . . . . . . . 74 Step 5. Loop with while; decide with if . . . . . . . . . . . 75 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xii Step 6. Iterate with foreach and for . . . . . . . . . . . . . 77 Conclusion ........................... 80 3 Next Steps in Scala 81 Step 7. Parameterize arrays with types . . . . . . . . . . . . 81 Step 8. Use lists ........................ 85 Step 9. Use tuples ....................... 90 Step 10. Use sets and maps ................... 91 Step 11. Learn to recognize the functional style . . . . . . . . 96 Step 12. Read lines from a file . . . . . . . . . . . . . . . . . 99 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4 Classes and Objects 103 4.1 Classes, fields, and methods . . . . . . . . . . . . . . . 103 4.2 Semicolon inference . . . . . . . . . . . . . . . . . . . 108 4.3 Singleton objects . . . . . . . . . . . . . . . . . . . . . 109 4.4 A Scala application . . . . . . . . . . . . . . . . . . . 112 4.5 The Application trait . . . . . . . . . . . . . . . . . . 115 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 116 5 Basic Types and Operations 117 5.1 Some basic types . . . . . . . . . . . . . . . . . . . . . 117 5.2 Literals . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.3 Operators are methods . . . . . . . . . . . . . . . . . . 125 5.4 Arithmetic operations . . . . . . . . . . . . . . . . . . 128 5.5 Relational and logical operations . . . . . . . . . . . . 129 5.6 Bitwise operations . . . . . . . . . . . . . . . . . . . . 131 5.7 Object equality . . . . . . . . . . . . . . . . . . . . . . 132 5.8 Operator precedence and associativity . . . . . . . . . . 134 5.9 Rich wrappers . . . . . . . . . . . . . . . . . . . . . . 137 5.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 137 6 Functional Objects 139 6.1 A specification for class Rational . . . . . . . . . . . 139 6.2 Constructing a Rational . . . . . . . . . . . . . . . . 140 6.3 Reimplementing the toString method . . . . . . . . . 142 6.4 Checking preconditions . . . . . . . . . . . . . . . . . 143 6.5 Adding fields . . . . . . . . . . . . . . . . . . . . . . . 143 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xiii 6.6 Self references . . . . . . . . . . . . . . . . . . . . . . 145 6.7 Auxiliary constructors . . . . . . . . . . . . . . . . . . 146 6.8 Private fields and methods . . . . . . . . . . . . . . . . 148 6.9 Defining operators . . . . . . . . . . . . . . . . . . . . 149 6.10 Identifiers in Scala . . . . . . . . . . . . . . . . . . . . 151 6.11 Method overloading . . . . . . . . . . . . . . . . . . . 154 6.12 Implicit conversions . . . . . . . . . . . . . . . . . . . 156 6.13 A word of caution . . . . . . . . . . . . . . . . . . . . 157 6.14 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 157 7 Built-in Control Structures 159 7.1 If expressions . . . . . . . . . . . . . . . . . . . . . . 160 7.2 While loops . . . . . . . . . . . . . . . . . . . . . . . 161 7.3 For expressions . . . . . . . . . . . . . . . . . . . . . . 164 7.4 Exception handling with try expressions . . . . . . . . 169 7.5 Match expressions . . . . . . . . . . . . . . . . . . . . 173 7.6 Living without break and continue . . . . . . . . . . 175 7.7 Variable scope . . . . . . . . . . . . . . . . . . . . . . 177 7.8 Refactoring imperative-style code . . . . . . . . . . . . 181 7.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 183 8 Functions and Closures 184 8.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . 184 8.2 Local functions . . . . . . . . . . . . . . . . . . . . . . 186 8.3 First-class functions . . . . . . . . . . . . . . . . . . . 188 8.4 Short forms of function literals . . . . . . . . . . . . . 190 8.5 Placeholder syntax . . . . . . . . . . . . . . . . . . . . 191 8.6 Partially applied functions . . . . . . . . . . . . . . . . 192 8.7 Closures . . . . . . . . . . . . . . . . . . . . . . . . . 195 8.8 Special function call forms . . . . . . . . . . . . . . . . 199 8.9 Tail recursion . . . . . . . . . . . . . . . . . . . . . . . 202 8.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 206 9 Control Abstraction 207 9.1 Reducing code duplication . . . . . . . . . . . . . . . . 207 9.2 Simplifying client code . . . . . . . . . . . . . . . . . 211 9.3 Currying . . . . . . . . . . . . . . . . . . . . . . . . . 213 9.4 Writing new control structures . . . . . . . . . . . . . . 215 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xiv 9.5 By-name parameters . . . . . . . . . . . . . . . . . . . 218 9.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 221 10 Composition and Inheritance 222 10.1 A two-dimensional layout library . . . . . . . . . . . . 222 10.2 Abstract classes . . . . . . . . . . . . . . . . . . . . . 223 10.3 Defining parameterless methods . . . . . . . . . . . . . 224 10.4 Extending classes . . . . . . . . . . . . . . . . . . . . 227 10.5 Overriding methods and fields . . . . . . . . . . . . . . 229 10.6 Defining parametric fields . . . . . . . . . . . . . . . . 230 10.7 Invoking superclass constructors . . . . . . . . . . . . . 232 10.8 Using override modifiers . . . . . . . . . . . . . . . . 233 10.9 Polymorphism and dynamic binding . . . . . . . . . . 235 10.10 Declaring final members . . . . . . . . . . . . . . . . . 237 10.11 Using composition and inheritance . . . . . . . . . . . 239 10.12 Implementing above, beside, and toString . . . . . . 240 10.13 Defining a factory object . . . . . . . . . . . . . . . . . 242 10.14 Heighten and widen . . . . . . . . . . . . . . . . . . . 244 10.15 Putting it all together . . . . . . . . . . . . . . . . . . . 248 10.16 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 249 11 Scala’s Hierarchy 250 11.1 Scala’s class hierarchy . . . . . . . . . . . . . . . . . . 250 11.2 How primitives are implemented . . . . . . . . . . . . 254 11.3 Bottom types . . . . . . . . . . . . . . . . . . . . . . . 256 11.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 257 12 Traits 258 12.1 How traits work . . . . . . . . . . . . . . . . . . . . . 258 12.2 Thin versus rich interfaces . . . . . . . . . . . . . . . . 261 12.3 Example: Rectangular objects . . . . . . . . . . . . . . 262 12.4 The Ordered trait . . . . . . . . . . . . . . . . . . . . 265 12.5 Traits as stackable modifications . . . . . . . . . . . . . 267 12.6 Why not multiple inheritance? . . . . . . . . . . . . . . 271 12.7 To trait, or not to trait? . . . . . . . . . . . . . . . . . . 275 12.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 276 13 Packages and Imports 277 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xv 13.1 Putting code in packages . . . . . . . . . . . . . . . . . 277 13.2 Concise access to related code . . . . . . . . . . . . . . 278 13.3 Imports . . . . . . . . . . . . . . . . . . . . . . . . . . 282 13.4 Implicit imports . . . . . . . . . . . . . . . . . . . . . 286 13.5 Access modifiers . . . . . . . . . . . . . . . . . . . . . 287 13.6 Package objects . . . . . . . . . . . . . . . . . . . . . 292 13.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 294 14 Assertions and Unit Testing 295 14.1 Assertions . . . . . . . . . . . . . . . . . . . . . . . . 295 14.2 Unit testing in Scala . . . . . . . . . . . . . . . . . . . 297 14.3 Informative failure reports . . . . . . . . . . . . . . . . 298 14.4 Using JUnit and TestNG . . . . . . . . . . . . . . . . . 300 14.5 Tests as specifications . . . . . . . . . . . . . . . . . . 302 14.6 Property-based testing . . . . . . . . . . . . . . . . . . 305 14.7 Organizing and running tests . . . . . . . . . . . . . . 306 14.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 308 15 Case Classes and Pattern Matching 309 15.1 A simple example . . . . . . . . . . . . . . . . . . . . 309 15.2 Kinds of patterns . . . . . . . . . . . . . . . . . . . . . 314 15.3 Pattern guards . . . . . . . . . . . . . . . . . . . . . . 324 15.4 Pattern overlaps . . . . . . . . . . . . . . . . . . . . . 325 15.5 Sealed classes . . . . . . . . . . . . . . . . . . . . . . 326 15.6 The Option type . . . . . . . . . . . . . . . . . . . . . 328 15.7 Patterns everywhere . . . . . . . . . . . . . . . . . . . 330 15.8 A larger example . . . . . . . . . . . . . . . . . . . . . 335 15.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 343 16 Working with Lists 344 16.1 List literals . . . . . . . . . . . . . . . . . . . . . . . . 344 16.2 The List type . . . . . . . . . . . . . . . . . . . . . . 345 16.3 Constructing lists . . . . . . . . . . . . . . . . . . . . . 345 16.4 Basic operations on lists . . . . . . . . . . . . . . . . . 346 16.5 List patterns . . . . . . . . . . . . . . . . . . . . . . . 347 16.6 First-order methods on class List . . . . . . . . . . . . 349 16.7 Higher-order methods on class List . . . . . . . . . . 361 16.8 Methods of the List object . . . . . . . . . . . . . . . 369 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xvi 16.9 Processing multiple lists together . . . . . . . . . . . . 371 16.10 Understanding Scala’s type inference algorithm . . . . . 372 16.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 376 17 Collections 377 17.1 Sequences . . . . . . . . . . . . . . . . . . . . . . . . 377 17.2 Sets and maps . . . . . . . . . . . . . . . . . . . . . . 381 17.3 Selecting mutable versus immutable collections . . . . 390 17.4 Initializing collections . . . . . . . . . . . . . . . . . . 392 17.5 Tuples . . . . . . . . . . . . . . . . . . . . . . . . . . 396 17.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 398 18 Stateful Objects 399 18.1 What makes an object stateful? . . . . . . . . . . . . . 399 18.2 Reassignable variables and properties . . . . . . . . . . 402 18.3 Case study: Discrete event simulation . . . . . . . . . . 405 18.4 A language for digital circuits . . . . . . . . . . . . . . 406 18.5 The Simulation API . . . . . . . . . . . . . . . . . . 409 18.6 Circuit Simulation . . . . . . . . . . . . . . . . . . . . 413 18.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 421 19 Type Parameterization 422 19.1 Functional queues . . . . . . . . . . . . . . . . . . . . 422 19.2 Information hiding . . . . . . . . . . . . . . . . . . . . 426 19.3 Variance annotations . . . . . . . . . . . . . . . . . . . 429 19.4 Checking variance annotations . . . . . . . . . . . . . . 433 19.5 Lower bounds . . . . . . . . . . . . . . . . . . . . . . 436 19.6 Contravariance . . . . . . . . . . . . . . . . . . . . . . 438 19.7 Object private data . . . . . . . . . . . . . . . . . . . . 441 19.8 Upper bounds . . . . . . . . . . . . . . . . . . . . . . 443 19.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 446 20 Abstract Members 447 20.1 A quick tour of abstract members . . . . . . . . . . . . 447 20.2 Type members . . . . . . . . . . . . . . . . . . . . . . 448 20.3 Abstract vals . . . . . . . . . . . . . . . . . . . . . . . 449 20.4 Abstract vars . . . . . . . . . . . . . . . . . . . . . . . 450 20.5 Initializing abstract vals . . . . . . . . . . . . . . . . . 451 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xvii 20.6 Abstract types . . . . . . . . . . . . . . . . . . . . . . 459 20.7 Path-dependent types . . . . . . . . . . . . . . . . . . 461 20.8 Structural subtyping . . . . . . . . . . . . . . . . . . . 464 20.9 Enumerations . . . . . . . . . . . . . . . . . . . . . . . 466 20.10 Case study: Currencies . . . . . . . . . . . . . . . . . . 468 20.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 478 21 Implicit Conversions and Parameters 479 21.1 Implicit conversions . . . . . . . . . . . . . . . . . . . 479 21.2 Rules for implicits . . . . . . . . . . . . . . . . . . . . 482 21.3 Implicit conversion to an expected type . . . . . . . . . 485 21.4 Converting the receiver . . . . . . . . . . . . . . . . . 486 21.5 Implicit parameters . . . . . . . . . . . . . . . . . . . . 489 21.6 View bounds . . . . . . . . . . . . . . . . . . . . . . . 495 21.7 When multiple conversions apply . . . . . . . . . . . . 498 21.8 Debugging implicits . . . . . . . . . . . . . . . . . . . 501 21.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 502 22 Implementing Lists 503 22.1 The List class in principle . . . . . . . . . . . . . . . 503 22.2 The ListBuffer class . . . . . . . . . . . . . . . . . . 509 22.3 The List class in practice . . . . . . . . . . . . . . . . 511 22.4 Functional on the outside . . . . . . . . . . . . . . . . 513 22.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 514 23 For Expressions Revisited 516 23.1 For expressions . . . . . . . . . . . . . . . . . . . . . . 517 23.2 The n-queens problem . . . . . . . . . . . . . . . . . . 519 23.3 Querying with for expressions . . . . . . . . . . . . . 522 23.4 Translation of for expressions . . . . . . . . . . . . . . 524 23.5 Going the other way . . . . . . . . . . . . . . . . . . . 528 23.6 Generalizing for . . . . . . . . . . . . . . . . . . . . . 529 23.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 531 24 The Scala Collections API 532 24.1 Mutable and immutable collections . . . . . . . . . . . 533 24.2 Collections consistency . . . . . . . . . . . . . . . . . 535 24.3 Trait Traversable . . . . . . . . . . . . . . . . . . . . 537 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xviii 24.4 Trait Iterable . . . . . . . . . . . . . . . . . . . . . . 542 24.5 The sequence traits Seq, IndexedSeq, and LinearSeq . 546 24.6 Sets ............................ 551 24.7 Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 24.8 Synchronized sets and maps . . . . . . . . . . . . . . . 562 24.9 Concrete immutable collection classes . . . . . . . . . 564 24.10 Concrete mutable collection classes . . . . . . . . . . . 571 24.11 Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . 578 24.12 Strings . . . . . . . . . . . . . . . . . . . . . . . . . . 583 24.13 Performance characteristics . . . . . . . . . . . . . . . 584 24.14 Equality . . . . . . . . . . . . . . . . . . . . . . . . . 585 24.15 Views . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 24.16 Iterators . . . . . . . . . . . . . . . . . . . . . . . . . 593 24.17 Creating collections from scratch . . . . . . . . . . . . 601 24.18 Conversions between Java and Scala collections . . . . 603 24.19 Migrating from Scala 2.7 . . . . . . . . . . . . . . . . 605 24.20 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 606 25 The Architecture of Scala Collections 607 25.1 Builders . . . . . . . . . . . . . . . . . . . . . . . . . 608 25.2 Factoring out common operations . . . . . . . . . . . . 609 25.3 Integrating new collections . . . . . . . . . . . . . . . 614 25.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 630 26 Extractors 631 26.1 An example: extracting email addresses . . . . . . . . . 631 26.2 Extractors . . . . . . . . . . . . . . . . . . . . . . . . 632 26.3 Patterns with zero or one variables . . . . . . . . . . . 635 26.4 Variable argument extractors . . . . . . . . . . . . . . . 637 26.5 Extractors and sequence patterns . . . . . . . . . . . . 640 26.6 Extractors versus case classes . . . . . . . . . . . . . . 641 26.7 Regular expressions . . . . . . . . . . . . . . . . . . . 642 26.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 646 27 Annotations 647 27.1 Why have annotations? . . . . . . . . . . . . . . . . . 647 27.2 Syntax of annotations . . . . . . . . . . . . . . . . . . 648 27.3 Standard annotations . . . . . . . . . . . . . . . . . . . 650 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xix 27.4 Conclusion........................ 654 28 Working with XML 655 28.1 Semi-structured data . . . . . . . . . . . . . . . . . . . 655 28.2 XML overview . . . . . . . . . . . . . . . . . . . . . . 656 28.3 XML literals . . . . . . . . . . . . . . . . . . . . . . . 657 28.4 Serialization . . . . . . . . . . . . . . . . . . . . . . . 659 28.5 Taking XML apart . . . . . . . . . . . . . . . . . . . . 661 28.6 Deserialization . . . . . . . . . . . . . . . . . . . . . . 662 28.7 Loading and saving . . . . . . . . . . . . . . . . . . . 663 28.8 Pattern matching on XML . . . . . . . . . . . . . . . . 665 28.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 668 29 Modular Programming Using Objects 669 29.1 The problem . . . . . . . . . . . . . . . . . . . . . . . 670 29.2 A recipe application . . . . . . . . . . . . . . . . . . . 671 29.3 Abstraction . . . . . . . . . . . . . . . . . . . . . . . . 674 29.4 Splitting modules into traits . . . . . . . . . . . . . . . 677 29.5 Runtime linking . . . . . . . . . . . . . . . . . . . . . 680 29.6 Tracking module instances . . . . . . . . . . . . . . . . 681 29.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 683 30 Object Equality 684 30.1 Equality in Scala . . . . . . . . . . . . . . . . . . . . . 684 30.2 Writing an equality method . . . . . . . . . . . . . . . 685 30.3 Defining equality for parameterized types . . . . . . . . 698 30.4 Recipes for equals and hashCode . . . . . . . . . . . 703 30.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 709 31 Combining Scala and Java 710 31.1 Using Scala from Java . . . . . . . . . . . . . . . . . . 710 31.2 Annotations . . . . . . . . . . . . . . . . . . . . . . . 713 31.3 Existential types . . . . . . . . . . . . . . . . . . . . . 718 31.4 Using synchronized . . . . . . . . . . . . . . . . . . 722 31.5 Compiling Scala and Java together . . . . . . . . . . . 722 31.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 723 32 Actors and Concurrency 724 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xx 32.1 Trouble in paradise . . . . . . . . . . . . . . . . . . . . 724 32.2 Actors and message passing . . . . . . . . . . . . . . . 725 32.3 Treating native threads as actors . . . . . . . . . . . . . 729 32.4 Better performance through thread reuse . . . . . . . . 730 32.5 Good actors style . . . . . . . . . . . . . . . . . . . . . 733 32.6 A longer example: Parallel discrete event simulation . . 740 32.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 757 33 Combinator Parsing 759 33.1 Example: Arithmetic expressions . . . . . . . . . . . . 760 33.2 Running your parser . . . . . . . . . . . . . . . . . . . 762 33.3 Basic regular expression parsers . . . . . . . . . . . . . 763 33.4 Another example: JSON . . . . . . . . . . . . . . . . . 764 33.5 Parser output . . . . . . . . . . . . . . . . . . . . . . . 766 33.6 Implementing combinator parsers . . . . . . . . . . . . 772 33.7 String literals and regular expressions . . . . . . . . . . 781 33.8 Lexing and parsing . . . . . . . . . . . . . . . . . . . . 782 33.9 Error reporting . . . . . . . . . . . . . . . . . . . . . . 782 33.10 Backtracking versus LL(1) . . . . . . . . . . . . . . . . 784 33.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 786 34 GUI Programming 788 34.1 A first Swing application . . . . . . . . . . . . . . . . . 788 34.2 Panels and layouts . . . . . . . . . . . . . . . . . . . . 791 34.3 Handling events . . . . . . . . . . . . . . . . . . . . . 793 34.4 Example: Celsius/Fahrenheit converter . . . . . . . . . 796 34.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 798 35 The SCells Spreadsheet 800 35.1 The visual framework . . . . . . . . . . . . . . . . . . 800 35.2 Disconnecting data entry and display . . . . . . . . . . 803 35.3 Formulas . . . . . . . . . . . . . . . . . . . . . . . . . 806 35.4 Parsing formulas . . . . . . . . . . . . . . . . . . . . . 808 35.5 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . 813 35.6 Operation libraries . . . . . . . . . . . . . . . . . . . . 816 35.7 Change propagation . . . . . . . . . . . . . . . . . . . 819 35.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 823 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Contents xxi A Scala Scripts on Unix and Windows 825 Glossary 826 Bibliography 842 About the Authors 845 Index 846 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index List of Figures 2.1 The basic form of a function definition in Scala. . . . . . . . 73 2.2 The syntax of a function literal in Scala. . . . . . . . . . . . 79 3.1 All operations are method calls in Scala. . . . . . . . . . . . 84 3.2 Class hierarchy for Scala sets. . . . . . . . . . . . . . . . . 92 3.3 Class hierarchy for Scala maps. . . . . . . . . . . . . . . . . 94 10.1 Class diagram for ArrayElement. . . . . . . . . . . . . . . 228 10.2 Class diagram for LineElement. . . . . . . . . . . . . . . . 233 10.3 Class hierarchy of layout elements. . . . . . . . . . . . . . . 236 10.4 Class hierarchy with revised LineElement. . . . . . . . . . 240 11.1 Class hierarchy of Scala. . . . . . . . . . . . . . . . . . . . 252 12.1 Inheritance hierarchy and linearization of class Cat. . . . . . 274 14.1 ScalaTest’s graphical reporter. . . . . . . . . . . . . . . . . 307 18.1 Basic gates. . . . . . . . . . . . . . . . . . . . . . . . . . . 406 18.2 A half-adder circuit. . . . . . . . . . . . . . . . . . . . . . . 408 18.3 A full-adder circuit. . . . . . . . . . . . . . . . . . . . . . . 409 19.1 Covariance and contravariance in function type parameters. . 441 22.1 Class hierarchy for Scala lists. . . . . . . . . . . . . . . . . 504 22.2 The structure of the Scala lists shown in Listing 22.2. . . . . 508 24.1 Collection hierarchy. . . . . . . . . . . . . . . . . . . . . . 536 25.1 An example Patricia trie. . . . . . . . . . . . . . . . . . . . 625 xxii List of Figures xxiii 34.1 A simple Swing application: initial (left) and resized (right). 789 34.2 A reactive Swing application: initial (left) after clicks (right). 791 34.3 A converter between degrees Celsius and Fahrenheit. . . . . 796 35.1 A simple spreadsheet table. . . . . . . . . . . . . . . . . . . 801 35.2 Cells displaying themselves. . . . . . . . . . . . . . . . . . 806 35.3 Cells displaying their formulas. . . . . . . . . . . . . . . . . 812 35.4 Cells that evaluate. . . . . . . . . . . . . . . . . . . . . . . 818 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index List of Tables 3.1 Some List methods and usages . . . . . . . . . . . . . . . 88 5.1 Some basic types . . . . . . . . . . . . . . . . . . . . . . . 118 5.2 Special character literal escape sequences . . . . . . . . . . 122 5.3 Operator precedence . . . . . . . . . . . . . . . . . . . . . 135 5.4 Some rich operations . . . . . . . . . . . . . . . . . . . . 138 5.5 Rich wrapper classes . . . . . . . . . . . . . . . . . . . . . 138 12.1 Linearization of types in Cat’s hierarchy . . . . . . . . . . 275 13.1 Effects of private qualifiers on LegOfJourney.distance . 290 16.1 Basic list operations . . . . . . . . . . . . . . . . . . . . . 347 17.1 Common operations for sets . . . . . . . . . . . . . . . . . 384 17.2 Common operations for maps . . . . . . . . . . . . . . . . 386 17.3 Default immutable set implementations . . . . . . . . . . . 388 17.4 Default immutable map implementations . . . . . . . . . . 388 24.1 Operations in trait Traversable . . . . . . . . . . . . . . 539 24.2 Operations in trait Iterable . . . . . . . . . . . . . . . . 544 24.3 Operations in trait Seq . . . . . . . . . . . . . . . . . . . 548 24.4 Operations in trait Buffer . . . . . . . . . . . . . . . . . 551 24.5 Operations in trait Set . . . . . . . . . . . . . . . . . . . 552 24.6 Operations in trait mutable.Set . . . . . . . . . . . . . . 553 24.7 Operations in trait Map . . . . . . . . . . . . . . . . . . . 558 24.8 Operations in trait mutable.Map . . . . . . . . . . . . . . 560 24.9 Operations in trait ConcurrentMap . . . . . . . . . . . . . 577 24.10 Performance characteristics of sequence types . . . . . . . 586 xxiv List of Tables xxv 24.11 Performance characteristics of set and map types . . . . . . 586 24.12 Operations in trait Iterator . . . . . . . . . . . . . . . . 595 24.13 Factory methods for sequences . . . . . . . . . . . . . . . 602 33.1 Summary of parser combinators . . . . . . . . . . . . . . . 770 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index List of Listings 3.1 Parameterizing an array with a type. . . . . . . . . . . . . 82 3.2 Creating and initializing an array. . . . . . . . . . . . . . . 85 3.3 Creating and initializing a list. . . . . . . . . . . . . . . . . 86 3.4 Creating and using a tuple. . . . . . . . . . . . . . . . . . 90 3.5 Creating, initializing, and using an immutable set. . . . . . 91 3.6 Creating, initializing, and using a mutable set. . . . . . . . 93 3.7 Creating, initializing, and using a mutable map. . . . . . . 94 3.8 Creating, initializing, and using an immutable map. . . . . 95 3.9 A function without side effects or vars. . . . . . . . . . . . 97 3.10 Reading lines from a file. . . . . . . . . . . . . . . . . . . 99 3.11 Printing formatted character counts for the lines of a file. . 102 4.1 Final version of class ChecksumAccumulator. . . . . . . . 107 4.2 Companion object for class ChecksumAccumulator. . . . . 110 4.3 The Summer application. . . . . . . . . . . . . . . . . . . . 112 4.4 Using the Application trait. . . . . . . . . . . . . . . . . 115 6.1 Rational with fields. . . . . . . . . . . . . . . . . . . . . 145 6.2 Rational with an auxiliary constructor. . . . . . . . . . . 147 6.3 Rational with a private field and method. . . . . . . . . . 148 6.4 Rational with operator methods. . . . . . . . . . . . . . . 150 6.5 Rational with overloaded methods. . . . . . . . . . . . . 155 7.1 Scala’s idiom for conditional initialization. . . . . . . . . . 160 7.2 Calculating greatest common divisor with a while loop. . . 161 7.3 Reading from the standard input with do-while. . . . . . . 162 7.4 Calculating greatest common divisor with recursion. . . . . 163 7.5 Listing files in a directory with a for expression. . . . . . . 164 xxvi List of Listings xxvii 7.6 Finding .scala files using a for with a filter. . . . . . . . 166 7.7 Using multiple filters in a for expression. . . . . . . . . . 166 7.8 Using multiple generators in a for expression. . . . . . . . 167 7.9 Mid-stream assignment in a for expression. . . . . . . . . 168 7.10 Transforming an Array[File] to Array[Int] with a for. 169 7.11 A try-catch clause in Scala. . . . . . . . . . . . . . . . . 171 7.12 A try-finally clause in Scala. . . . . . . . . . . . . . . 172 7.13 A catch clause that yields a value. . . . . . . . . . . . . . 173 7.14 A match expression with side effects. . . . . . . . . . . . . 174 7.15 A match expression that yields a value. . . . . . . . . . . . 174 7.16 Looping without break or continue. . . . . . . . . . . . . 176 7.17 A recursive alternative to looping with vars. . . . . . . . . 176 7.18 Variable scoping when printing a multiplication table. . . . 179 7.19 A functional way to create a multiplication table. . . . . . . 182 8.1 LongLines with a private processLine method. . . . . . . 185 8.2 LongLines with a local processLine function. . . . . . . 187 8.3 A parameter with a default value. . . . . . . . . . . . . . . 201 8.4 A function with two parameters that have defaults. . . . . . 202 9.1 Using closures to reduce code duplication. . . . . . . . . . 211 9.2 Defining and invoking a “plain old” function. . . . . . . . . 214 9.3 Defining and invoking a curried function. . . . . . . . . . . 214 9.4 Using the loan pattern to write to a file. . . . . . . . . . . . 218 9.5 Using a by-name parameter. . . . . . . . . . . . . . . . . . 219 10.1 Defining an abstract method and class. . . . . . . . . . . . 224 10.2 Defining parameterless methods width and height. . . . . 225 10.3 Defining ArrayElement as a subclass of Element. . . . . . 227 10.4 Overriding a parameterless method with a field. . . . . . . 229 10.5 Defining contents as a parametric field. . . . . . . . . . . 231 10.6 Invoking a superclass constructor. . . . . . . . . . . . . . . 232 10.7 Declaring a final method. . . . . . . . . . . . . . . . . . . 238 10.8 Declaring a final class. . . . . . . . . . . . . . . . . . . . . 238 10.9 Class Element with above, beside, and toString. . . . . 243 10.10 A factory object with factory methods. . . . . . . . . . . . 244 10.11 Class Element refactored to use factory methods. . . . . . 245 10.12 Hiding implementation with private classes. . . . . . . . . 246 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index List of Listings xxviii 10.13 Element with widen and heighten methods. . . . . . . . 247 10.14 The Spiral application. . . . . . . . . . . . . . . . . . . . 248 12.1 The definition of trait Philosophical. . . . . . . . . . . . 258 12.2 Mixing in a trait using extends. . . . . . . . . . . . . . . 259 12.3 Mixing in a trait using with. . . . . . . . . . . . . . . . . 260 12.4 Mixing in multiple traits. . . . . . . . . . . . . . . . . . . 260 12.5 Defining an enrichment trait. . . . . . . . . . . . . . . . . 264 12.6 Abstract class IntQueue. . . . . . . . . . . . . . . . . . . 268 12.7 A BasicIntQueue implemented with an ArrayBuffer. . . 268 12.8 The Doubling stackable modification trait. . . . . . . . . . 269 12.9 Mixing in a trait when instantiating with new. . . . . . . . . 270 12.10 Stackable modification traits Incrementing and Filtering. 270 13.1 Placing the contents of an entire file into a package. . . . . 278 13.2 Long form of a simple package declaration. . . . . . . . . 278 13.3 Multiple packages in the same file. . . . . . . . . . . . . . 279 13.4 Concise access to classes and packages. . . . . . . . . . . . 279 13.5 Symbols in enclosing packages not automatically available. 280 13.6 Accessing hidden package names. . . . . . . . . . . . . . . 280 13.7 Bob’s delightful fruits, ready for import. . . . . . . . . . . 283 13.8 Importing the members of a regular (not singleton) object. . 283 13.9 Importing a package name. . . . . . . . . . . . . . . . . . 284 13.10 How private access differs in Scala and Java. . . . . . . . . 287 13.11 How protected access differs in Scala and Java. . . . . . . . 288 13.12 Flexible scope of protection with access qualifiers. . . . . . 289 13.13 Accessing private members of companion classes and objects. 292 13.14 A package object. . . . . . . . . . . . . . . . . . . . . . . 293 14.1 Using an assertion. . . . . . . . . . . . . . . . . . . . . . . 296 14.2 Using ensuring to assert a function’s result. . . . . . . . . 296 14.3 Writing a test method with Suite. . . . . . . . . . . . . . 297 14.4 Writing a test function with FunSuite. . . . . . . . . . . . 298 14.5 Writing a JUnit test with JUnit3Suite. . . . . . . . . . . 301 14.6 Writing a TestNG test with TestNGSuite. . . . . . . . . . 302 14.7 Specifying and testing behavior with a ScalaTest FlatSpec. 303 14.8 Specifying and testing behavior with the specs framework. . 304 14.9 Writing property-based tests with ScalaCheck. . . . . . . . 305 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index List of Listings xxix 15.1 Defining case classes. . . . . . . . . . . . . . . . . . . . . 310 15.2 The simplifyTop function, which does a pattern match. . . 312 15.3 A pattern match with an empty “default” case. . . . . . . . 314 15.4 A pattern match with wildcard patterns. . . . . . . . . . . . 315 15.5 A pattern match with constant patterns. . . . . . . . . . . . 315 15.6 A pattern match with a variable pattern. . . . . . . . . . . . 316 15.7 A pattern match with a constructor pattern. . . . . . . . . . 318 15.8 A sequence pattern with a fixed length. . . . . . . . . . . . 318 15.9 A sequence pattern with an arbitrary length. . . . . . . . . 319 15.10 A pattern match with a tuple pattern. . . . . . . . . . . . . 319 15.11 A pattern match with typed patterns. . . . . . . . . . . . . 320 15.12 Using isInstanceOf and asInstanceOf (poor style). . . . 321 15.13 A pattern with a variable binding (via the @ sign). . . . . . 323 15.14 A match expression with a pattern guard. . . . . . . . . . . 324 15.15 Match expression in which case order matters. . . . . . . . 325 15.16 A sealed hierarchy of case classes. . . . . . . . . . . . . . 327 15.17 Defining multiple variables with one assignment. . . . . . . 330 15.18 A for expression with a tuple pattern. . . . . . . . . . . . 334 15.19 Picking elements of a list that match a pattern. . . . . . . . 334 15.20 The top half of the expression formatter. . . . . . . . . . . 337 15.21 The bottom half of the expression formatter. . . . . . . . . 338 15.22 An application that prints formatted expressions. . . . . . . 341 16.1 A merge sort function for Lists. . . . . . . . . . . . . . . 360 17.1 Default map and set definitions in Predef. . . . . . . . . . 382 18.1 A mutable bank account class. . . . . . . . . . . . . . . . . 400 18.2 A class with public vars. . . . . . . . . . . . . . . . . . . 402 18.3 How public vars are expanded into getter and setter methods. 403 18.4 Defining getter and setter methods directly. . . . . . . . . . 403 18.5 Defining a getter and setter without an associated field. . . 404 18.6 The halfAdder method. . . . . . . . . . . . . . . . . . . . 407 18.7 The fullAdder method. . . . . . . . . . . . . . . . . . . . 408 18.8 The Simulation class. . . . . . . . . . . . . . . . . . . . 410 18.9 The first half of the BasicCircuitSimulation class. . . . 414 18.10 The second half of the BasicCircuitSimulation class. . 415 18.11 The CircuitSimulation class. . . . . . . . . . . . . . . . 419 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index List of Listings xxx 19.1 A basic functional queue. . . . . . . . . . . . . . . . . . . 425 19.2 Hiding a primary constructor by making it private. . . . . . 426 19.3 An apply factory method in a companion object. . . . . . . 427 19.4 Type abstraction for functional queues. . . . . . . . . . . . 428 19.5 A nonvariant (rigid) Cell class. . . . . . . . . . . . . . . . 431 19.6 A type parameter with a lower bound. . . . . . . . . . . . . 437 19.7 A contravariant output channel. . . . . . . . . . . . . . . . 438 19.8 Covariance and contravariance of Function1s. . . . . . . . 439 19.9 Demonstration of function type parameter variance. . . . . 440 19.10 An optimized functional queue. . . . . . . . . . . . . . . . 442 19.11 A Person class that mixes in the Ordered trait. . . . . . . 444 19.12 A merge sort function with an upper bound. . . . . . . . . 444 20.1 Overriding abstract vals and parameterless methods. . . . 450 20.2 Declaring abstract vars. . . . . . . . . . . . . . . . . . . . 450 20.3 How abstract vars are expanded into getters and setters. . . 451 20.4 A trait that uses its abstract vals. . . . . . . . . . . . . . . 452 20.5 Pre-initialized fields in an anonymous class expression. . . 454 20.6 Pre-initialized fields in an object definition. . . . . . . . . . 454 20.7 Pre-initialized fields in a class definition. . . . . . . . . . . 455 20.8 Initializing a trait with lazy vals. . . . . . . . . . . . . . . 456 20.9 Modeling suitable food with an abstract type. . . . . . . . . 460 20.10 Implementing an abstract type in a subclass. . . . . . . . . 461 20.11 The US currency zone. . . . . . . . . . . . . . . . . . . . . 473 20.12 Currency zones for Europe and Japan. . . . . . . . . . . . 475 20.13 A converter object with an exchange rates map. . . . . . . 476 20.14 The full code of class CurrencyZone. . . . . . . . . . . . 477 21.1 An implicit parameter list with multiple parameters. . . . . 491 21.2 A function with an upper bound. . . . . . . . . . . . . . . 493 21.3 A function with an implicit parameter. . . . . . . . . . . . 494 21.4 A function that uses an implicit parameter internally. . . . . 496 21.5 A function with a view bound. . . . . . . . . . . . . . . . . 497 21.6 Sample code that uses an implicit parameter. . . . . . . . . 500 21.7 Sample code after type checking and insertion of implicits. 500 22.1 The definition of the Nil singleton object. . . . . . . . . . 505 22.2 Prepending a supertype element to a subtype list. . . . . . . 507 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index List of Listings xxxi 22.3 The definition of method :: (cons) in class List. . . . . . 507 22.4 The definition of method ::: in class List. . . . . . . . . 509 22.5 The definition of method map in class List. . . . . . . . . 511 22.6 The definition of the :: subclass of List. . . . . . . . . . 512 24.1 Mixing in the SynchronizedMap trait. . . . . . . . . . . . 563 25.1 An outline of the Builder class. . . . . . . . . . . . . . . 608 25.2 Implementation of filter in TraversableLike. . . . . . 609 25.3 Implementation of map in TraversableLike. . . . . . . . 612 25.4 The CanBuildFrom trait. . . . . . . . . . . . . . . . . . . 612 25.5 RNA Bases. . . . . . . . . . . . . . . . . . . . . . . . . . 614 25.6 RNA strands class, first version. . . . . . . . . . . . . . . . 615 25.7 RNA strands class, second version. . . . . . . . . . . . . . 618 25.8 RNA strands class, final version. . . . . . . . . . . . . . . 622 25.9 RNA companion object—final version. . . . . . . . . . . . 623 25.10 An implementation of prefix maps with Patricia tries. . . . 626 25.11 The companion object for prefix maps. . . . . . . . . . . . 629 26.1 The EMail string extractor object. . . . . . . . . . . . . . . 633 26.2 The Twice string extractor object. . . . . . . . . . . . . . . 636 26.3 The UpperCase string extractor object. . . . . . . . . . . . 636 26.4 The Domain string extractor object. . . . . . . . . . . . . . 638 26.5 The ExpandedEMail extractor object. . . . . . . . . . . . . 639 26.6 An extractor that defines an unapplySeq method. . . . . . 640 26.7 How the r method is defined in StringOps. . . . . . . . . 644 29.1 A simple Food entity class. . . . . . . . . . . . . . . . . . 671 29.2 Simple Recipe entity class. . . . . . . . . . . . . . . . . . 672 29.3 Food and Recipe examples for use in tests. . . . . . . . . . 672 29.4 Mock database and browser modules. . . . . . . . . . . . . 673 29.5 Database and browser modules with categories added. . . . 674 29.6 A Browser class with an abstract database val. . . . . . . 675 29.7 A Database class with abstract methods. . . . . . . . . . . 676 29.8 The SimpleDatabase object as a Database subclass. . . . 676 29.9 The SimpleBrowser object as a Browser subclass. . . . . 677 29.10 A student database and browser. . . . . . . . . . . . . . . . 677 29.11 A trait for food categories. . . . . . . . . . . . . . . . . . . 678 29.12 A Database class that mixes in the FoodCategories trait. 678 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index List of Listings xxxii 29.13 A SimpleDatabase object composed solely of mixins. . . 678 29.14 A SimpleFoods trait. . . . . . . . . . . . . . . . . . . . . 678 29.15 A SimpleRecipes trait with a self type. . . . . . . . . . . 679 29.16 An app that dynamically selects a module implementation. 680 29.17 Using a singleton type. . . . . . . . . . . . . . . . . . . . 682 30.1 A superclass equals method that calls canEqual. . . . . . 696 30.2 A subclass equals method that calls canEqual. . . . . . . 697 30.3 Hierarchy for binary trees. . . . . . . . . . . . . . . . . . . 699 30.4 A parameterized type with equals and hashCode. . . . . . 703 30.5 Class Rational with equals and hashCode. . . . . . . . . 704 31.1 A Scala method that declares a Java throws clause. . . . . 715 32.1 A simple actor. . . . . . . . . . . . . . . . . . . . . . . . . 726 32.2 An actor that calls receive. . . . . . . . . . . . . . . . . . 728 32.3 An actor that calls react. . . . . . . . . . . . . . . . . . . 732 32.4 An actor’s act method that uses loop. . . . . . . . . . . . 733 32.5 An actor that uses a helper actor to avoid blocking itself. . . 735 32.6 An actor that uses case classes for messages. . . . . . . . . 740 32.7 The Simulant trait. . . . . . . . . . . . . . . . . . . . . . 748 32.8 Adder components. . . . . . . . . . . . . . . . . . . . . . 755 33.1 An arithmetic expression parser. . . . . . . . . . . . . . . . 761 33.2 A regular expression parser for Java identifiers. . . . . . . . 763 33.3 Data in JSON format. . . . . . . . . . . . . . . . . . . . . 765 33.4 A simple JSON parser. . . . . . . . . . . . . . . . . . . . . 766 33.5 A full JSON parser that returns meaningful results. . . . . . 770 33.6 The ~ combinator method. . . . . . . . . . . . . . . . . . . 778 34.1 A simple Swing application in Scala. . . . . . . . . . . . . 789 34.2 Component assembly on a panel. . . . . . . . . . . . . . . 791 34.3 Implementing a reactive Swing application. . . . . . . . . . 795 34.4 An implementation of the temperature converter. . . . . . . 797 35.1 Code for spreadsheet in Figure 35.1. . . . . . . . . . . . . 802 35.2 The main program for the spreadsheet application. . . . . . 803 35.3 A spreadsheet with a rendererComponent method. . . . . 804 35.4 First version of the Model class. . . . . . . . . . . . . . . . 805 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index List of Listings xxxiii 35.5 Classes representing formulas. . . . . . . . . . . . . . . . 807 35.6 A spreadsheet that parses formulas. . . . . . . . . . . . . . 811 35.7 The evaluate method of trait Evaluator. . . . . . . . . . 814 35.8 A library for arithmetic operations. . . . . . . . . . . . . . 816 35.9 The finished spreadsheet component. . . . . . . . . . . . . 822 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Foreword I’m not sure where I first came across the Scala language. Maybe on a fo- rum for programming language enthusiasts such as Lambda the Ultimate, or maybe in more pedestrian quarters: Reddit, or the like. Although I was intrigued at first blush, I owe my deeper exploration and enthusiasm for the language to two individuals: David Pollak, creator of the Lift web frame- work, and Steve Jenson, a former colleague at Twitter and generally brilliant programmer. Following David and Steve, I arrived to Scala in the late-middle stage of the language’s history to date. By 2008, Scala had spent five years evolving from its initial release, and had formed around it a tight-knit community of academics, tinkerers, and even a few consultants. The mailing lists were full of spirited debates, announcements of exciting libraries, and a general camaraderie and shared joy for seeing what this powerful new tool could do. What Scala lacked, at that point, was a collection of success stories around major production deployments. The decision to use Scala at Twitter, where I then worked, was not an easy one to make. Our infrastructure was buckling under the weight of extreme growth. Picking a relative unknown as our language of choice for building the high-performance distributed systems that would keep our fledgling service alive was risky. Still, the benefits that Scala offered were (and are) compelling, and our engineers were quickly able to produce proto- types that proved out the language’s effectiveness. In the intervening time, I’ve seen a heartening number of companies large and small adopting Scala. In that time, too, the question of Scala’s complex- ity has been raised. From the outside, Scala’s many features might appear to be a kind of complexity. To understand Scala, though, is to understand its goal of being a scalable language. You can be writing real-world code in Scala in an afternoon. As your understanding of the language and, indeed, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Foreword xxxv of the art and science of programming as a whole expands, there’s more of Scala there to wield to your advantage. That’s not complexity. It’s flexibility. To be clear: Scala will challenge you. That’s part of the joy of using it. You won’t understand the full power of its type system by the end of your first day. You won’t understand the zen of objects being functions and functions being objects in your first week. Each feature of the language is another light bulb waiting to switch on over your head. I’m certain you’ll enjoy the experience of being gradually illuminated as you read this book and write code. I’ve watched programmers learn Scala on the job and succeed. It can be done, and it can be fun. As Scala programmers like me have grown to better understand what this powerful language can do, so too has Scala evolved to meet program- mers’ needs. Scala 2.8 smoothes out some rough spots in the collection libraries and adds useful features like named and default arguments to meth- ods. While Scala has been a perfectly productive language to work with for some time, as of 2.8 it feels even more solid and polished. The new 2.8 release is icing on the cake. In my experience, Scala was ready for production deployments two years ago. Today, it’s even better, and I can’t imagine building a new system with- out it. Presently, I’m doing just that. For me, Scala has gone from being a risky gamble to a trusted tool in two short years. I look forward to taking advantage of the latest features in Scala 2.8, and to using this book as the definitive reference for it, direct from the creator of the language I’ve grown to depend on. Alex Payne Portland, Oregon October 27, 2010 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Foreword to the First Edition Martin Odersky made a huge impact on the Java world with his design of the Pizza language. Although Pizza itself never became popular, it demonstrated that object-oriented and functional language features, when combined with skill and taste, form a natural and powerful combination. Pizza’s design be- came the basis for generics in Java, and Martin’s GJ (Generic Java) compiler was Sun Microsystem’s standard compiler starting in 1.3 (though with gener- ics disabled). I had the pleasure of maintaining this compiler for a number of years, so I can report from first-hand experience that Martin’s skill in lan- guage design extends to language implementation. Since that time, we at Sun tried to simplify program development by ex- tending the language with piecemeal solutions to particular problems, like the for-each loop, enums, and autoboxing. Meanwhile, Martin continued his work on more powerful orthogonal language primitives that allow program- mers to provide solutions in libraries. Lately, there has been a backlash against statically typed languages. Ex- perience with Java has shown that programming in a static language results in an abundance of boilerplate. The common wisdom is that one must aban- don static typing to eliminate the boilerplate, and there is a rising interest in dynamic languages such as Python, Ruby, and Groovy. This common wisdom is debunked by the existence of Martin’s latest brainchild, Scala. Scala is a tastefully typed language: it is statically typed, but explicit types appear in just the right places. Scala takes powerful features from object-oriented and functional languages, and combines them with a few novel ideas in a beautifully coherent whole. The syntax is so lightweight, and its primitives so expressive, that APIs can be used with virtually no syn- tactic overhead at all. Examples can be found in standard libraries such as parser combinators and actors. In this sense Scala supports embedded domain-specific languages. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Foreword to the First Edition xxxvii Will Scala be the next great language? Only time will tell. Martin Oder- sky’s team certainly has the taste and skill for the job. One thing is sure: Scala sets a new standard against which future languages will be measured. Neal Gafter San Jose, California September 3, 2008 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Acknowledgments Many people have contributed to this book and to the material it covers. We are grateful to all of them. Scala itself has been a collective effort of many people. The design and the implementation of version 1.0 was helped by Philippe Altherr, Vin- cent Cremet, Gilles Dubochet, Burak Emir, Stéphane Micheloud, Nikolay Mihaylov, Michel Schinz, Erik Stenman, and Matthias Zenger. Phil Bag- well, Antonio Cunei, Iulian Dragos, Gilles Dubochet, Miguel Garcia, Philipp Haller, Sean McDirmid, Ingo Maier, Donna Malayeri, Adriaan Moors, Hu- bert Plociniczak, Paul Phillips, Aleksandar Prokopec, Tiark Rompf, Lukas Rytz, and Geoffrey Washburn joined in the effort to develop the second and current version of the language and tools. Gilad Bracha, Nathan Bronson, Caoyuan, Aemon Cannon, Craig Cham- bers, Chris Conrad, Erik Ernst, Matthias Felleisen, Mark Harrah, Shriram Krishnamurti, Gary Leavens, David MacIver, Sebastian Maneth, Rickard Nilsson, Erik Meijer, Lalit Pant, David Pollak, Jon Pretty, Klaus Ostermann, Jorge Ortiz, Didier Rémy, Miles Sabin, Vijay Saraswat, Daniel Spiewak, James Strachan, Don Syme, Erik Torreborre, Mads Torgersen, Philip Wadler, Jamie Webb, John Williams, Kevin Wright, and Jason Zaugg have shaped the design of the language by graciously sharing their ideas with us in lively and inspiring discussions, by contributing important pieces of code to the open source effort, as well as through comments on previous versions of this doc- ument. The contributors to the Scala mailing list have also given very useful feedback that helped us improve the language and its tools. George Berger has worked tremendously to make the build process and the web presence for the book work smoothly. As a result this project has been delightfully free of technical snafus. Many people gave us valuable feedback on early versions of the text. Thanks goes to Eric Armstrong, George Berger, Alex Blewitt, Gilad Bracha, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Acknowledgments xxxix William Cook, Bruce Eckel, Stéphane Micheloud, Todd Millstein, David Pollak, Frank Sommers, Philip Wadler, and Matthias Zenger. Thanks also to the Silicon Valley Patterns group for their very helpful review: Dave Astels, Tracy Bialik, John Brewer, Andrew Chase, Bradford Cross, Raoul Duke, John P. Eurich, Steven Ganz, Phil Goodwin, Ralph Jocham, Yan-Fa Li, Tao Ma, Jeffery Miller, Suresh Pai, Russ Rufer, Dave W. Smith, Scott Turnquest, Walter Vannini, Darlene Wallach, and Jonathan Andrew Wolter. And we’d like to thank Dewayne Johnson and Kim Leedy for their help with the cover art, and Frank Sommers for his work on the index. We’d also like to extend a special thanks to all of our readers who con- tributed comments. Your comments were very helpful to us in shaping this into an even better book. We couldn’t print the names of everyone who con- tributed comments, but here are the names of readers who submitted at least five comments during the eBook PrePrint™ stage by clicking on the Suggest link, sorted first by the highest total number of comments submitted, then alphabetically. Thanks goes to: David Biesack, Donn Stephan, Mats Hen- ricson, Rob Dickens, Blair Zajac, Tony Sloane, Nigel Harrison, Javier Diaz Soto, William Heelan, Justin Forder, Gregor Purdy, Colin Perkins, Bjarte S. Karlsen, Ervin Varga, Eric Willigers, Mark Hayes, Martin Elwin, Calum MacLean, Jonathan Wolter, Les Pruszynski, Seth Tisue, Andrei Formiga, Dmitry Grigoriev, George Berger, Howard Lovatt, John P. Eurich, Marius Scurtescu, Jeff Ervin, Jamie Webb, Kurt Zoglmann, Dean Wampler, Nikolaj Lindberg, Peter McLain, Arkadiusz Stryjski, Shanky Surana, Craig Borde- lon, Alexandre Patry, Filip Moens, Fred Janon, Jeff Heon, Boris Lorbeer, Jim Menard, Tim Azzopardi, Thomas Jung, Walter Chang, Jeroen Dijkmei- jer, Casey Bowman, Martin Smith, Richard Dallaway, Antony Stubbs, Lars Westergren, Maarten Hazewinkel, Matt Russell, Remigiusz Michalowski, Andrew Tolopko, Curtis Stanford, Joshua Cough, Zemian Deng, Christo- pher Rodrigues Macias, Juan Miguel Garcia Lopez, Michel Schinz, Peter Moore, Randolph Kahle, Vladimir Kelman, Daniel Gronau, Dirk Detering, Hiroaki Nakamura, Ole Hougaard, Bhaskar Maddala, David Bernard, Derek Mahar, George Kollias, Kristian Nordal, Normen Mueller, Rafael Ferreira, Binil Thomas, John Nilsson, Jorge Ortiz, Marcus Schulte, Vadim Gerassi- mov, Cameron Taggart, Jon-Anders Teigen, Silvestre Zabala, Will McQueen, and Sam Owen. We would also like to think those who submitted comments and errata after the first edition was published, including Felix Siegrist, Lothar Meyer- Lerbs, Diethard Michaelis, Roshan Dawrani, Donn Stephan, William Uther, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Acknowledgments xl Francisco Reverbel, Jim Balter, and Freek de Bruijn. Lex would like to thank Aaron Abrams, Jason Adams, Henry and Emily Crutcher, Joey Gibson, Gunnar Hillert, Matthew Link, Toby Reyelts, Jason Snape, John and Melinda Weathers, and all of the Atlanta Scala Enthusiasts for many helpful discussions about the language design, its mathematical underpinnings, and how to present Scala to working engineers. Lastly, Bill would also like to thank Gary Cornell, Greg Doench, Andy Hunt, Mike Leonard, Tyler Ortman, Bill Pollock, Dave Thomas, and Adam Wright for providing insight and advice on book publishing. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Introduction This book is a tutorial for the Scala programming language, written by peo- ple directly involved in the development of Scala. Our goal is that by reading this book, you can learn everything you need to be a productive Scala pro- grammer. All examples in this book compile with Scala version 2.8.1. Who should read this book The main target audience for this book is programmers who want to learn to program in Scala. If you want to do your next software project in Scala, then this is the book for you. In addition, the book should be interesting to programmers wishing to expand their horizons by learning new concepts. If you’re a Java programmer, for example, reading this book will expose you to many concepts from functional programming as well as advanced object- oriented ideas. We believe learning about Scala, and the ideas behind it, can help you become a better programmer in general. General programming knowledge is assumed. While Scala is a fine first programming language, this is not the book to use to learn programming. On the other hand, no specific knowledge of programming languages is required. Even though most people use Scala on the Java platform, this book does not presume you know anything about Java. However, we expect many readers to be familiar with Java, and so we sometimes compare Scala to Java to help such readers understand the differences. How to use this book Because the main purpose of this book is to serve as a tutorial, the recom- mended way to read this book is in chapter order, from front to back. We have tried hard to introduce one topic at a time, and explain new topics only Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Introduction xlii in terms of topics we’ve already introduced. Thus, if you skip to the back to get an early peek at something, you may find it explained in terms of concepts you don’t quite understand. To the extent you read the chapters in order, we think you’ll find it quite straightforward to gain competency in Scala, one step at a time. If you see a term you do not know, be sure to check the glossary and the index. Many readers will skim parts of the book, and that is just fine. The glossary and index can help you backtrack whenever you skim over something too quickly. After you have read the book once, it should also serve as a language reference. There is a formal specification of the Scala language, but the lan- guage specification tries for precision at the expense of readability. Although this book doesn’t cover every detail of Scala, it is quite comprehensive and should serve as an approachable language reference as you become more adept at programming in Scala. How to learn Scala You will learn a lot about Scala simply by reading this book from cover to cover. You can learn Scala faster and more thoroughly, though, if you do a few extra things. First of all, you can take advantage of the many program examples in- cluded in the book. Typing them in yourself is a way to force your mind through each line of code. Trying variations is a way to make them more fun and to make sure you really understand how they work. Second, keep in touch with the numerous online forums. That way, you and other Scala enthusiasts can help each other. There are numerous mailing lists, discussion forums, a chat room, a wiki, and multiple Scala-specific article feeds. Take some time to find ones that fit your information needs. You will spend a lot less time stuck on little problems, so you can spend your time on deeper, more important questions. Finally, once you have read enough, take on a programming project of your own. Work on a small program from scratch, or develop an add-in to a larger program. You can only go so far by reading. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Introduction xliii EBook features This book is available in both paper and PDF eBook form. The eBook is not simply an electronic copy of the paper version of the book. While the content is the same as in the paper version, the eBook has been carefully designed and optimized for reading on a computer screen. The first thing to notice is that most references within the eBook are hyperlinked. If you select a reference to a chapter, figure, or glossary entry, your PDF viewer should take you immediately to the selected item so that you do not have to flip around to find it. Additionally, at the bottom of each page in the eBook are a number of navigation links. The “Cover,” “Overview,” and “Contents” links take you to the front matter of the book. The “Glossary” and “Index” links take you to reference parts of the book. Finally, the “Discuss” link takes you to an online forum where you discuss questions with other readers, the authors, and the larger Scala community. If you find a typo, or something you think could be explained better, please click on the “Suggest” link, which will take you to an online web application where you can give the authors feedback. Although the same pages appear in the eBook as the printed book, blank pages are removed and the remaining pages renumbered. The pages are num- bered differently so that it is easier for you to determine PDF page numbers when printing only a portion of the eBook. The pages in the eBook are, therefore, numbered exactly as your PDF viewer will number them. Typographic conventions The first time a term is used, it is italicized. Small code examples, such as x + 1, are written inline with a mono-spaced font. Larger code examples are put into mono-spaced quotation blocks like this: def hello() { println("Hello, world!") } When interactive shells are shown, responses from the shell are shown in a lighter font: scala>3+ 4 res0: Int = 7 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Introduction xliv Content overview • Chapter 1, “A Scalable Language,” gives an overview of Scala’s design as well as the reasoning, and history, behind it. • Chapter 2, “First Steps in Scala,” shows you how to do a number of ba- sic programming tasks in Scala, without going into great detail about how they work. The goal of this chapter is to get your fingers started typing and running Scala code. • Chapter 3, “Next Steps in Scala,” shows you several more basic pro- gramming tasks that will help you get up to speed quickly in Scala. After completing this chapter, you should be able to start using Scala for simple scripting tasks. • Chapter 4, “Classes and Objects,” starts the in-depth coverage of Scala with a description of its basic object-oriented building blocks and in- structions on how to compile and run a Scala application. • Chapter 5, “Basic Types and Operations,” covers Scala’s basic types, their literals, the operations you can perform on them, how precedence and associativity works, and what rich wrappers are. • Chapter 6, “Functional Objects,” dives more deeply into the object- oriented features of Scala, using functional (i.e., immutable) rational numbers as an example. • Chapter 7, “Built-in Control Structures,” shows you how to use Scala’s built-in control structures: if, while, for, try, and match. • Chapter 8, “Functions and Closures,” provides in-depth coverage of functions, the basic building block of functional languages. • Chapter 9, “Control Abstraction,” shows how to augment Scala’s basic control structures by defining your own control abstractions. • Chapter 10, “Composition and Inheritance,” discusses more of Scala’s support for object-oriented programming. The topics are not as funda- mental as those in Chapter 4, but they frequently arise in practice. • Chapter 11, “Scala’s Hierarchy,” explains Scala’s inheritance hierar- chy and discusses its universal methods and bottom types. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Introduction xlv • Chapter 12, “Traits,” covers Scala’s mechanism for mixin composi- tion. The chapter shows how traits work, describes common uses, and explains how traits improve on traditional multiple inheritance. • Chapter 13, “Packages and Imports,” discusses issues with program- ming in the large, including top-level packages, import statements, and access control modifiers like protected and private. • Chapter 14, “Assertions and Unit Testing,” shows Scala’s assertion mechanism and gives a tour of the various tools available for writing tests in Scala. • Chapter 15, “Case Classes and Pattern Matching,” introduces twin constructs that support you when writing regular, non-encapsulated data structures. Case classes and pattern matching are particularly helpful for tree-like recursive data. • Chapter 16, “Working with Lists,” explains in detail lists, which are probably the most commonly used data structure in Scala programs. • Chapter 17, “Collections,” shows you how to use the basic Scala col- lections, such as lists, arrays, tuples, sets, and maps. • Chapter 18, “Stateful Objects,” explains stateful (i.e., mutable) objects, and the syntax Scala provides to express them. The chapter concludes with a case study on discrete event simulation, which shows some stateful objects in action. • Chapter 19, “Type Parameterization,” explains some of the techniques for information hiding introduced in Chapter 13 by means of a con- crete example: the design of a class for purely functional queues. The chapter builds up to a description of variance of type parameters and how it interacts with information hiding. • Chapter 20, “Abstract Members,” describes all kinds of abstract mem- bers that Scala supports. Not only methods, but also fields and types can be declared abstract. • Chapter 21, “Implicit Conversions and Parameters,” covers two con- structs that can help you omit tedious details from source code, letting the compiler supply them instead. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Introduction xlvi • Chapter 22, “Implementing Lists,” describes the implementation of class List. It is important to understand how lists work in Scala, and furthermore the implementation demonstrates the use of several of Scala’s features. • Chapter 23, “For Expressions Revisited,” shows how for expressions are translated to invocations of map, flatMap, filter, and foreach. • Chapter 24, “The Scala Collections API,” gives a detailed tour of the collections library. • Chapter 25, “The Architecture of Scala Collections,” shows how the collection library is built and how you can implement your own col- lections. • Chapter 26, “Extractors,” shows how to pattern match against arbitrary classes, not just case classes. • Chapter 27, “Annotations,” shows how to work with language exten- sion via annotation. The chapter describes several standard annota- tions and shows you how to make your own. • Chapter 28, “Working with XML,” explains how to process XML in Scala. The chapter shows you idioms for generating XML, parsing it, and processing it once it is parsed. • Chapter 29, “Objects As Modules,” shows how Scala’s objects are rich enough to remove the need for a separate modules system. • Chapter 30, “Object Equality,” points out several issues to consider when writing an equals method. There are several pitfalls to avoid. • Chapter 31, “Combining Scala and Java,” discusses issues that arise when combining Scala and Java together in the same project, and sug- gests ways to deal with them. • Chapter 32, “Actors and Concurrency,” shows you how to use Scala’s actors concurrency library. Although you can use the Java Platform’s concurrency primitives and libraries from Scala programs, actors can help you avoid the deadlocks and race conditions that plague the tra- ditional “threads and locks” approach to concurrency. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Introduction xlvii • Chapter 33, “Combinator Parsing,” shows how to build parsers using Scala’s library of parser combinators. • Chapter 34, “GUI Programming,” gives a quick tour of a Scala library that simplifies GUI programming with Swing. • Chapter 35, “The SCells Spreadsheet,” ties everything together by showing a complete spreadsheet application written in Scala. Resources At http://www.scala-lang.org, the main website for Scala, you’ll find the latest Scala release and links to documentation and community resources. For a more condensed page of links to Scala resources, visit this book’s web- site: http://booksites.artima.com/programming_in_scala_2ed. To interact with other readers of this book, check out the Programming in Scala Forum, at: http://www.artima.com/forums/forum.jsp?forum=282. Source code You can download a ZIP file containing the source code of this book, which is released under the Apache 2.0 open source license, from the book’s website: http://booksites.artima.com/programming_in_scala_2ed. Errata Although this book has been heavily reviewed and checked, errors will in- evitably slip through. For a (hopefully short) list of errata for this book, visit http://booksites.artima.com/programming_in_scala_2ed/errata. If you find an error, please report it at the above URL, so that we can be sure to fix it in a future printing or edition of this book. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Programming in Scala Second Edition println("Hello, reader!") Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 1 A Scalable Language The name Scala stands for “scalable language.” The language is so named because it was designed to grow with the demands of its users. You can apply Scala to a wide range of programming tasks, from writing small scripts to building large systems.1 Scala is easy to get into. It runs on the standard Java platform and in- teroperates seamlessly with all Java libraries. It’s quite a good language for writing scripts that pull together Java components. But it can apply its strengths even more when used for building large systems and frameworks of reusable components. Technically, Scala is a blend of object-oriented and functional program- ming concepts in a statically typed language. The fusion of object-oriented and functional programming shows up in many different aspects of Scala; it is probably more pervasive than in any other widely used language. The two programming styles have complementary strengths when it comes to scalability. Scala’s functional programming constructs make it easy to build interesting things quickly from simple parts. Its object-oriented constructs make it easy to structure larger systems and to adapt them to new demands. The combination of both styles in Scala makes it possible to express new kinds of programming patterns and component abstractions. It also leads to a legible and concise programming style. And because it is so malleable, programming in Scala can be a lot of fun. This initial chapter answers the question, “Why Scala?” It gives a high- level view of Scala’s design and the reasoning behind it. After reading the chapter you should have a basic feel for what Scala is and what kinds of 1Scala is pronounced skah-lah. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.1 Chapter 1 · A Scalable Language 50 tasks it might help you accomplish. Although this book is a Scala tutorial, this chapter isn’t really part of the tutorial. If you’re eager to start writing some Scala code, you should jump ahead to Chapter 2. 1.1 A language that grows on you Programs of different sizes tend to require different programming constructs. Consider, for example, the following small Scala program: var capital = Map("US" -> "Washington", "France" -> "Paris") capital += ("Japan" -> "Tokyo") println(capital("France")) This program sets up a map from countries to their capitals, modifies the map by adding a new binding ("Japan" -> "Tokyo"), and prints the capital asso- ciated with the country France.2 The notation in this example is high-level, to the point, and not cluttered with extraneous semicolons or type annotations. Indeed, the feel is that of a modern “scripting” language like Perl, Python, or Ruby. One common characteristic of these languages, which is relevant for the example above, is that they each support an “associative map” construct in the syntax of the language. Associative maps are very useful because they help keep programs leg- ible and concise. However, sometimes you might not agree with their “one size fits all” philosophy, because you need to control the properties of the maps you use in your program in a more fine-grained way. Scala gives you this fine-grained control if you need it, because maps in Scala are not lan- guage syntax. They are library abstractions that you can extend and adapt. In the above program, you’ll get a default Map implementation, but you can easily change that. You could for example specify a particular implemen- tation, such as a HashMap or a TreeMap, or you could specify that the map should be thread-safe, by mixing in a SynchronizedMap trait. You could specify a default value for the map, or you could override any other method of the map you create. In each case, you can use the same easy access syntax for maps as in the example above. 2Please bear with us if you don’t understand all details of this program. They will be explained in the next two chapters. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.1 Chapter 1 · A Scalable Language 51 This example shows that Scala can give you both convenience and flex- ibility. Scala has a set of convenient constructs that help you get started quickly and let you program in a pleasantly concise style. At the same time, you have the assurance that you will not outgrow the language. You can al- ways tailor the program to your requirements, because everything is based on library modules that you can select and adapt as needed. Growing new types Eric Raymond introduced the cathedral and bazaar as two metaphors of soft- ware development.3 The cathedral is a near-perfect building that takes a long time to build. Once built, it stays unchanged for a long time. The bazaar, by contrast, is adapted and extended each day by the people working in it. In Raymond’s work the bazaar is a metaphor for open-source software devel- opment. Guy Steele noted in a talk on “growing a language” that the same distinction can be applied to language design.4 Scala is much more like a bazaar than a cathedral, in the sense that it is designed to be extended and adapted by the people programming in it. Instead of providing all constructs you might ever need in one “perfectly complete” language, Scala puts the tools for building such constructs into your hands. Here’s an example. Many applications need a type of integer that can become arbitrarily large without overflow or “wrap-around” of arithmetic operations. Scala defines such a type in library class scala.BigInt. Here is the definition of a method using that type, which calculates the factorial of a passed integer value:5 def factorial(x: BigInt): BigInt = if (x == 0) 1 else x * factorial(x - 1) Now, if you call factorial(30) you would get: 265252859812191058636308480000000 BigInt looks like a built-in type, because you can use integer literals and operators such as * and - with values of that type. Yet it is just a class that 3Raymond, The Cathedral and the Bazaar.[Ray99] 4Steele, “Growing a language.” [Ste99] 5factorial(x), or x! in mathematical notation, is the result of computing 1 * 2 * ... * x, with 0! defined to be 1. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.1 Chapter 1 · A Scalable Language 52 happens to be defined in Scala’s standard library.6 If the class were missing, it would be straightforward for any Scala programmer to write an implemen- tation, for instance, by wrapping Java’s class java.math.BigInteger (in fact that’s how Scala’s BigInt class is implemented). Of course, you could also use Java’s class directly. But the result is not nearly as pleasant, because although Java allows you to create new types, those types don’t feel much like native language support: import java.math.BigInteger def factorial(x: BigInteger): BigInteger = if (x == BigInteger.ZERO) BigInteger.ONE else x.multiply(factorial(x.subtract(BigInteger.ONE))) BigInt is representative of many other number-like types—big decimals, complex numbers, rational numbers, confidence intervals, polynomials—the list goes on. Some programming languages implement some of these types natively. For instance, Lisp, Haskell, and Python implement big integers; Fortran and Python implement complex numbers. But any language that attempted to implement all of these abstractions at the same time would sim- ply become too big to be manageable. What’s more, even if such a language were to exist, some applications would surely benefit from other number- like types that were not supplied. So the approach of attempting to provide everything in one language doesn’t scale very well. Instead, Scala allows users to grow and adapt the language in the directions they need by defining easy-to-use libraries that feel like native language support. Growing new control constructs The previous example demonstrates that Scala lets you add new types that can be used as conveniently as built-in types. The same extension principle also applies to control structures. This kind of extensibility is illustrated by Scala’s API for “actor-based” concurrent programming. 6Scala comes with a standard library, some of which will be covered in this book. For more information, you can also consult the library’s Scaladoc documentation, which is avail- able in the distribution and online at http://www.scala-lang.org. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.1 Chapter 1 · A Scalable Language 53 As multicore processors proliferate in the coming years, achieving ac- ceptable performance may increasingly require that you exploit more paral- lelism in your applications. Often, this will mean rewriting your code so that computations are distributed over several concurrent threads. Unfortunately, creating dependable multi-threaded applications has proven challenging in practice. Java’s threading model is built around shared memory and locking, a model that is often difficult to reason about, especially as systems scale up in size and complexity. It is hard to be sure you don’t have a race condi- tion or deadlock lurking—something that didn’t show up during testing, but might just show up in production. An arguably safer alternative is a mes- sage passing architecture such as the “actors” approach used by the Erlang programming language. Java comes with a rich, thread-based concurrency library. Scala pro- grams can use it like any other Java API. However, Scala also offers an ad- ditional library that essentially implements Erlang’s actor model. Actors are concurrency abstractions that can be implemented on top of threads. They communicate by sending messages to each other. An actor can perform two basic operations, message send and receive. The send operation, denoted by an exclamation point (!), sends a message to an actor. Here’s an example in which the actor is named recipient: recipient ! msg A send is asynchronous; that is, the sending actor can proceed immediately, without waiting for the message to be received and processed. Every actor has a mailbox in which incoming messages are queued. An actor handles messages that have arrived in its mailbox via a receive block: receive { case Msg1 => ... // handle Msg1 case Msg2 => ... // handle Msg2 // ... } A receive block consists of a number of cases that each query the mailbox with a message pattern. The first message in the mailbox that matches any of the cases is selected, and the corresponding action is performed on it. If the mailbox does not contain any messages that match one of the given cases, the actor suspends and waits for further incoming messages. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.1 Chapter 1 · A Scalable Language 54 As an example, here is a simple Scala actor implementing a checksum calculator service: actor { var sum = 0 loop { receive { case Data(bytes) => sum += hash(bytes) case GetSum(requester) => requester ! sum } } } This actor first defines a local variable named sum with initial value zero. It then repeatedly waits in a loop for messages, using a receive statement. If it receives a Data message, it adds a hash of the sent bytes to the sum variable. If it receives a GetSum message, it sends the current value of sum back to the requester using the message send requester ! sum. The requester field is embedded in the GetSum message; it usually refers to the actor that made the request. We don’t expect you to understand fully the actor example at this point. Rather, what’s significant about this example for the topic of scalability is that neither actor nor loop nor receive nor message send (!) are built-in operations in Scala. Even though actor, loop, and receive look and act very much like built-in control constructs such as while or for loops, they are in fact methods defined in Scala’s actors library. Likewise, even though ‘!’ looks like a built-in operator, it too is just a method defined in the actors library. All four of these constructs are completely independent of the Scala programming language. The receive block and send (!) syntax look in Scala much like they look in Erlang, but in Erlang, these constructs are built into the language. Scala also implements most of Erlang’s other concurrent programming con- structs, such as monitoring failed actors and time-outs. All in all, actors have turned out to be a very pleasant means for expressing concurrent and dis- tributed computations. Even though they are defined in a library, actors feel like an integral part of the Scala language. This example illustrates that you can “grow” the Scala language in new directions even as specialized as concurrent programming. To be sure, you need good architects and programmers to do this. But the crucial thing is Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.2 Chapter 1 · A Scalable Language 55 that it is feasible—you can design and implement abstractions in Scala that address radically new application domains, yet still feel like native language support. 1.2 What makes Scala scalable? Scalability is influenced by many factors, ranging from syntax details to component abstraction constructs. If we were forced to name just one as- pect of Scala that helps scalability, though, we’d pick its combination of object-oriented and functional programming (well, we cheated, that’s really two aspects, but they are intertwined). Scala goes further than all other well-known languages in fusing object- oriented and functional programming into a uniform language design. For instance, where other languages might have objects and functions as two dif- ferent concepts, in Scala a function value is an object. Function types are classes that can be inherited by subclasses. This might seem nothing more than an academic nicety, but it has deep consequences for scalability. In fact the actor concept shown previously could not have been implemented with- out this unification of functions and objects. This section gives an overview of Scala’s way of blending object-oriented and functional concepts. Scala is object-oriented Object-oriented programming has been immensely successful. Starting from Simula in the mid-60’s and Smalltalk in the 70’s, it is now available in more languages than not. In some domains objects have taken over completely. While there is not a precise definition of what object-oriented means, there is clearly something about objects that appeals to programmers. In principle, the motivation for object-oriented programming is very sim- ple: all but the most trivial programs need some sort of structure. The most straightforward way to do this is to put data and operations into some form of containers. The great idea of object-oriented programming is to make these containers fully general, so that they can contain operations as well as data, and that they are themselves values that can be stored in other containers, or passed as parameters to operations. Such containers are called objects. Alan Kay, the inventor of Smalltalk, remarked that in this way the simplest object has the same construction principle as a full computer: it combines data with Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.2 Chapter 1 · A Scalable Language 56 operations under a formalized interface.7 So objects have a lot to do with language scalability: the same techniques apply to the construction of small as well as large programs. Even though object-oriented programming has been mainstream for a long time, there are relatively few languages that have followed Smalltalk in pushing this construction principle to its logical conclusion. For instance, many languages admit values that are not objects, such as the primitive val- ues in Java. Or they allow static fields and methods that are not members of any object. These deviations from the pure idea of object-oriented pro- gramming look quite harmless at first, but they have an annoying tendency to complicate things and limit scalability. By contrast, Scala is an object-oriented language in pure form: every value is an object and every operation is a method call. For example, when you say 1 + 2 in Scala, you are actually invoking a method named + defined in class Int. You can define methods with operator-like names that clients of your API can then use in operator notation. This is how the designer of Scala’s actors API enabled you to use expressions such as requester ! sum shown in the previous example: ‘!’ is a method of the Actor class. Scala is more advanced than most other languages when it comes to com- posing objects. An example is Scala’s traits. Traits are like interfaces in Java, but they can also have method implementations and even fields. Objects are constructed by mixin composition, which takes the members of a class and adds the members of a number of traits to them. In this way, different as- pects of classes can be encapsulated in different traits. This looks a bit like multiple inheritance, but differs when it comes to the details. Unlike a class, a trait can add some new functionality to an unspecified superclass. This makes traits more “pluggable” than classes. In particular, it avoids the clas- sical “diamond inheritance” problems of multiple inheritance, which arise when the same class is inherited via several different paths. Scala is functional In addition to being a pure object-oriented language, Scala is also a full- blown functional language. The ideas of functional programming are older than (electronic) computers. Their foundation was laid in Alonzo Church’s lambda calculus, which he developed in the 1930s. The first functional pro- gramming language was Lisp, which dates from the late 50s. Other popular 7Kay, “The Early History of Smalltalk.” [Kay96] Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.2 Chapter 1 · A Scalable Language 57 functional languages are Scheme, SML, Erlang, Haskell, OCaml, and F#. For a long time, functional programming has been a bit on the sidelines, popular in academia, but not that widely used in industry. However, recent years have seen an increased interest in functional programming languages and techniques. Functional programming is guided by two main ideas. The first idea is that functions are first-class values. In a functional language, a function is a value of the same status as, say, an integer or a string. You can pass func- tions as arguments to other functions, return them as results from functions, or store them in variables. You can also define a function inside another function, just as you can define an integer value inside a function. And you can define functions without giving them a name, sprinkling your code with function literals as easily as you might write integer literals like 42. Functions that are first-class values provide a convenient means for ab- stracting over operations and creating new control structures. This general- ization of functions provides great expressiveness, which often leads to very legible and concise programs. It also plays an important role for scalability. As an example, the receive construct shown previously in the actor exam- ple is an invocation of a method that takes a function as argument. The code inside the receive construct is a function that is passed unexecuted into the receive method. In most traditional languages, by contrast, functions are not values. Lan- guages that do have function values often relegate them to second-class sta- tus. For example, the function pointers of C and C++ do not have the same status as non-functional values in those languages: function pointers can only refer to global functions, they do not allow you to define first-class nested functions that refer to some values in their environment. Nor do they allow you to define unnamed function literals. The second main idea of functional programming is that the operations of a program should map input values to output values rather than change data in place. To see the difference, consider the implementation of strings in Ruby and in Java. In Ruby, a string is an array of characters. Charac- ters in a string can be changed individually. For instance you can change a semicolon character in a string to a period inside the same string object. In Java and Scala, on the other hand, a string is a sequence of characters in the mathematical sense. Replacing a character in a string using an expression like s.replace(';', '.') yields a new string object, which is different from s. Another way of expressing this is that strings are immutable in Java Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.3 Chapter 1 · A Scalable Language 58 whereas they are mutable in Ruby. So looking at just strings, Java is a func- tional language, whereas Ruby is not. Immutable data structures are one of the cornerstones of functional programming. The Scala libraries define many more immutable data types on top of those found in the Java APIs. For instance, Scala has immutable lists, tuples, maps, and sets. Another way of stating this second idea of functional programming is that methods should not have any side effects. They should communicate with their environment only by taking arguments and returning results. For instance, the replace method in Java’s String class fits this description. It takes a string and two characters and yields a new string where all occur- rences of one character are replaced by the other. There is no other effect of calling replace. Methods like replace are called referentially transparent, which means that for any given input the method call could be replaced by its result without affecting the program’s semantics. Functional languages encourage immutable data structures and referen- tially transparent methods. Some functional languages even require them. Scala gives you a choice. When you want to, you can write in an imper- ative style, which is what programming with mutable data and side effects is called. But Scala generally makes it easy to avoid imperative constructs when you want, because good functional alternatives exist. 1.3 Why Scala? Is Scala for you? You will have to see and decide for yourself. We have found that there are actually many reasons besides scalability to like programming in Scala. Four of the most important aspects will be discussed in this section: compatibility, brevity, high-level abstractions, and advanced static typing. Scala is compatible Scala doesn’t require you to leap backwards off the Java platform to step for- ward from the Java language. It allows you to add value to existing code—to build on what you already have—because it was designed for seamless in- teroperability with Java.8 Scala programs compile to JVM bytecodes. Their run-time performance is usually on par with Java programs. Scala code can 8There is also a Scala variant that runs on the .NET platform, but the JVM variant cur- rently has better support. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.3 Chapter 1 · A Scalable Language 59 call Java methods, access Java fields, inherit from Java classes, and imple- ment Java interfaces. None of this requires special syntax, explicit interface descriptions, or glue code. In fact, almost all Scala code makes heavy use of Java libraries, often without programmers being aware of this fact. Another aspect of full interoperability is that Scala heavily re-uses Java types. Scala’s Ints are represented as Java primitive integers of type int, Floats are represented as floats, Booleans as booleans, and so on. Scala arrays are mapped to Java arrays. Scala also re-uses many of the stan- dard Java library types. For instance, the type of a string literal "abc" in Scala is java.lang.String, and a thrown exception must be a subclass of java.lang.Throwable. Scala not only re-uses Java’s types, but also “dresses them up” to make them nicer. For instance, Scala’s strings support methods like toInt or toFloat, which convert the string to an integer or floating-point number. So you can write str.toInt instead of Integer.parseInt(str). How can this be achieved without breaking interoperability? Java’s String class certainly has no toInt method! In fact, Scala has a very general solution to solve this tension between advanced library design and interoperability. Scala lets you define implicit conversions, which are always applied when types would not normally match up, or when non-existing members are se- lected. In the case above, when looking for a toInt method on a string, the Scala compiler will find no such member of class String, but it will find an implicit conversion that converts a Java String to an instance of the Scala class StringOps, which does define such a member. The conversion will then be applied implicitly before performing the toInt operation. Scala code can also be invoked from Java code. This is sometimes a bit more subtle, because Scala is a richer language than Java, so some of Scala’s more advanced features need to be encoded before they can be mapped to Java. Chapter 31 explains the details. Scala is concise Scala programs tend to be short. Scala programmers have reported reduc- tions in number of lines of up to a factor of ten compared to Java. These might be extreme cases. A more conservative estimate would be that a typ- ical Scala program should have about half the number of lines of the same program written in Java. Fewer lines of code mean not only less typing, but also less effort at reading and understanding programs and fewer possibili- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.3 Chapter 1 · A Scalable Language 60 ties of defects. There are several factors that contribute to this reduction in lines of code. First, Scala’s syntax avoids some of the boilerplate that burdens Java programs. For instance, semicolons are optional in Scala and are usually left out. There are also several other areas where Scala’s syntax is less noisy. As an example, compare how you write classes and constructors in Java and Scala. In Java, a class with a constructor often looks like this: // this is Java class MyClass { private int index; private String name; public MyClass(int index, String name) { this.index = index; this.name = name; } } In Scala, you would likely write this instead: class MyClass(index: Int, name: String) Given this code, the Scala compiler will produce a class that has two private instance variables, an Int named index and a String named name, and a constructor that takes initial values for those variables as parameters. The code of this constructor will initialize the two instance variables with the values passed as parameters. In short, you get essentially the same function- ality as the more verbose Java version.9 The Scala class is quicker to write, easier to read, and most importantly, less error prone than the Java class. Scala’s type inference is another factor that contributes to its concise- ness. Repetitive type information can be left out, so programs become less cluttered and more readable. But probably the most important key to compact code is code you don’t have to write because it is done in a library for you. Scala gives you many tools to define powerful libraries that let you capture and factor out common behavior. For instance, different aspects of library classes can be separated 9The only real difference is that the instance variables produced in the Scala case will be final. You’ll learn how to make them non-final in Section 10.6. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.3 Chapter 1 · A Scalable Language 61 out into traits, which can then be mixed together in flexible ways. Or, li- brary methods can be parameterized with operations, which lets you define constructs that are, in effect, your own control structures. Together, these constructs allow the definition of libraries that are both high-level and flexi- ble to use. Scala is high-level Programmers are constantly grappling with complexity. To program pro- ductively, you must understand the code on which you are working. Overly complex code has been the downfall of many a software project. Unfortu- nately, important software usually has complex requirements. Such com- plexity can’t be avoided; it must instead be managed. Scala helps you manage complexity by letting you raise the level of ab- straction in the interfaces you design and use. As an example, imagine you have a String variable name, and you want to find out whether or not that String contains an upper case character. In Java, you might write this: // this is Java boolean nameHasUpperCase = false; for (int i = 0; i < name.length(); ++i) { if (Character.isUpperCase(name.charAt(i))) { nameHasUpperCase = true; break; } } Whereas in Scala, you could write this: val nameHasUpperCase = name.exists(_.isUpper) The Java code treats strings as low-level entities that are stepped through character by character in a loop. The Scala code treats the same strings as higher-level sequences of characters that can be queried with predicates. Clearly the Scala code is much shorter and—for trained eyes—easier to un- derstand than the Java code. So the Scala code weighs less heavily on the total complexity budget. It also gives you less opportunity to make mistakes. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.3 Chapter 1 · A Scalable Language 62 The predicate _.isUpper is an example of a function literal in Scala.10 It describes a function that takes a character argument (represented by the underscore character), and tests whether it is an upper case letter.11 In principle, such control abstractions are possible in Java as well. You’d need to define an interface that contains a method with the abstracted func- tionality. For instance, if you wanted to support querying over strings, you might invent an interface, named CharacterProperty, which has just one method, hasProperty: // this is Java interface CharacterProperty { boolean hasProperty(char ch); } With that interface you could formulate a method exists in Java: It takes a string and CharacterProperty and returns true if there’s a character in the string that satisfies the property. You could then invoke exists as follows: // this is Java exists(name, new CharacterProperty() { public boolean hasProperty(char ch) { return Character.isUpperCase(ch); } }); However, all this feels rather heavy. So heavy, in fact, that most Java pro- grammers would not bother. They would just write out the loops and live with the increased complexity in their code. On the other hand, function literals in Scala are really lightweight, so they are used frequently. As you get to know Scala better you’ll find more and more opportunities to define and use your own control abstractions. You’ll find that this helps avoid code duplication and thus keeps your programs shorter and clearer. Scala is statically typed A static type system classifies variables and expressions according to the kinds of values they hold and compute. Scala stands out as a language with 10A function literal can be called a predicate if its result type is Boolean. 11This use of the underscore as a placeholder for arguments is described in Section 8.5. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.3 Chapter 1 · A Scalable Language 63 a very advanced static type system. Starting from a system of nested class types much like Java’s, it allows you to parameterize types with generics, to combine types using intersections, and to hide details of types using abstract types.12 These give a strong foundation for building and composing your own types, so that you can design interfaces that are at the same time safe and flexible to use. If you like dynamic languages such as Perl, Python, Ruby, or Groovy, you might find it a bit strange that Scala’s static type system is listed as one of its strong points. After all, the absence of a static type system has been cited by some as a major advantage of dynamic languages. The most com- mon arguments against static types are that they make programs too verbose, prevent programmers from expressing themselves as they wish, and make impossible certain patterns of dynamic modifications of software systems. However, often these arguments do not go against the idea of static types in general, but against specific type systems, which are perceived to be too ver- bose or too inflexible. For instance, Alan Kay, the inventor of the Smalltalk language, once remarked: “I’m not against types, but I don’t know of any type systems that aren’t a complete pain, so I still like dynamic typing.”13 We hope to convince you in this book that Scala’s type system is far from being a “complete pain.” In fact, it addresses nicely two of the usual concerns about static typing: verbosity is avoided through type inference and flexibility is gained through pattern matching and several new ways to write and compose types. With these impediments out of the way, the classical benefits of static type systems can be better appreciated. Among the most important of these benefits are verifiable properties of program abstractions, safe refactorings, and better documentation. Verifiable properties. Static type systems can prove the absence of certain run-time errors. For instance, they can prove properties like: booleans are never added to integers; private variables are not accessed from outside their class; functions are applied to the right number of arguments; only strings are ever added to a set of strings. Other kinds of errors are not detected by today’s static type systems. For instance, they will usually not detect non-terminating functions, array 12Generics are discussed in Chapter 19, intersections in Chapter 12, and abstract types in Chapter 20. 13Kay, in an email on the meaning of object-oriented programming. [Kay03] Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.3 Chapter 1 · A Scalable Language 64 bounds violations, or divisions by zero. They will also not detect that your program does not conform to its specification (assuming there is a spec, that is!). Static type systems have therefore been dismissed by some as not being very useful. The argument goes that since such type systems can only de- tect simple errors, whereas unit tests provide more extensive coverage, why bother with static types at all? We believe that these arguments miss the point. Although a static type system certainly cannot replace unit testing, it can reduce the number of unit tests needed by taking care of some properties that would otherwise need to be tested. Likewise, unit testing can not replace static typing. After all, as Edsger Dijkstra said, testing can only prove the presence of errors, never their absence.14 So the guarantees that static typing gives may be simple, but they are real guarantees of a form no amount of testing can deliver. Safe refactorings. A static type system provides a safety net that lets you make changes to a codebase with a high degree of confidence. Consider for instance a refactoring that adds an additional parameter to a method. In a statically typed language you can do the change, re-compile your system and simply fix all lines that cause a type error. Once you have finished with this, you are sure to have found all places that need to be changed. The same holds for many other simple refactorings like changing a method name, or moving methods from one class to another. In all cases a static type check will provide enough assurance that the new system works just like the old. Documentation. Static types are program documentation that is checked by the compiler for correctness. Unlike a normal comment, a type annota- tion can never be out of date (at least not if the source file that contains it has recently passed a compiler). Furthermore, compilers and integrated de- velopment environments can make use of type annotations to provide better context help. For instance, an integrated development environment can dis- play all the members available for a selection by determining the static type of the expression on which the selection is made and looking up all members of that type. Even though static types are generally useful for program documentation, they can sometimes be annoying when they clutter the program. Typically, 14Dijkstra, “Notes on Structured Programming,” [Dij70] Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.4 Chapter 1 · A Scalable Language 65 useful documentation is what readers of a program cannot easily derive by themselves. In a method definition like: def f(x: String) = ... it’s useful to know that f’s argument should be a String. On the other hand, at least one of the two annotations in the following example is annoying: val x: HashMap[Int, String] = new HashMap[Int, String]() Clearly, it should be enough to say just once that x is a HashMap with Ints as keys and Strings as values; there’s no need to repeat the same phrase twice. Scala has a very sophisticated type inference system that lets you omit almost all type information that’s usually considered annoying. In the previ- ous example, the following two less annoying alternatives would work just as well: val x = new HashMap[Int, String]() val x: Map[Int, String] = new HashMap() Type inference in Scala can go quite far. In fact, it’s not uncommon for user code to have no explicit types at all. Therefore, Scala programs often look a bit like programs written in a dynamically typed scripting language. This holds particularly for client application code, which glues together pre- written library components. It’s less true for the library components them- selves, because these often employ fairly sophisticated types to allow flexible usage patterns. This is only natural. After all, the type signatures of the mem- bers that make up the interface of a reusable component should be explicitly given, because they constitute an essential part of the contract between the component and its clients. 1.4 Scala’s roots Scala’s design has been influenced by many programming languages and ideas in programming language research. In fact, only a few features of Scala are genuinely new; most have been already applied in some form in other languages. Scala’s innovations come primarily from how its constructs are put together. In this section, we list the main influences on Scala’s design. The list cannot be exhaustive—there are simply too many smart ideas around in programming language design to enumerate them all here. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.4 Chapter 1 · A Scalable Language 66 At the surface level, Scala adopts a large part of the syntax of Java and C#, which in turn borrowed most of their syntactic conventions from C and C++. Expressions, statements, and blocks are mostly as in Java, as is the syntax of classes, packages and imports.15 Besides syntax, Scala adopts other elements of Java, such as its basic types, its class libraries, and its execution model. Scala also owes much to other languages. Its uniform object model was pioneered by Smalltalk and taken up subsequently by Ruby. Its idea of uni- versal nesting (almost every construct in Scala can be nested inside any other construct) is also present in Algol, Simula, and, more recently in Beta and gbeta. Its uniform access principle for method invocation and field selection comes from Eiffel. Its approach to functional programming is quite simi- lar in spirit to the ML family of languages, which has SML, OCaml, and F# as prominent members. Many higher-order functions in Scala’s standard library are also present in ML or Haskell. Scala’s implicit parameters were motivated by Haskell’s type classes; they achieve analogous results in a more classical object-oriented setting. Scala’s actor-based concurrency library was heavily inspired by Erlang. Scala is not the first language to emphasize scalability and extensibil- ity. The historic root of extensible languages that can span different appli- cation areas is Peter Landin’s 1966 paper “The Next 700 Programming Lan- guages.”16 (The language described in this paper, Iswim, stands beside Lisp as one of the pioneering functional languages.) The specific idea of treating an infix operator as a function can be traced back to Iswim and Smalltalk. Another important idea is to permit a function literal (or block) as a param- eter, which enables libraries to define control structures. Again, this goes back to Iswim and Smalltalk. Smalltalk and Lisp both have a flexible syntax that has been applied extensively for building internal domain-specific lan- guages. C++ is another scalable language that can be adapted and extended 15 The major deviation from Java concerns the syntax for type annotations—it’s “variable: Type” instead of “Type variable” in Java. Scala’s postfix type syntax re- sembles Pascal, Modula-2, or Eiffel. The main reason for this deviation has to do with type inference, which often lets you omit the type of a variable or the return type of a method. Using the “variable: Type” syntax this is easy—just leave out the colon and the type. But in C-style “Type variable” syntax you cannot simply leave off the type—there would be no marker to start the definition anymore. You’d need some alternative keyword to be a place- holder for a missing type (C# 3.0, which does some type inference, uses var for this purpose). Such an alternative keyword feels more ad-hoc and less regular than Scala’s approach. 16Landin, “The Next 700 Programming Languages.” [Lan66] Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 1.5 Chapter 1 · A Scalable Language 67 through operator overloading and its template system; compared to Scala it is built on a lower-level, more systems-oriented core. Scala is also not the first language to integrate functional and object- oriented programming, although it probably goes furthest in this direction. Other languages that have integrated some elements of functional program- ming into OOP include Ruby, Smalltalk, and Python. On the Java platform, Pizza, Nice, and Multi-Java have all extended a Java-like core with functional ideas. There are also primarily functional languages that have acquired an object system; examples are OCaml, F#, and PLT-Scheme. Scala has also contributed some innovations to the field of programming languages. For instance, its abstract types provide a more object-oriented alternative to generic types, its traits allow for flexible component assembly, and its extractors provide a representation-independent way to do pattern matching. These innovations have been presented in papers at programming language conferences in recent years.17 1.5 Conclusion In this chapter, we gave you a glimpse of what Scala is and how it might help you in your programming. To be sure, Scala is not a silver bullet that will magically make you more productive. To advance, you will need to apply Scala artfully, and that will require some learning and practice. If you’re coming to Scala from Java, the most challenging aspects of learning Scala may involve Scala’s type system (which is richer than Java’s) and its support for functional programming. The goal of this book is to guide you gently up Scala’s learning curve, one step at a time. We think you’ll find it a rewarding intellectual experience that will expand your horizons and make you think differently about program design. Hopefully, you will also gain pleasure and inspiration from programming in Scala. In the next chapter, we’ll get you started writing some Scala code. 17For more information, see [Ode03], [Ode05], and [Emi07] in the bibliography. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 2 First Steps in Scala It’s time to write some Scala code. Before we start on the in-depth Scala tutorial, we put in two chapters that will give you the big picture of Scala, and most importantly, get you writing code. We encourage you to actually try out all the code examples presented in this chapter and the next as you go. The best way to start learning Scala is to program in it. To run the examples in this chapter, you should have a standard Scala installation. To get one, go to http://www.scala-lang.org/downloads and follow the directions for your platform. You can also use a Scala plug- in for Eclipse, IntelliJ, or NetBeans, but for the steps in this chapter, we’ll assume you’re using the Scala distribution from scala-lang.org.1 If you are a veteran programmer new to Scala, the next two chapters should give you enough understanding to enable you to start writing useful programs in Scala. If you are less experienced, some of the material may seem a bit mysterious to you. But don’t worry. To get you up to speed quickly, we had to leave out some details. Everything will be explained in a less “fire hose” fashion in later chapters. In addition, we inserted quite a few footnotes in these next two chapters to point you to later sections of the book where you’ll find more detailed explanations. Step 1. Learn to use the Scala interpreter The easiest way to get started with Scala is by using the Scala interpreter, an interactive “shell” for writing Scala expressions and programs. Simply type an expression into the interpreter and it will evaluate the expression and print 1We tested the examples in this book with Scala version 2.8.1. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 1 Chapter 2 · First Steps in Scala 69 the resulting value. The interactive shell for Scala is simply called scala. You use it by typing scala at a command prompt:2 $ scala Welcome to Scala version 2.8.1. Type in expressions to have them evaluated. Type :help for more information. scala> After you type an expression, such as 1 + 2, and hit enter: scala> 1 + 2 The interpreter will print: res0: Int = 3 This line includes: • an automatically generated or user-defined name to refer to the com- puted value (res0, which means result 0), • a colon (:), followed by the type of the expression (Int), • an equals sign (=), • the value resulting from evaluating the expression (3). The type Int names the class Int in the package scala. Packages in Scala are similar to packages in Java: they partition the global namespace and provide a mechanism for information hiding.3 Values of class Int corre- spond to Java’s int values. More generally, all of Java’s primitive types have corresponding classes in the scala package. For example, scala.Boolean corresponds to Java’s boolean. scala.Float corresponds to Java’s float. And when you compile your Scala code to Java bytecodes, the Scala com- piler will use Java’s primitive types where possible to give you the perfor- mance benefits of the primitive types. 2If you’re using Windows, you’ll need to type the scala command into the “Command Prompt” DOS box. 3If you’re not familiar with Java packages, you can think of them as providing a full name for classes. Because Int is a member of package scala,“Int” is the class’s simple name, and “scala.Int” is its full name. The details of packages are explained in Chapter 13. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 2 Chapter 2 · First Steps in Scala 70 The resX identifier may be used in later lines. For instance, since res0 was set to 3 previously, res0 * 3 will be 9: scala> res0 * 3 res1: Int = 9 To print the necessary, but not sufficient, Hello, world! greeting, type: scala> println("Hello, world!") Hello, world! The println function prints the passed string to the standard output, similar to System.out.println in Java. Step 2. Define some variables Scala has two kinds of variables, vals and vars. A val is similar to a final variable in Java. Once initialized, a val can never be reassigned. A var, by contrast, is similar to a non-final variable in Java. A var can be reassigned throughout its lifetime. Here’s a val definition: scala> val msg = "Hello, world!" msg: java.lang.String = Hello, world! This statement introduces msg as a name for the string "Hello, world!". The type of msg is java.lang.String, because Scala strings are imple- mented by Java’s String class. If you’re used to declaring variables in Java, you’ll notice one striking difference here: neither java.lang.String nor String appear anywhere in the val definition. This example illustrates type inference, Scala’s ability to figure out types you leave off. In this case, because you initialized msg with a string literal, Scala inferred the type of msg to be String. When the Scala interpreter (or compiler) can infer types, it is often best to let it do so rather than fill the code with unnecessary, explicit type annotations. You can, however, specify a type explicitly if you wish, and sometimes you prob- ably should. An explicit type annotation can both ensure the Scala compiler infers the type you intend, as well as serve as useful documentation for fu- ture readers of the code. In contrast to Java, where you specify a variable’s type before its name, in Scala you specify a variable’s type after its name, separated by a colon. For example: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 2 Chapter 2 · First Steps in Scala 71 scala> val msg2: java.lang.String = "Hello again, world!" msg2: java.lang.String = Hello again, world! Or, since java.lang types are visible with their simple names4 in Scala programs, simply: scala> val msg3: String = "Hello yet again, world!" msg3: String = Hello yet again, world! Going back to the original msg, now that it is defined, you can use it as you’d expect, for example: scala> println(msg) Hello, world! What you can’t do with msg, given that it is a val, not a var, is reassign it.5 For example, see how the interpreter complains when you attempt the following: scala> msg = "Goodbye cruel world!" :6: error: reassignment to val msg = "Goodbye cruel world!" ˆ If reassignment is what you want, you’ll need to use a var, as in: scala> var greeting = "Hello, world!" greeting: java.lang.String = Hello, world! Since greeting is a var not a val, you can reassign it later. If you are feeling grouchy later, for example, you could change your greeting to: scala> greeting = "Leave me alone, world!" greeting: java.lang.String = Leave me alone, world! To enter something into the interpreter that spans multiple lines, just keep typing after the first line. If the code you typed so far is not complete, the interpreter will respond with a vertical bar on the next line. 4The simple name of java.lang.String is String. 5In the interpreter, however, you can define a new val with a name that was already used before. This mechanism is explained in Section 7.7. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 3 Chapter 2 · First Steps in Scala 72 scala> val multiLine = | "This is the next line." multiLine: java.lang.String = This is the next line. If you realize you have typed something wrong, but the interpreter is still waiting for more input, you can escape by pressing enter twice: scala> val oops = | | You typed two blank lines. Starting a new command. scala> In the rest of the book, we’ll leave out the vertical bars to make the code easier to read (and easier to copy and paste from the PDF eBook into the interpreter). Step 3. Define some functions Now that you’ve worked with Scala variables, you’ll probably want to write some functions. Here’s how you do that in Scala: scala> def max(x: Int, y: Int): Int = { if (x > y) x else y } max: (x: Int,y: Int)Int Function definitions start with def. The function’s name, in this case max, is followed by a comma-separated list of parameters in parentheses. A type an- notation must follow every function parameter, preceded by a colon, because the Scala compiler (and interpreter, but from now on we’ll just say compiler) does not infer function parameter types. In this example, the function named max takes two parameters, x and y, both of type Int. After the close paren- thesis of max’s parameter list you’ll find another “: Int” type annotation. This one defines the result type of the max function itself.6 Following the 6In Java, the type of the value returned from a method is its return type. In Scala, that same concept is called result type. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 3 Chapter 2 · First Steps in Scala 73 def max(x: Int, y: Int): Int = { if (x > y) x else y } “def” starts a function definition function name parameter list in parentheses equals sign function’s result type function body in curly braces Figure 2.1· The basic form of a function definition in Scala. function’s result type is an equals sign and pair of curly braces that contain the body of the function. In this case, the body contains a single if expres- sion, which selects either x or y, whichever is greater, as the result of the max function. As demonstrated here, Scala’s if expression can result in a value, similar to Java’s ternary operator. For example, the Scala expression “if (x > y) x else y” behaves similarly to “(x > y) ? x : y” in Java. The equals sign that precedes the body of a function hints that in the functional world view, a function defines an expression that results in a value. The basic structure of a function is illustrated in Figure 2.1. Sometimes the Scala compiler will require you to specify the result type of a function. If the function is recursive,7 for example, you must explicitly specify the function’s result type. In the case of max however, you may leave the result type off and the compiler will infer it.8 Also, if a function consists of just one statement, you can optionally leave off the curly braces. Thus, you could alternatively write the max function like this: scala> def max2(x: Int, y: Int) = if (x > y) x else y max2: (x: Int,y: Int)Int 7A function is recursive if it calls itself. 8Nevertheless, it is often a good idea to indicate function result types explicitly, even when the compiler doesn’t require it. Such type annotations can make the code easier to read, because the reader need not study the function body to figure out the inferred result type. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 4 Chapter 2 · First Steps in Scala 74 Once you have defined a function, you can call it by name, as in: scala> max(3, 5) res4: Int = 5 Here’s the definition of a function that takes no parameters and returns no interesting result: scala> def greet() = println("Hello, world!") greet: ()Unit When you define the greet() function, the interpreter will respond with greet: ()Unit.“greet” is, of course, the name of the function. The empty parentheses indicate the function takes no parameters. And Unit is greet’s result type. A result type of Unit indicates the function returns no interesting value. Scala’s Unit type is similar to Java’s void type, and in fact every void-returning method in Java is mapped to a Unit-returning method in Scala. Methods with the result type of Unit, therefore, are only executed for their side effects. In the case of greet(), the side effect is a friendly greeting printed to the standard output. In the next step, you’ll place Scala code in a file and run it as a script. If you wish to exit the interpreter, you can do so by entering :quit or :q. scala> :quit $ Step 4. Write some Scala scripts Although Scala is designed to help programmers build very large-scale sys- tems, it also scales down nicely to scripting. A script is just a sequence of statements in a file that will be executed sequentially. Put this into a file named hello.scala: println("Hello, world, from a script!") then run:9 9You can run scripts without typing “scala” on Unix and Windows using a “pound- bang” syntax, which is shown in Appendix A. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 5 Chapter 2 · First Steps in Scala 75 $ scala hello.scala And you should get yet another greeting: Hello, world, from a script! Command line arguments to a Scala script are available via a Scala array named args. In Scala, arrays are zero based, and you access an element by specifying an index in parentheses. So the first element in a Scala array named steps is steps(0), not steps[0], as in Java. To try this out, type the following into a new file named helloarg.scala: // Say hello to the first argument println("Hello, "+ args(0) +"!") then run: $ scala helloarg.scala planet In this command, "planet" is passed as a command line argument, which is accessed in the script as args(0). Thus, you should see: Hello, planet! Note that this script included a comment. The Scala compiler will ignore characters between // and the next end of line and any characters between /* and */. This example also shows Strings being concatenated with the + operator. This works as you’d expect. The expression "Hello, "+"world!" will result in the string "Hello, world!".10 Step 5. Loop with while; decide with if To try out a while, type the following into a file named printargs.scala: var i = 0 while (i < args.length) { println(args(i)) i += 1 } 10You can also put spaces around the plus operator, as in "Hello, " + "world!". In this book, however, we’ll leave the space off between ‘+’ and string literals. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 5 Chapter 2 · First Steps in Scala 76 Note Although the examples in this section help explain while loops, they do not demonstrate the best Scala style. In the next section, you’ll see better approaches that avoid iterating through arrays with indexes. This script starts with a variable definition, var i = 0. Type inference gives i the type scala.Int, because that is the type of its initial value, 0. The while construct on the next line causes the block (the code between the curly braces) to be repeatedly executed until the boolean expression i < args.length is false. args.length gives the length of the args array. The block contains two statements, each indented two spaces, the recom- mended indentation style for Scala. The first statement, println(args(i)), prints out the ith command line argument. The second statement, i += 1, in- crements i by one. Note that Java’s ++i and i++ don’t work in Scala. To increment in Scala, you need to say either i = i + 1 or i += 1. Run this script with the following command: $ scala printargs.scala Scala is fun And you should see: Scala is fun For even more fun, type the following code into a new file with the name echoargs.scala: var i = 0 while (i < args.length) { if (i != 0) print("") print(args(i)) i += 1 } println() In this version, you’ve replaced the println call with a print call, so that all the arguments will be printed out on the same line. To make this readable, you’ve inserted a single space before each argument except the first via the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 6 Chapter 2 · First Steps in Scala 77 if (i != 0) construct. Since i != 0 will be false the first time through the while loop, no space will get printed before the initial argument. Lastly, you’ve added one more println to the end, to get a line return after printing out all the arguments. Your output will be very pretty indeed. If you run this script with the following command: $ scala echoargs.scala Scala is even more fun You’ll get: Scala is even more fun Note that in Scala, as in Java, you must put the boolean expression for a while or an if in parentheses. (In other words, you can’t say in Scala things like if i < 10 as you can in a language such as Ruby. You must say if (i < 10) in Scala.) Another similarity to Java is that if a block has only one statement, you can optionally leave off the curly braces, as demonstrated by the if statement in echoargs.scala. And although you haven’t seen any of them, Scala does use semicolons to separate statements as in Java, except that in Scala the semicolons are very often optional, giving some welcome relief to your right little finger. If you had been in a more verbose mood, therefore, you could have written the echoargs.scala script as follows: var i = 0; while (i < args.length) { if (i != 0){ print(""); } print(args(i)); i += 1; } println(); Step 6. Iterate with foreach and for Although you may not have realized it, when you wrote the while loops in the previous step, you were programming in an imperative style. In the im- perative style, which is the style you normally use with languages like Java, C++, and C, you give one imperative command at a time, iterate with loops, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 6 Chapter 2 · First Steps in Scala 78 and often mutate state shared between different functions. Scala enables you to program imperatively, but as you get to know Scala better, you’ll likely often find yourself programming in a more functional style. In fact, one of the main aims of this book is to help you become as comfortable with the functional style as you are with imperative style. One of the main characteristics of a functional language is that functions are first class constructs, and that’s very true in Scala. For example, another (far more concise) way to print each command line argument is: args.foreach(arg => println(arg)) In this code, you call the foreach method on args, and pass in a function. In this case, you’re passing in a function literal that takes one parameter named arg. The body of the function is println(arg). If you type the above code into a new file named pa.scala, and execute with the command: $ scala pa.scala Concise is nice You should see: Concise is nice In the previous example, the Scala interpreter infers the type of arg to be String, since String is the element type of the array on which you’re calling foreach. If you’d prefer to be more explicit, you can mention the type name, but when you do you’ll need to wrap the argument portion in parentheses (which is the normal form of the syntax anyway): args.foreach((arg: String) => println(arg)) Running this script has the same behavior as the previous one. If you’re in the mood for more conciseness instead of more explicitness, you can take advantage of a special shorthand in Scala. If a function literal consists of one statement that takes a single argument, you need not explicitly name and specify the argument.11 Thus, the following code also works: args.foreach(println) 11This shorthand, called a partially applied function, is described in Section 8.6. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 6 Chapter 2 · First Steps in Scala 79 (x: Int, y: Int) => x + y function parameters in parentheses function body right arrow Figure 2.2· The syntax of a function literal in Scala. To summarize, the syntax for a function literal is a list of named parameters, in parentheses, a right arrow, and then the body of the function. This syntax is illustrated in Figure 2.2. Now, by this point you may be wondering what happened to those trusty for loops you have been accustomed to using in imperative languages such as Java or C. In an effort to guide you in a functional direction, only a func- tional relative of the imperative for (called a for expression) is available in Scala. While you won’t see their full power and expressiveness until you reach (or peek ahead to) Section 7.3, we’ll give you a glimpse here. In a new file named forargs.scala, type the following: for (arg <- args) println(arg) The parentheses after the “for” contain arg <- args.12 To the right of the <- symbol is the familiar args array. To the left of <- is “arg”, the name of a val, not a var. (Because it is always a val, you just write “arg” by itself, not “val arg”.) Although arg may seem to be a var, because it will get a new value on each iteration, it really is a val: arg can’t be reassigned inside the body of the for expression. Instead, for each element of the args array, a new arg val will be created and initialized to the element value, and the body of the for will be executed. If you run the forargs.scala script with the command: $ scala forargs.scala for arg in args 12You can say “in” for the <- symbol. You’d read for (arg <- args), therefore, as “for arg in args.” Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Conclusion Chapter 2 · First Steps in Scala 80 You’ll see: for arg in args Scala’s for expression can do much more than this, but this example is enough to get you started. We’ll show you more about for in Section 7.3 and Chapter 23. Conclusion In this chapter, you learned some Scala basics and, hopefully, took advantage of the opportunity to write a bit of Scala code. In the next chapter, we’ll continue this introductory overview and get into more advanced topics. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 3 Next Steps in Scala This chapter continues the previous chapter’s introduction to Scala. In this chapter, we’ll introduce some more advanced features. When you complete this chapter, you should have enough knowledge to enable you to start writ- ing useful scripts in Scala. As with the previous chapter, we recommend you try out these examples as you go. The best way to get a feel for Scala is to start writing Scala code. Step 7. Parameterize arrays with types In Scala, you can instantiate objects, or class instances, using new. When you instantiate an object in Scala, you can parameterize it with values and types. Parameterization means “configuring” an instance when you create it. You parameterize an instance with values by passing objects to a constructor in parentheses. For example, the following Scala code instantiates a new java.math.BigInteger and parameterizes it with the value "12345": val big = new java.math.BigInteger("12345") You parameterize an instance with types by specifying one or more types in square brackets. An example is shown in Listing 3.1. In this example, greetStrings is a value of type Array[String] (an “array of string”) that is initialized to length 3 by parameterizing it with the value 3 in the first line of code. If you run the code in Listing 3.1 as a script, you’ll see yet another Hello, world! greeting. Note that when you parameterize an instance with both a type and a value, the type comes first in its square brackets, followed by the value in parentheses. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 7 Chapter 3 · Next Steps in Scala 82 val greetStrings = new Array[String](3) greetStrings(0) = "Hello" greetStrings(1) = ", " greetStrings(2) = "world!\n" for (i <- 0 to 2) print(greetStrings(i)) Listing 3.1· Parameterizing an array with a type. Note Although the code in Listing 3.1 demonstrates important concepts, it does not show the recommended way to create and initialize an array in Scala. You’ll see a better way in Listing 3.2 on page 85. Had you been in a more explicit mood, you could have specified the type of greetStrings explicitly like this: val greetStrings: Array[String] = new Array[String](3) Given Scala’s type inference, this line of code is semantically equivalent to the actual first line of Listing 3.1. But this form demonstrates that while the type parameterization portion (the type names in square brackets) forms part of the type of the instance, the value parameterization part (the values in parentheses) does not. The type of greetStrings is Array[String], not Array[String](3). The next three lines of code in Listing 3.1 initialize each element of the greetStrings array: greetStrings(0) = "Hello" greetStrings(1) = ", " greetStrings(2) = "world!\n" As mentioned previously, arrays in Scala are accessed by placing the index inside parentheses, not square brackets as in Java. Thus the zeroth element of the array is greetStrings(0), not greetStrings[0]. These three lines of code illustrate an important concept to understand about Scala concerning the meaning of val. When you define a variable with val, the variable can’t be reassigned, but the object to which it refers could potentially still be changed. So in this case, you couldn’t reassign Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 7 Chapter 3 · Next Steps in Scala 83 greetStrings to a different array; greetStrings will always point to the same Array[String] instance with which it was initialized. But you can change the elements of that Array[String] over time, so the array itself is mutable. The final two lines in Listing 3.1 contain a for expression that prints out each greetStrings array element in turn: for (i <- 0 to 2) print(greetStrings(i)) The first line of code in this for expression illustrates another general rule of Scala: if a method takes only one parameter, you can call it without a dot or parentheses. The to in this example is actually a method that takes one Int argument. The code 0 to 2 is transformed into the method call (0).to(2).1 Note that this syntax only works if you explicitly specify the receiver of the method call. You cannot write “println 10”, but you can write “Console println 10”. Scala doesn’t technically have operator overloading, because it doesn’t actually have operators in the traditional sense. Instead, characters such as +, -, *, and / can be used in method names. Thus, when you typed 1 + 2 into the Scala interpreter in Step 1, you were actually invoking a method named + on the Int object 1, passing in 2 as a parameter. As illustrated in Figure 3.1, you could alternatively have written 1 + 2 using traditional method invocation syntax, (1).+(2). Another important idea illustrated by this example will give you insight into why arrays are accessed with parentheses in Scala. Scala has fewer special cases than Java. Arrays are simply instances of classes like any other class in Scala. When you apply parentheses surrounding one or more values to a variable, Scala will transform the code into an invocation of a method named apply on that variable. So greetStrings(i) gets transformed into greetStrings.apply(i). Thus accessing an element of an array in Scala is simply a method call like any other. This principle is not restricted to arrays: any application of an object to some arguments in parentheses will be transformed to an apply method call. Of course this will compile only if that type of object actually defines an apply method. So it’s not a special case; it’s a general rule. 1This to method actually returns not an array but a different kind of sequence, containing the values 0, 1, and 2, which the for expression iterates over. Sequences and other collections will be described in Chapter 17. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 7 Chapter 3 · Next Steps in Scala 84 Int object with value 1 Passing the Int object 2 to the ‘+’ method invoking on 1 a method named ‘+’ (1).+(2) 1 + 2 Figure 3.1· All operations are method calls in Scala. Similarly, when an assignment is made to a variable to which parentheses and one or more arguments have been applied, the compiler will transform that into an invocation of an update method that takes the arguments in parentheses as well as the object to the right of the equals sign. For example: greetStrings(0) = "Hello" will be transformed into: greetStrings.update(0, "Hello") Thus, the following is semantically equivalent to the code in Listing 3.1: val greetStrings = new Array[String](3) greetStrings.update(0, "Hello") greetStrings.update(1, ", ") greetStrings.update(2, "world!\n") for (i <- 0.to(2)) print(greetStrings.apply(i)) Scala achieves a conceptual simplicity by treating everything, from ar- rays to expressions, as objects with methods. You don’t have to remember special cases, such as the differences in Java between primitive and their cor- responding wrapper types, or between arrays and regular objects. Moreover, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 8 Chapter 3 · Next Steps in Scala 85 this uniformity does not incur a significant performance cost. The Scala com- piler uses Java arrays, primitive types, and native arithmetic where possible in the compiled code. Although the examples you’ve seen so far in this step compile and run just fine, Scala provides a more concise way to create and initialize ar- rays that you would normally use. It looks as shown in Listing 3.2. This code creates a new array of length three, initialized to the passed strings, "zero", "one", and "two". The compiler infers the type of the array to be Array[String], because you passed strings to it. val numNames = Array("zero", "one", "two") Listing 3.2· Creating and initializing an array. What you’re actually doing in Listing 3.2 is calling a factory method, named apply, which creates and returns the new array. This apply method takes a variable number of arguments2 and is defined on the Array compan- ion object. You’ll learn more about companion objects in Section 4.3. If you’re a Java programmer, you can think of this as calling a static method named apply on class Array. A more verbose way to call the same apply method is: val numNames2 = Array.apply("zero", "one", "two") Step 8. Use lists One of the big ideas of the functional style of programming is that methods should not have side effects. A method’s only act should be to compute and return a value. Some benefits gained when you take this approach are that methods become less entangled, and therefore more reliable and reusable. Another benefit (in a statically typed language) is that everything that goes into and out of a method is checked by a type checker, so logic errors are more likely to manifest themselves as type errors. Applying this functional philosophy to the world of objects means making objects immutable. As you’ve seen, a Scala array is a mutable sequence of objects that all share the same type. An Array[String] contains only strings, for example. 2Variable-length argument lists, or repeated parameters, are described in Section 8.8. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 8 Chapter 3 · Next Steps in Scala 86 Although you can’t change the length of an array after it is instantiated, you can change its element values. Thus, arrays are mutable objects. For an immutable sequence of objects that share the same type you can use Scala’s List class. As with arrays, a List[String] contains only strings. Scala’s List, scala.List, differs from Java’s java.util.List type in that Scala Lists are always immutable (whereas Java Lists can be mutable). More generally, Scala’s List is designed to enable a functional style of programming. Creating a list is easy. Listing 3.3 shows how: val oneTwoThree = List(1, 2, 3) Listing 3.3· Creating and initializing a list. The code in Listing 3.3 establishes a new val named oneTwoThree, ini- tialized with a new List[Int] with the integer elements 1, 2, and 3.3 Be- cause Lists are immutable, they behave a bit like Java strings: when you call a method on a list that might seem by its name to imply the list will mutate, it instead creates and returns a new list with the new value. For example, List has a method named ‘:::’ for list concatenation. Here’s how you use it: val oneTwo = List(1, 2) val threeFour = List(3, 4) val oneTwoThreeFour = oneTwo ::: threeFour println(oneTwo +" and "+ threeFour +" were not mutated.") println("Thus, "+ oneTwoThreeFour +" is a new list.") If you run this script, you’ll see: List(1, 2) and List(3, 4) were not mutated. Thus, List(1, 2, 3, 4) is a new list. Perhaps the most common operator you’ll use with lists is ‘::’, which is pronounced “cons.” Cons prepends a new element to the beginning of an existing list, and returns the resulting list. For example, if you run this script: val twoThree = List(2, 3) val oneTwoThree = 1 :: twoThree println(oneTwoThree) 3You don’t need to say new List because “List.apply()” is defined as a factory method on the scala.List companion object. You’ll read more on companion objects in Section 4.3. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 8 Chapter 3 · Next Steps in Scala 87 You’ll see: List(1, 2, 3) Note In the expression “1 :: twoThree”, :: is a method of its right operand, the list, twoThree. You might suspect there’s something amiss with the associativity of the :: method, but it is actually a simple rule to remember: If a method is used in operator notation, such as a * b, the method is invoked on the left operand, as in a.*(b)—unless the method name ends in a colon. If the method name ends in a colon, the method is invoked on the right operand. Therefore, in 1 :: twoThree, the :: method is invoked on twoThree, passing in 1, like this: twoThree.::(1). Operator associativity will be described in more detail in Section 5.8. Given that a shorthand way to specify an empty list is Nil, one way to initialize new lists is to string together elements with the cons operator, with Nil as the last element.4 For example, the following script will produce the same output as the previous one, “List(1, 2, 3)”: val oneTwoThree = 1 :: 2 :: 3 :: Nil println(oneTwoThree) Scala’s List is packed with useful methods, many of which are shown in Table 3.1. The full power of lists will be revealed in Chapter 16. Why not append to lists? Class List does offer an “append” operation —it’s written :+ and is explained in Chapter 24— but this operation is rarely used, because the time it takes to append to a list grows linearly with the size of the list, whereas prepending with :: takes constant time. Your options if you want to build a list efficiently by appending elements is to prepend them, then when you’re done call reverse; or use a ListBuffer, a mutable list that does offer an append operation, and when you’re done call toList. ListBuffer will be described in Section 22.2. 4The reason you need Nil at the end is that :: is defined on class List. If you try to just say 1 :: 2 :: 3, it won’t compile because 3 is an Int, which doesn’t have a :: method. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 8 Chapter 3 · Next Steps in Scala 88 Table 3.1 · Some List methods and usages What it is What it does List() or Nil The empty List List("Cool", "tools", "rule") Creates a new List[String] with the three values "Cool", "tools", and "rule" val thrill = "Will" :: "fill" :: "until" :: Nil Creates a new List[String] with the three values "Will", "fill", and "until" List("a", "b") ::: List("c", "d") Concatenates two lists (returns a new List[String] with values "a", "b", "c", and "d") thrill(2) Returns the element at index 2 (zero based) of the thrill list (returns "until") thrill.count(s => s.length == 4) Counts the number of string elements in thrill that have length 4 (returns 2) thrill.drop(2) Returns the thrill list without its first 2 elements (returns List("until")) thrill.dropRight(2) Returns the thrill list without its rightmost 2 elements (returns List("Will")) thrill.exists(s => s == "until") Determines whether a string element exists in thrill that has the value "until" (returns true) thrill.filter(s => s.length == 4) Returns a list of all elements, in order, of the thrill list that have length 4 (returns List("Will", "fill")) thrill.forall(s => s.endsWith("l")) Indicates whether all elements in the thrill list end with the letter "l" (returns true) thrill.foreach(s => print(s)) Executes the print statement on each of the strings in the thrill list (prints "Willfilluntil") Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 8 Chapter 3 · Next Steps in Scala 89 Table 3.1 · continued thrill.foreach(print) Same as the previous, but more concise (also prints "Willfilluntil") thrill.head Returns the first element in the thrill list (returns "Will") thrill.init Returns a list of all but the last element in the thrill list (returns List("Will", "fill")) thrill.isEmpty Indicates whether the thrill list is empty (returns false) thrill.last Returns the last element in the thrill list (returns "until") thrill.length Returns the number of elements in the thrill list (returns 3) thrill.map(s => s + "y") Returns a list resulting from adding a "y" to each string element in the thrill list (returns List("Willy", "filly", "untily")) thrill.mkString(", ") Makes a string with the elements of the list (returns "Will, fill, until") thrill.remove(s => s.length == 4) Returns a list of all elements, in order, of the thrill list except those that have length 4 (returns List("until")) thrill.reverse Returns a list containing all elements of the thrill list in reverse order (returns List("until", "fill", "Will")) thrill.sort((s, t) => s.charAt(0).toLower < t.charAt(0).toLower) Returns a list containing all elements of the thrill list in alphabetical order of the first character lowercased (returns List("fill", "until", "Will")) thrill.tail Returns the thrill list minus its first element (returns List("fill", "until")) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 9 Chapter 3 · Next Steps in Scala 90 Step 9. Use tuples Another useful container object is the tuple. Like lists, tuples are immutable, but unlike lists, tuples can contain different types of elements. Whereas a list might be a List[Int] or a List[String], a tuple could contain both an integer and a string at the same time. Tuples are very useful, for example, if you need to return multiple objects from a method. Whereas in Java you would often create a JavaBean-like class to hold the multiple return values, in Scala you can simply return a tuple. And it is simple: to instantiate a new tuple that holds some objects, just place the objects in parentheses, separated by commas. Once you have a tuple instantiated, you can access its elements individually with a dot, underscore, and the one-based index of the element. An example is shown in Listing 3.4: val pair = (99, "Luftballons") println(pair._1) println(pair._2) Listing 3.4· Creating and using a tuple. In the first line of Listing 3.4, you create a new tuple that contains the integer 99, as its first element, and the string, "Luftballons", as its second element. Scala infers the type of the tuple to be Tuple2[Int, String], and gives that type to the variable pair as well. In the second line, you access the _1 field, which will produce the first element, 99. The “.” in the second line is the same dot you’d use to access a field or invoke a method. In this case you are accessing a field named _1. If you run this script, you’ll see: 99 Luftballons The actual type of a tuple depends on the number of elements it contains and the types of those elements. Thus, the type of (99, "Luftballons") is Tuple2[Int, String]. The type of ('u', 'r', "the", 1, 4, "me") is Tuple6[Char, Char, String, Int, Int, String].5 5Although conceptually you could create tuples of any length, currently the Scala library only defines them up to Tuple22. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 10 Chapter 3 · Next Steps in Scala 91 Accessing the elements of a tuple You may be wondering why you can’t access the elements of a tuple like the elements of a list, for example, with “pair(0)”. The reason is that a list’s apply method always returns the same type, but each element of a tuple may be a different type: _1 can have one result type, _2 another, and so on. These _N numbers are one-based, instead of zero-based, because starting with 1 is a tradition set by other languages with statically typed tuples, such as Haskell and ML. Step 10. Use sets and maps Because Scala aims to help you take advantage of both functional and im- perative styles, its collections libraries make a point to differentiate between mutable and immutable collections. For example, arrays are always muta- ble; lists are always immutable. Scala also provides mutable and immutable alternatives for sets and maps, but uses the same simple names for both ver- sions. For sets and maps, Scala models mutability in the class hierarchy. For example, the Scala API contains a base trait for sets, where a trait is similar to a Java interface. (You’ll find out more about traits in Chapter 12.) Scala then provides two subtraits, one for mutable sets and another for im- mutable sets. As you can see in Figure 3.2, these three traits all share the same simple name, Set. Their fully qualified names differ, however, because each resides in a different package. Concrete set classes in the Scala API, such as the HashSet classes shown in Figure 3.2, extend either the mutable or immutable Set trait. (Although in Java you “implement” interfaces, in Scala you “extend” or “mix in” traits.) Thus, if you want to use a HashSet, you can choose between mutable and immutable varieties depending upon your needs. The default way to create a set is shown in Listing 3.5: var jetSet = Set("Boeing", "Airbus") jetSet += "Lear" println(jetSet.contains("Cessna")) Listing 3.5· Creating, initializing, and using an immutable set. In the first line of code in Listing 3.5, you define a new var named Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 10 Chapter 3 · Next Steps in Scala 92 scala.collection.immutable Set «trait» scala.collection.mutable Set «trait» scala.collection Set «trait» scala.collection.immutable HashSet scala.collection.mutable HashSet Figure 3.2· Class hierarchy for Scala sets. jetSet, and initialize it with an immutable set containing the two strings, "Boeing" and "Airbus". As this example shows, you can create sets in Scala similarly to how you create lists and arrays: by invoking a factory method named apply on a Set companion object. In Listing 3.5, you invoke apply on the companion object for scala.collection.immutable.Set, which returns an instance of a default, immutable Set. The Scala compiler infers jetSet’s type to be the immutable Set[String]. To add a new element to a set, you call + on the set, passing in the new el- ement. Both mutable and immutable sets offer a + method, but their behavior differs. Whereas a mutable set will add the element to itself, an immutable set will create and return a new set with the element added. In Listing 3.5, you’re working with an immutable set, thus the + invocation will yield a brand new set. Although mutable sets offer an actual += method, immutable sets do not. In this case, the second line of code, “jetSet += "Lear"”, is essentially a shorthand for: jetSet = jetSet + "Lear" Thus, in the second line of Listing 3.5, you reassign the jetSet var with a new set containing "Boeing", "Airbus", and "Lear". Finally, the last line Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 10 Chapter 3 · Next Steps in Scala 93 of Listing 3.5 prints out whether or not the set contains the string "Cessna". (As you’d expect, it prints false.) If you want a mutable set, you’ll need to use an import, as shown in Listing 3.6: import scala.collection.mutable.Set val movieSet = Set("Hitch", "Poltergeist") movieSet += "Shrek" println(movieSet) Listing 3.6· Creating, initializing, and using a mutable set. In the first line of Listing 3.6 you import the mutable Set. As with Java, an import statement allows you to use a simple name, such as Set, instead of the longer, fully qualified name. As a result, when you say Set on the third line, the compiler knows you mean scala.collection.mutable.Set. On that line, you initialize movieSet with a new mutable set that contains the strings "Hitch" and "Poltergeist". The subsequent line adds "Shrek" to the mutable set by calling the += method on the set, passing in the string "Shrek". As mentioned previously, += is an actual method defined on mu- table sets. Had you wanted to, instead of writing movieSet += "Shrek", therefore, you could have written movieSet.+=("Shrek").6 Although the default set implementations produced by the mutable and immutable Set factory methods shown thus far will likely be sufficient for most situations, occasionally you may want an explicit set class. Fortunately, the syntax is similar. Simply import that class you need, and use the factory method on its companion object. For example, if you need an immutable HashSet, you could do this: import scala.collection.immutable.HashSet val hashSet = HashSet("Tomatoes", "Chilies") println(hashSet + "Coriander") Another useful collection class in Scala is Map. As with sets, Scala pro- vides mutable and immutable versions of Map, using a class hierarchy. As 6Because the set in Listing 3.6 is mutable, there is no need to reassign movieSet, which is why it can be a val. By contrast, using += with the immutable set in Listing 3.5 required reassigning jetSet, which is why it must be a var. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 10 Chapter 3 · Next Steps in Scala 94 scala.collection.immutable Map «trait» scala.collection.mutable Map «trait» scala.collection Map «trait» scala.collection.immutable HashMap scala.collection.mutable HashMap Figure 3.3· Class hierarchy for Scala maps. you can see in Figure 3.3, the class hierarchy for maps looks a lot like the one for sets. There’s a base Map trait in package scala.collection, and two subtrait Maps: a mutable Map in scala.collection.mutable and an immutable one in scala.collection.immutable. Implementations of Map, such as the HashMaps shown in the class hier- archy in Figure 3.3, extend either the mutable or immutable trait. You can create and initialize maps using factory methods similar to those used for arrays, lists, and sets. For example, Listing 3.7 shows a mutable map in action. import scala.collection.mutable.Map val treasureMap = Map[Int, String]() treasureMap += (1 -> "Go to island.") treasureMap += (2 -> "Find big X on ground.") treasureMap += (3 -> "Dig.") println(treasureMap(2)) Listing 3.7· Creating, initializing, and using a mutable map. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 10 Chapter 3 · Next Steps in Scala 95 On the first line of Listing 3.7, you import the mutable Map. You then de- fine a val named treasureMap and initialize it with an empty mutable Map that has integer keys and string values. The map is empty because you pass nothing to the factory method (the parentheses in “Map[Int, String]()” are empty).7 On the next three lines you add key/value pairs to the map using the -> and += methods. As illustrated previously, the Scala compiler transforms a binary operation expression like 1 -> "Go to island." into (1).->("Go to island."). Thus, when you say 1 -> "Go to island.", you are actually calling a method named -> on an integer with the value 1, passing in a string with the value "Go to island." This -> method, which you can invoke on any object in a Scala program, returns a two-element tuple containing the key and value.8 You then pass this tuple to the += method of the map object to which treasureMap refers. Finally, the last line prints the value that corresponds to the key 2 in the treasureMap. If you run this code, it will print: Find big X on ground. If you prefer an immutable map, no import is necessary, as immutable is the default map. An example is shown in Listing 3.8: val romanNumeral = Map( 1 -> "I", 2 -> "II", 3 -> "III", 4 -> "IV", 5 -> "V" ) println(romanNumeral(4)) Listing 3.8· Creating, initializing, and using an immutable map. Given there are no imports, when you say Map in the first line of List- ing 3.8, you’ll get the default: a scala.collection.immutable.Map. You pass five key/value tuples to the map’s factory method, which returns an im- mutable Map containing the passed key/value pairs. If you run the code in Listing 3.8 it will print “IV”. 7The explicit type parameterization, “[Int, String]”, is required in Listing 3.7 because without any values passed to the factory method, the compiler is unable to infer the map’s type parameters. By contrast, the compiler can infer the type parameters from the values passed to the map factory shown in Listing 3.8, thus no explicit type parameters are needed. 8The Scala mechanism that allows you to invoke -> on any object, implicit conversion, will be covered in Chapter 21. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 11 Chapter 3 · Next Steps in Scala 96 Step 11. Learn to recognize the functional style As mentioned in Chapter 1, Scala allows you to program in an imperative style, but encourages you to adopt a more functional style. If you are coming to Scala from an imperative background—for example, if you are a Java programmer—one of the main challenges you may face when learning Scala is figuring out how to program in the functional style. We realize this style might be unfamiliar at first, and in this book we try hard to guide you through the transition. It will require some work on your part, and we encourage you to make the effort. If you come from an imperative background, we believe that learning to program in a functional style will not only make you a better Scala programmer, it will expand your horizons and make you a better programmer in general. The first step is to recognize the difference between the two styles in code. One telltale sign is that if code contains any vars, it is probably in an imperative style. If the code contains no vars at all—i.e., it contains only vals—it is probably in a functional style. One way to move towards a functional style, therefore, is to try to program without vars. If you’re coming from an imperative background, such as Java, C++, or C#, you may think of var as a regular variable and val as a special kind of variable. On the other hand, if you’re coming from a functional background, such as Haskell, OCaml, or Erlang, you might think of val as a regular vari- able and var as akin to blasphemy. The Scala perspective, however, is that val and var are just two different tools in your toolbox, both useful, neither inherently evil. Scala encourages you to lean towards vals, but ultimately reach for the best tool given the job at hand. Even if you agree with this bal- anced philosophy, however, you may still find it challenging at first to figure out how to get rid of vars in your code. Consider the following while loop example, adapted from Chapter 2, which uses a var and is therefore in the imperative style: def printArgs(args: Array[String]): Unit = { var i = 0 while (i < args.length) { println(args(i)) i += 1 } } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 11 Chapter 3 · Next Steps in Scala 97 You can transform this bit of code into a more functional style by getting rid of the var, for example, like this: def printArgs(args: Array[String]): Unit = { for (arg <- args) println(arg) } or this: def printArgs(args: Array[String]): Unit = { args.foreach(println) } This example illustrates one benefit of programming with fewer vars. The refactored (more functional) code is clearer, more concise, and less error-prone than the original (more imperative) code. The reason Scala en- courages a functional style, in fact, is that the functional style can help you write more understandable, less error-prone code. You can go even further, though. The refactored printArgs method is not purely functional, because it has side effects—in this case, its side effect is printing to the standard output stream. The telltale sign of a function with side effects is that its result type is Unit. If a function isn’t returning any interesting value, which is what a result type of Unit means, the only way that function can make a difference in the world is through some kind of side effect. A more functional approach would be to define a method that formats the passed args for printing, but just returns the formatted string, as shown in Listing 3.9: def formatArgs(args: Array[String]) = args.mkString("\n") Listing 3.9· A function without side effects or vars. Now you’re really functional: no side effects or vars in sight. The mkString method, which you can call on any iterable collection (includ- ing arrays, lists, sets, and maps), returns a string consisting of the result of calling toString on each element, separated by the passed string. Thus if args contains three elements "zero", "one", and "two", formatArgs will return "zero\none\ntwo". Of course, this function doesn’t actually print Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 11 Chapter 3 · Next Steps in Scala 98 anything out like the printArgs methods did, but you can easily pass its result to println to accomplish that: println(formatArgs(args)) Every useful program is likely to have side effects of some form, be- cause otherwise it wouldn’t be able to provide value to the outside world. Preferring methods without side effects encourages you to design programs where side-effecting code is minimized. One benefit of this approach is that it can help make your programs easier to test. For example, to test any of the three printArgs methods shown earlier in this section, you’d need to redefine println, capture the output passed to it, and make sure it is what you expect. By contrast, you could test the formatArgs function simply by checking its result: val res = formatArgs(Array("zero", "one", "two")) assert(res == "zero\none\ntwo") Scala’s assert method checks the passed Boolean and if it is false, throws AssertionError. If the passed Boolean is true, assert just returns quietly. You’ll learn more about assertions and testing in Chapter 14. That said, bear in mind that neither vars nor side effects are inherently evil. Scala is not a pure functional language that forces you to program everything in the functional style. Scala is a hybrid imperative/functional language. You may find that in some situations an imperative style is a better fit for the problem at hand, and in such cases you should not hesitate to use it. To help you learn how to program without vars, however, we’ll show you many specific examples of code with vars and how to transform those vars to vals in Chapter 7. A balanced attitude for Scala programmers Prefer vals, immutable objects, and methods without side effects. Reach for them first. Use vars, mutable objects, and methods with side effects when you have a specific need and justification for them. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 12 Chapter 3 · Next Steps in Scala 99 Step 12. Read lines from a file Scripts that perform small, everyday tasks often need to process lines in files. In this section, you’ll build a script that reads lines from a file and prints them out prepended with the number of characters in each line. The first version is shown in Listing 3.10: import scala.io.Source if (args.length > 0){ for (line <- Source.fromFile(args(0)).getLines()) println(line.length +""+ line) } else Console.err.println("Please enter filename") Listing 3.10· Reading lines from a file. This script starts with an import of a class named Source from package scala.io. It then checks to see if at least one argument was specified on the command line. If so, the first argument is interpreted as a filename to open and process. The expression Source.fromFile(args(0)) attempts to open the specified file and returns a Source object, on which you call getLines. The getLines method returns an Iterator[String], which provides one line on each iteration, excluding the end-of-line character. The for expression iterates through these lines and prints for each the length of the line, a space, and the line itself. If there were no arguments supplied on the command line, the final else clause will print a message to the standard error stream. If you place this code in a file named countchars1.scala, and run it on itself with: $ scala countchars1.scala countchars1.scala You should see: 22 import scala.io.Source 0 22 if (args.length > 0) { 0 51 for (line <- Source.fromFile(args(0)).getLines()) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 12 Chapter 3 · Next Steps in Scala 100 35 println(line.length +" "+ line) 1 } 4 else 46 Console.err.println("Please enter filename") Although the script in its current form prints out the needed information, you may wish to line up the numbers, right adjusted, and add a pipe character, so that the output looks instead like: 22 | import scala.io.Source 0 | 22 | if (args.length > 0) { 0 | 51 | for (line <- Source.fromFile(args(0)).getLines()) 35 | println(line.length +" "+ line) 1 | } 4 | else 46 | Console.err.println("Please enter filename") To accomplish this, you can iterate through the lines twice. The first time through you’ll determine the maximum width required by any line’s charac- ter count. The second time through you’ll print the output, using the max- imum width calculated previously. Because you’ll be iterating through the lines twice, you may as well assign them to a variable: val lines = Source.fromFile(args(0)).getLines().toList The final toList is required because the getLines method returns an itera- tor. Once you’ve iterated through an iterator, it is spent. By transforming it into a list via the toList call, you gain the ability to iterate as many times as you wish, at the cost of storing all lines from the file in memory at once. The lines variable, therefore, references a list of strings that contains the contents of the file specified on the command line. Next, because you’ll be calculating the width of each line’s character count twice, once per iteration, you might factor that expression out into a small function, which calculates the character width of the passed string’s length: def widthOfLength(s: String) = s.length.toString.length With this function, you could calculate the maximum width like this: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Step 12 Chapter 3 · Next Steps in Scala 101 var maxWidth = 0 for (line <- lines) maxWidth = maxWidth.max(widthOfLength(line)) Here you iterate through each line with a for expression, calculate the char- acter width of that line’s length, and, if it is larger than the current maximum, assign it to maxWidth, a var that was initialized to 0. (The max method, which you can invoke on any Int, returns the greater of the value on which it was invoked and the value passed to it.) Alternatively, if you prefer to find the maximum without vars, you could first find the longest line like this: val longestLine = lines.reduceLeft( (a, b) => if (a.length > b.length) a else b ) The reduceLeft method applies the passed function to the first two elements in lines, then applies it to the result of the first application and the next element in lines, and so on, all the way through the list. On each such application, the result will be the longest line encountered so far, because the passed function, (a, b) => if (a.length > b.length) a else b, returns the longest of the two passed strings. “reduceLeft” will return the result of the last application of the function, which in this case will be the longest string element contained in lines. Given this result, you can calculate the maximum width by passing the longest line to widthOfLength: val maxWidth = widthOfLength(longestLine) All that remains is to print out the lines with proper formatting. You can do that like this: for (line <- lines) { val numSpaces = maxWidth - widthOfLength(line) val padding = ""* numSpaces println(padding + line.length +" | "+ line) } In this for expression, you once again iterate through the lines. For each line, you first calculate the number of spaces required before the line length and assign it to numSpaces. Then you create a string containing numSpaces Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Conclusion Chapter 3 · Next Steps in Scala 102 spaces with the expression ""* numSpaces. Finally, you print out the in- formation with the desired formatting. The entire script looks as shown in Listing 3.11: import scala.io.Source def widthOfLength(s: String) = s.length.toString.length if (args.length > 0){ val lines = Source.fromFile(args(0)).getLines().toList val longestLine = lines.reduceLeft( (a, b) => if (a.length > b.length) a else b ) val maxWidth = widthOfLength(longestLine) for (line <- lines) { val numSpaces = maxWidth - widthOfLength(line) val padding = ""* numSpaces println(padding + line.length +" | "+ line) } } else Console.err.println("Please enter filename") Listing 3.11· Printing formatted character counts for the lines of a file. Conclusion With the knowledge you’ve gained in this chapter, you should already be able to get started using Scala for small tasks, especially scripts. In future chapters, we will dive into more detail in these topics, and introduce other topics that weren’t even hinted at here. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 4 Classes and Objects You’ve already seen the basics of classes and objects in Scala in the previous two chapters. In this chapter, we’ll take you a bit deeper. You’ll learn more about classes, fields, and methods, and get an overview of semicolon infer- ence. You’ll learn more about singleton objects, including how to use them to write and run a Scala application. If you are familiar with Java, you’ll find the concepts in Scala are similar, but not exactly the same. So even if you’re a Java guru, it will pay to read on. 4.1 Classes, fields, and methods A class is a blueprint for objects. Once you define a class, you can create objects from the class blueprint with the keyword new. For example, given the class definition: class ChecksumAccumulator{ // class definition goes here } You can create ChecksumAccumulator objects with: new ChecksumAccumulator Inside a class definition, you place fields and methods, which are collectively called members. Fields, which you define with either val or var, are vari- ables that refer to objects. Methods, which you define with def, contain executable code. The fields hold the state, or data, of an object, whereas the methods use that data to do the computational work of the object. When you Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.1 Chapter 4 · Classes and Objects 104 instantiate a class, the runtime sets aside some memory to hold the image of that object’s state—i.e., the content of its variables. For example, if you defined a ChecksumAccumulator class and gave it a var field named sum: class ChecksumAccumulator { var sum = 0 } and you instantiated it twice with: val acc = new ChecksumAccumulator val csa = new ChecksumAccumulator The image of the objects in memory might look like: 0 sum acc sum csa Since sum, a field declared inside class ChecksumAccumulator, is a var, not a val, you can later reassign to sum a different Int value, like this: acc.sum =3 Now the picture would look like: 0 sum acc sum csa 3 One thing to notice about this picture is that there are two sum variables, one in the object referenced by acc and the other in the object referenced Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.1 Chapter 4 · Classes and Objects 105 by csa. Fields are also known as instance variables, because every instance gets its own set of the variables. Collectively, an object’s instance variables make up the memory image of the object. You can see this illustrated here not only in that you see two sum variables, but also that when you changed one, the other was unaffected. Another thing to note in this example is that you were able to mutate the object acc referred to, even though acc is a val. What you can’t do with acc (or csa), given that they are vals, not vars, is reassign a different object to them. For example, the following attempt would fail: // Won’t compile, because acc is a val acc = new ChecksumAccumulator What you can count on, therefore, is that acc will always refer to the same ChecksumAccumulator object with which you initialize it, but the fields contained inside that object might change over time. One important way to pursue robustness of an object is to ensure that the object’s state—the values of its instance variables—remains valid during its entire lifetime. The first step is to prevent outsiders from accessing the fields directly by making the fields private. Because private fields can only be accessed by methods defined in the same class, all the code that can update the state will be localized to the class. To declare a field private, you place a private access modifier in front of the field, like this: class ChecksumAccumulator { private var sum = 0 } Given this definition of ChecksumAccumulator, any attempt to access sum from the outside of the class would fail: val acc = new ChecksumAccumulator acc.sum = 5 // Won’t compile, because sum is private Note The way you make members public in Scala is by not explicitly specifying any access modifier. Put another way, where you’d say “public” in Java, you simply say nothing in Scala. Public is Scala’s default access level. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.1 Chapter 4 · Classes and Objects 106 Now that sum is private, the only code that can access sum is code defined inside the body of the class itself. Thus, ChecksumAccumulator won’t be of much use to anyone unless we define some methods in it: class ChecksumAccumulator { private var sum = 0 def add(b: Byte): Unit = { sum += b } def checksum(): Int = { return ~(sum & 0xFF) + 1 } } The ChecksumAccumulator now has two methods, add and checksum, both of which exhibit the basic form of a function definition, shown in Figure 2.1 on page 73. Any parameters to a method can be used inside the method. One im- portant characteristic of method parameters in Scala is that they are vals, not vars.1 If you attempt to reassign a parameter inside a method in Scala, therefore, it won’t compile: def add(b: Byte): Unit = { b = 1 // This won’t compile, because b is a val sum += b } Although add and checksum in this version of ChecksumAccumulator correctly implement the desired functionality, you can express them using a more concise style. First, the return at the end of the checksum method is superfluous and can be dropped. In the absence of any explicit return statement, a Scala method returns the last value computed by the method. The recommended style for methods is in fact to avoid having explicit, and especially multiple, return statements. Instead, think of each method as an expression that yields one value, which is returned. This philosophy will encourage you to make methods quite small, to factor larger methods 1The reason parameters are vals is that vals are easier to reason about. You needn’t look further to determine if a val is reassigned, as you must do with a var. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.1 Chapter 4 · Classes and Objects 107 into multiple smaller ones. On the other hand, design choices depend on the design context, and Scala makes it easy to write methods that have multiple, explicit returns if that’s what you desire. Because all checksum does is calculate a value, it does not need an ex- plicit return. Another shorthand for methods is that you can leave off the curly braces if a method computes only a single result expression. If the result expression is short, it can even be placed on the same line as the def itself. With these changes, class ChecksumAccumulator looks like this: class ChecksumAccumulator { private var sum = 0 def add(b: Byte): Unit = sum += b def checksum(): Int = ~(sum & 0xFF) + 1 } Methods with a result type of Unit, such as ChecksumAccumulator’s add method, are executed for their side effects. A side effect is generally defined as mutating state somewhere external to the method or performing an I/O action. In add’s case, for example, the side effect is that sum is reas- signed. Another way to express such methods is to leave off the result type and the equals sign, and enclose the body of the method in curly braces. In this form, the method looks like a procedure, a method that is executed only for its side effects. The add method in Listing 4.1 illustrates this style: // In file ChecksumAccumulator.scala class ChecksumAccumulator{ private var sum = 0 def add(b: Byte) { sum += b } def checksum(): Int = ~(sum & 0xFF) + 1 } Listing 4.1· Final version of class ChecksumAccumulator. One puzzler to watch out for is that whenever you leave off the equals sign before the body of a function, its result type will definitely be Unit. This is true no matter what the body contains, because the Scala compiler can convert any type to Unit. For example, if the last result of a method is a String, but the method’s result type is declared to be Unit, the String will be converted to Unit and its value lost. Here’s an example: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.2 Chapter 4 · Classes and Objects 108 scala> def f(): Unit = "this String gets lost" f: ()Unit In this example, the String is converted to Unit because Unit is the de- clared result type of function f. The Scala compiler treats a function defined in the procedure style, i.e., with curly braces but no equals sign, essentially the same as a function that explicitly declares its result type to be Unit: scala> def g() { "this String gets lost too" } g: ()Unit The puzzler occurs, therefore, if you intend to return a non-Unit value, but forget the equals sign. To get what you want, you’ll need to insert the missing equals sign: scala> def h() = { "this String gets returned!" } h: ()java.lang.String scala> h res0: java.lang.String = this String gets returned! 4.2 Semicolon inference In a Scala program, a semicolon at the end of a statement is usually optional. You can type one if you want but you don’t have to if the statement appears by itself on a single line. On the other hand, a semicolon is required if you write multiple statements on a single line: val s = "hello"; println(s) If you want to enter a statement that spans multiple lines, most of the time you can simply enter it and Scala will separate the statements in the correct place. For example, the following is treated as one four-line statement: if (x < 2) println("too small") else println("ok") Occasionally, however, Scala will split a statement into two parts against your wishes: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.3 Chapter 4 · Classes and Objects 109 x + y This parses as two statements x and +y. If you intend it to parse as one statement x + y, you can always wrap it in parentheses: (x + y) Alternatively, you can put the + at the end of a line. For just this reason, whenever you are chaining an infix operation such as +, it is a common Scala style to put the operators at the end of the line instead of the beginning: x + y + z The rules of semicolon inference The precise rules for statement separation are surprisingly simple for how well they work. In short, a line ending is treated as a semicolon unless one of the following conditions is true: 1. The line in question ends in a word that would not be legal as the end of a statement, such as a period or an infix operator. 2. The next line begins with a word that cannot start a statement. 3. The line ends while inside parentheses (...) or brackets [...], because these cannot contain multiple statements anyway. 4.3 Singleton objects As mentioned in Chapter 1, one way in which Scala is more object-oriented than Java is that classes in Scala cannot have static members. Instead, Scala has singleton objects. A singleton object definition looks like a class defi- nition, except instead of the keyword class you use the keyword object. Listing 4.2 shows an example. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.3 Chapter 4 · Classes and Objects 110 // In file ChecksumAccumulator.scala import scala.collection.mutable.Map object ChecksumAccumulator{ private val cache = Map[String, Int]() def calculate(s: String): Int = if (cache.contains(s)) cache(s) else { val acc = new ChecksumAccumulator for (c <- s) acc.add(c.toByte) val cs = acc.checksum() cache += (s -> cs) cs } } Listing 4.2· Companion object for class ChecksumAccumulator. The singleton object in this figure is named ChecksumAccumulator, the same name as the class in the previous example. When a singleton object shares the same name with a class, it is called that class’s companion object. You must define both the class and its companion object in the same source file. The class is called the companion class of the singleton object. A class and its companion object can access each other’s private members. The ChecksumAccumulator singleton object has one method, named calculate, which takes a String and calculates a checksum for the char- acters in the String. It also has one private field, cache, a mutable map in which previously calculated checksums are cached.2 The first line of the method, “if (cache.contains(s))”, checks the cache to see if the passed string is already contained as a key in the map. If so, it just returns the 2We used a cache here to show a singleton object with a field. A cache such as this is a performance optimization that trades off memory for computation time. In general, you would likely use such a cache only if you encountered a performance problem that the cache solves, and might use a weak map, such as WeakHashMap in scala.collection.jcl, so that entries in the cache could be garbage collected if memory becomes scarce. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.3 Chapter 4 · Classes and Objects 111 mapped value, cache(s). Otherwise, it executes the else clause, which cal- culates the checksum. The first line of the else clause defines a val named acc and initializes it with a new ChecksumAccumulator instance.3 The next line is a for expression, which cycles through each character in the passed string, converts the character to a Byte by invoking toByte on it, and passes that to the add method of the ChecksumAccumulator instances to which acc refers. After the for expression completes, the next line of the method invokes checksum on acc, which gets the checksum for the passed String, and stores it into a val named cs. In the next line, cache += (s -> cs), the passed string key is mapped to the integer checksum value, and this key- value pair is added to the cache map. The last expression of the method, cs, ensures the checksum is the result of the method. If you are a Java programmer, one way to think of singleton objects is as the home for any static methods you might have written in Java. You can invoke methods on singleton objects using a similar syntax: the name of the singleton object, a dot, and the name of the method. For example, you can invoke the calculate method of singleton object ChecksumAccumulator like this: ChecksumAccumulator.calculate("Every value is an object.") A singleton object is more than a holder of static methods, however. It is a first-class object. You can think of a singleton object’s name, therefore, as a “name tag” attached to the object: cache ChecksumAccumulator mutable map Defining a singleton object doesn’t define a type (at the Scala level of abstraction). Given just a definition of object ChecksumAccumulator, you can’t make a variable of type ChecksumAccumulator. Rather, the type named ChecksumAccumulator is defined by the singleton object’s com- panion class. However, singleton objects extend a superclass and can mix in traits. Given each singleton object is an instance of its superclasses and 3Because the keyword new is only used to instantiate classes, the new object created here is an instance of the ChecksumAccumulator class, not the singleton object of the same name. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.4 Chapter 4 · Classes and Objects 112 mixed-in traits, you can invoke its methods via these types, refer to it from variables of these types, and pass it to methods expecting these types. We’ll show some examples of singleton objects inheriting from classes and traits in Chapter 13. One difference between classes and singleton objects is that singleton objects cannot take parameters, whereas classes can. Because you can’t in- stantiate a singleton object with the new keyword, you have no way to pass parameters to it. Each singleton object is implemented as an instance of a synthetic class referenced from a static variable, so they have the same initialization semantics as Java statics.4 In particular, a singleton object is initialized the first time some code accesses it. A singleton object that does not share the same name with a companion class is called a standalone object. You can use standalone objects for many purposes, including collecting related utility methods together, or defining an entry point to a Scala application. This use case is shown in the next section. 4.4 A Scala application To run a Scala program, you must supply the name of a standalone singleton object with a main method that takes one parameter, an Array[String], and has a result type of Unit. Any standalone object with a main method of the proper signature can be used as the entry point into an application. An example is shown in Listing 4.3: // In file Summer.scala import ChecksumAccumulator.calculate object Summer{ def main(args: Array[String]){ for (arg <- args) println(arg +": "+ calculate(arg)) } } Listing 4.3· The Summer application. 4The name of the synthetic class is the object name plus a dollar sign. Thus the synthetic class for the singleton object named ChecksumAccumulator is ChecksumAccumulator$. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.4 Chapter 4 · Classes and Objects 113 The name of the singleton object in Listing 4.3 is Summer. Its main method has the proper signature, so you can use it as an application. The first statement in the file is an import of the calculate method defined in the ChecksumAccumulator object in the previous example. This import state- ment allows you to use the method’s simple name in the rest of the file.5 The body of the main method simply prints out each argument and the checksum for the argument, separated by a colon. Note Scala implicitly imports members of packages java.lang and scala, as well as the members of a singleton object named Predef, into every Scala source file. Predef, which resides in package scala, contains many useful methods. For example, when you say println in a Scala source file, you’re actually invoking println on Predef.(Predef.println turns around and invokes Console.println, which does the real work.) When you say assert, you’re invoking Predef.assert. To run the Summer application, place the code from Listing 4.3 into a file named Summer.scala. Because Summer uses ChecksumAccumulator, place the code for ChecksumAccumulator, both the class shown in List- ing 4.1 and its companion object shown in Listing 4.2, into a file named ChecksumAccumulator.scala. One difference between Scala and Java is that whereas Java requires you to put a public class in a file named after the class—for example, you’d put class SpeedRacer in file SpeedRacer.java—in Scala, you can name .scala files anything you want, no matter what Scala classes or code you put in them. In general in the case of non-scripts, however, it is recommended style to name files after the classes they contain as is done in Java, so that programmers can more easily locate classes by looking at file names. This is the approach we’ve taken with the two files in this example, Summer.scala and ChecksumAccumulator.scala. Neither ChecksumAccumulator.scala nor Summer.scala are scripts, because they end in a definition. A script, by contrast, must end in a re- sult expression. Thus if you try to run Summer.scala as a script, the Scala interpreter will complain that Summer.scala does not end in a result expres- sion (assuming of course you didn’t add any expression of your own after 5If you’re a Java programmer, you can think of this import as similar to the static im- port feature introduced in Java 5. One difference in Scala, however, is that you can import members from any object, not just singleton objects. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.4 Chapter 4 · Classes and Objects 114 the Summer object definition). Instead, you’ll need to actually compile these files with the Scala compiler, then run the resulting class files. One way to do this is to use scalac, which is the basic Scala compiler, like this: $ scalac ChecksumAccumulator.scala Summer.scala This compiles your source files, but there may be a perceptible delay before the compilation finishes. The reason is that every time the compiler starts up, it spends time scanning the contents of jar files and doing other initial work before it even looks at the fresh source files you submit to it. For this reason, the Scala distribution also includes a Scala compiler daemon called fsc (for fast Scala compiler). You use it like this: $ fsc ChecksumAccumulator.scala Summer.scala The first time you run fsc, it will create a local server daemon attached to a port on your computer. It will then send the list of files to compile to the daemon via the port, and the daemon will compile the files. The next time you run fsc, the daemon will already be running, so fsc will simply send the file list to the daemon, which will immediately compile the files. Using fsc, you only need to wait for the Java runtime to startup the first time. If you ever want to stop the fsc daemon, you can do so with fsc -shutdown. Running either of these scalac or fsc commands will produce Java class files that you can then run via the scala command, the same command you used to invoke the interpreter in previous examples. However, instead of giving it a filename with a .scala extension containing Scala code to interpret as you did in every previous example,6 in this case you’ll give it the name of a standalone object containing a main method of the proper signature. You can run the Summer application, therefore, by typing: $ scala Summer of love You will see checksums printed for the two command line arguments: of: -213 love: -182 6The actual mechanism that the scala program uses to “interpret” a Scala source file is that it compiles the Scala source code to Java bytecodes, loads them immediately via a class loader, and executes them. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.5 Chapter 4 · Classes and Objects 115 4.5 The Application trait Scala provides a trait, scala.Application, that can save you some finger typing. Although we haven’t yet covered everything you’ll need to under- stand exactly how this trait works, we figured you’d want to know about it now anyway. Listing 4.4 shows an example: import ChecksumAccumulator.calculate object FallWinterSpringSummer extends Application { for (season <- List("fall", "winter", "spring")) println(season +": "+ calculate(season)) } Listing 4.4· Using the Application trait. To use the trait, you first write “extends Application” after the name of your singleton object. Then instead of writing a main method, you place the code you would have put in the main method directly between the curly braces of the singleton object. That’s it. You can compile and run this appli- cation just like any other. The way this works is that trait Application declares a main method of the appropriate signature, which your singleton object inherits, making it usable as a Scala application. The code between the curly braces is collected into a primary constructor of the singleton object, and is executed when the class is initialized. Don’t worry if you don’t understand what all this means. It will be explained in later chapters, and in the meantime you can use the trait without fully understanding the details. Inheriting from Application is shorter than writing an explicit main method, but it also has some shortcomings. First, you can’t use this trait if you need to access command-line arguments, because the args array isn’t available. For example, because the Summer application uses command-line arguments, it must be written with an explicit main method, as shown in List- ing 4.3. Second, because of some restrictions in the JVM threading model, you need an explicit main method if your program is multi-threaded. Finally, some implementations of the JVM do not optimize the initialization code of an object which is executed by the Application trait. So you should in- herit from Application only when your program is relatively simple and single-threaded. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 4.6 Chapter 4 · Classes and Objects 116 4.6 Conclusion This chapter has given you the basics of classes and objects in Scala, and shown you how to compile and run applications. In the next chapter, you’ll learn about Scala’s basic types and how to use them. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 5 Basic Types and Operations Now that you’ve seen classes and objects in action, it’s a good time to look at Scala’s basic types and operations in more depth. If you’re familiar with Java, you’ll be glad to find that Java’s basic types and operators have the same meaning in Scala. However there are some interesting differences that will make this chapter worthwhile reading even if you’re an experienced Java developer. Because some of the aspects of Scala covered in this chapter are essentially the same in Java, we’ve inserted notes indicating what Java developers can safely skip, to expedite your progress. In this chapter, you’ll get an overview of Scala’s basic types, including Strings and the value types Int, Long, Short, Byte, Float, Double, Char, and Boolean. You’ll learn the operations you can perform on these types, including how operator precedence works in Scala expressions. You’ll also learn how implicit conversions can “enrich” variants of these basic types, giving you additional operations beyond those supported by Java. 5.1 Some basic types Several fundamental types of Scala, along with the ranges of values instances of these types may have, are shown in Table 5.1. Collectively, types Byte, Short, Int, Long, and Char are called integral types. The integral types plus Float and Double are called numeric types. Other than String, which resides in package java.lang, all of the types shown in Table 5.1 are members of package scala.1 For example, the full 1Packages, which were briefly described in Step 2 in Chapter 2, will be covered in depth in Chapter 13. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.2 Chapter 5 · Basic Types and Operations 118 Table 5.1 · Some basic types Value type Range Byte 8-bit signed two’s complement integer (-27 to 27 - 1, inclusive) Short 16-bit signed two’s complement integer (-215 to 215 - 1, inclusive) Int 32-bit signed two’s complement integer (-231 to 231 - 1, inclusive) Long 64-bit signed two’s complement integer (-263 to 263 - 1, inclusive) Char 16-bit unsigned Unicode character (0 to 216 - 1, inclusive) String a sequence of Chars Float 32-bit IEEE 754 single-precision float Double 64-bit IEEE 754 double-precision float Boolean true or false name of Int is scala.Int. However, given that all the members of package scala and java.lang are automatically imported into every Scala source file, you can just use the simple names (i.e., names like Boolean, Char, or String) everywhere. Savvy Java developers will note that Scala’s basic types have the exact same ranges as the corresponding types in Java. This enables the Scala com- piler to transform instances of Scala value types, such as Int or Double, down to Java primitive types in the bytecodes it produces. 5.2 Literals All of the basic types listed in Table 5.1 can be written with literals. A literal is a way to write a constant value directly in code. Fast track for Java programmers The syntax of most literals shown in this section are exactly the same as in Java, so if you’re a Java master, you can safely skip much of this section. The two differences you should read about are Scala’s literals for raw strings and symbols, which are described starting on page 122. Integer literals Integer literals for the types Int, Long, Short, and Byte come in three forms: decimal, hexadecimal, and octal. The way an integer literal begins Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.2 Chapter 5 · Basic Types and Operations 119 indicates the base of the number. If the number begins with a 0x or 0X, it is hexadecimal (base 16), and may contain 0 through 9 as well as upper or lowercase digits A through F. Some examples are: scala> val hex = 0x5 hex: Int = 5 scala> val hex2 = 0x00FF hex2: Int = 255 scala> val magic = 0xcafebabe magic: Int = -889275714 Note that the Scala shell always prints integer values in base 10, no mat- ter what literal form you may have used to initialize it. Thus the interpreter displays the value of the hex2 variable you initialized with literal 0x00FF as decimal 255. (Of course, you don’t need to take our word for it. A good way to start getting a feel for the language is to try these statements out in the interpreter as you read this chapter.) If the number begins with a zero, it is octal (base 8), and may, therefore, only contain digits 0 through 7. Some examples are: scala> val oct = 035 // (35 octal is 29 decimal) oct: Int = 29 scala> val nov = 0777 nov: Int = 511 scala> val dec = 0321 dec: Int = 209 If the number begins with a non-zero digit, and is otherwise undecorated, it is decimal (base 10). For example: scala> val dec1 = 31 dec1: Int = 31 scala> val dec2 = 255 dec2: Int = 255 scala> val dec3 = 20 dec3: Int = 20 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.2 Chapter 5 · Basic Types and Operations 120 If an integer literal ends in an L or l, it is a Long, otherwise it is an Int. Some examples of Long integer literals are: scala> val prog = 0XCAFEBABEL prog: Long = 3405691582 scala> val tower = 35L tower: Long = 35 scala> val of = 31l of: Long = 31 If an Int literal is assigned to a variable of type Short or Byte, the literal is treated as if it were a Short or Byte type so long as the literal value is within the valid range for that type. For example: scala> val little: Short = 367 little: Short = 367 scala> val littler: Byte = 38 littler: Byte = 38 Floating point literals Floating point literals are made up of decimal digits, optionally containing a decimal point, and optionally followed by an E or e and an exponent. Some examples of floating-point literals are: scala> val big = 1.2345 big: Double = 1.2345 scala> val bigger = 1.2345e1 bigger: Double = 12.345 scala> val biggerStill = 123E45 biggerStill: Double = 1.23E47 Note that the exponent portion means the power of 10 by which the other portion is multiplied. Thus, 1.2345e1 is 1.2345 times 101, which is 12.345. If a floating-point literal ends in an F or f, it is a Float, otherwise it is a Double. Optionally, a Double floating-point literal can end in D or d. Some examples of Float literals are: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.2 Chapter 5 · Basic Types and Operations 121 scala> val little = 1.2345F little: Float = 1.2345 scala> val littleBigger = 3e5f littleBigger: Float = 300000.0 That last value expressed as a Double could take these (and other) forms: scala> val anotherDouble = 3e5 anotherDouble: Double = 300000.0 scala> val yetAnother = 3e5D yetAnother: Double = 300000.0 Character literals Character literals are composed of any Unicode character between single quotes, such as: scala> val a = 'A' a: Char = A In addition to providing an explicit character between the single quotes, you can provide an octal or hex number for the character code point preceded by a backslash. The octal number must be between '\0' and '\377'. For example, the Unicode character code point for the letter A is 101 octal. Thus: scala> val c = '\101' c: Char = A A character literal can also be given as a general Unicode character consist- ing of four hex digits and preceded by a \u, as in: scala> val d = '\u0041' d: Char = A scala> val f = '\u0044' f: Char = D In fact, such Unicode characters can appear anywhere in a Scala program. For instance you could also write an identifier like this: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.2 Chapter 5 · Basic Types and Operations 122 Table 5.2 · Special character literal escape sequences Literal Meaning \n line feed (\u000A) \b backspace (\u0008) \t tab (\u0009) \f form feed (\u000C) \r carriage return (\u000D) \" double quote (\u0022) \' single quote (\u0027) \\ backslash (\u005C) scala> val B\u0041\u0044 = 1 BAD: Int = 1 This identifier is treated as identical to BAD, the result of expanding the two Unicode characters in the code above. In general, it is a bad idea to name identifiers like this, because it is hard to read. Rather, this syntax is intended to allow Scala source files that include non-ASCII Unicode characters to be represented in ASCII. Finally, there are also a few character literals represented by special es- cape sequences, shown in Table 5.2. For example: scala> val backslash = '\\' backslash: Char = \ String literals A string literal is composed of characters surrounded by double quotes: scala> val hello = "hello" hello: java.lang.String = hello The syntax of the characters within the quotes is the same as with character literals. For example: scala> val escapes = "\\\"\'" escapes: java.lang.String = \"' Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.2 Chapter 5 · Basic Types and Operations 123 Because this syntax is awkward for strings that contain a lot of escape sequences or strings that span multiple lines, Scala includes a special syntax for raw strings. You start and end a raw string with three double quotation marks in a row ("""). The interior of a raw string may contain any characters whatsoever, including newlines, quotation marks, and special characters, ex- cept of course three quotes in a row. For example, the following program prints out a message using a raw string: println("""Welcome to Ultamix 3000. Type "HELP" for help.""") Running this code does not produce quite what is desired, however: Welcome to Ultamix 3000. Type "HELP" for help. The issue is that the leading spaces before the second line are included in the string! To help with this common situation, you can call stripMargin on strings. To use this method, put a pipe character (|) at the front of each line, and then call stripMargin on the whole string: println("""|Welcome to Ultamix 3000. |Type "HELP" for help.""".stripMargin) Now the code behaves as desired: Welcome to Ultamix 3000. Type "HELP" for help. Symbol literals A symbol literal is written 'ident, where ident can be any alphanumeric identifier. Such literals are mapped to instances of the predefined class scala.Symbol. Specifically, the literal 'cymbal will be expanded by the compiler to a factory method invocation: Symbol("cymbal"). Symbol lit- erals are typically used in situations where you would use just an identifier in a dynamically typed language. For instance, you might want to define a method that updates a record in a database: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.2 Chapter 5 · Basic Types and Operations 124 scala> def updateRecordByName(r: Symbol, value: Any){ // code goes here } updateRecordByName: (Symbol,Any)Unit The method takes as parameters a symbol indicating the name of a record field and a value with which the field should be updated in the record. In a dynamically typed language, you could invoke this operation passing an undeclared field identifier to the method, but in Scala this would not compile: scala> updateRecordByName(favoriteAlbum, "OK Computer") :6: error: not found: value favoriteAlbum updateRecordByName(favoriteAlbum, "OK Computer") ˆ Instead, and almost as concisely, you can pass a symbol literal: scala> updateRecordByName('favoriteAlbum, "OK Computer") There is not much you can do with a symbol, except find out its name: scala> val s = 'aSymbol s: Symbol = 'aSymbol scala> s.name res20: String = aSymbol Another thing that’s noteworthy is that symbols are interned. If you write the same symbol literal twice, both expressions will refer to the exact same Symbol object. Boolean literals The Boolean type has two literals, true and false: scala> val bool = true bool: Boolean = true scala> val fool = false fool: Boolean = false That’s all there is to it. You are now literally2 an expert in Scala. 2figuratively speaking Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.3 Chapter 5 · Basic Types and Operations 125 5.3 Operators are methods Scala provides a rich set of operators for its basic types. As mentioned in previous chapters, these operators are actually just a nice syntax for ordinary method calls. For example, 1 + 2 really means the same thing as (1).+(2). In other words, class Int contains a method named + that takes an Int and returns an Int result. This + method is invoked when you add two Ints: scala> val sum = 1 + 2 // Scala invokes (1).+(2) sum: Int = 3 To prove this to yourself, you can write the expression explicitly as a method invocation: scala> val sumMore = (1).+(2) sumMore: Int = 3 In fact, Int contains several overloaded + methods that take different parameter types.3 For example, Int has another method, also named +, that takes and returns a Long. If you add a Long to an Int, this alternate + method will be invoked, as in: scala> val longSum = 1 + 2L // Scala invokes (1).+(2L) longSum: Long = 3 The + symbol is an operator—an infix operator to be specific. Operator notation is not limited to methods like + that look like operators in other languages. You can use any method in operator notation. For example, class String has a method, indexOf, that takes one Char parameter. The indexOf method searches the string for the first occurrence of the specified character, and returns its index or -1 if it doesn’t find the character. You can use indexOf as an operator, like this: scala> val s = "Hello, world!" s: java.lang.String = Hello, world! scala> s indexOf 'o' // Scala invokes s.indexOf(’o’) res0: Int = 4 3Overloaded methods have the same name but different argument types. More on method overloading in Section 6.11. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.3 Chapter 5 · Basic Types and Operations 126 In addition, String offers an overloaded indexOf method that takes two parameters, the character for which to search and an index at which to start. (The other indexOf method, shown previously, starts at index zero, the beginning of the String.) Even though this indexOf method takes two arguments, you can use it in operator notation. But whenever you call a method that takes multiple arguments using operator notation, you have to place those arguments in parentheses. For example, here’s how you use this other indexOf form as an operator (continuing from the previous example): scala> s indexOf ('o', 5) // Scala invokes s.indexOf(’o’, 5) res1: Int = 8 Any method can be an operator In Scala operators are not special language syntax: any method can be an operator. What makes a method an operator is how you use it. When you write “s.indexOf('o')”, indexOf is not an operator. But when you write “s indexOf 'o'”, indexOf is an operator, because you’re using it in operator notation. So far, you’ve seen examples of infix operator notation, which means the method to invoke sits between the object and the parameter or parameters you wish to pass to the method, as in “7 + 2”. Scala also has two other operator notations: prefix and postfix. In prefix notation, you put the method name before the object on which you are invoking the method, for example, the ‘-’ in -7. In postfix notation, you put the method after the object, for example, the “toLong” in “7 toLong”. In contrast to the infix operator notation—in which operators take two operands, one to the left and the other to the right—prefix and postfix oper- ators are unary: they take just one operand. In prefix notation, the operand is to the right of the operator. Some examples of prefix operators are -2.0, !found, and ~0xFF. As with the infix operators, these prefix operators are a shorthand way of invoking methods. In this case, however, the name of the method has “unary_” prepended to the operator character. For in- stance, Scala will transform the expression -2.0 into the method invoca- tion “(2.0).unary_-”. You can demonstrate this to yourself by typing the method call both via operator notation and explicitly: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.3 Chapter 5 · Basic Types and Operations 127 scala> -2.0 // Scala invokes (2.0).unary_- res2: Double = -2.0 scala> (2.0).unary_- res3: Double = -2.0 The only identifiers that can be used as prefix operators are +, -, !, and ~. Thus, if you define a method named unary_!, you could invoke that method on a value or variable of the appropriate type using prefix operator notation, such as !p. But if you define a method named unary_*, you wouldn’t be able to use prefix operator notation, because * isn’t one of the four identifiers that can be used as prefix operators. You could invoke the method normally, as in p.unary_*, but if you attempted to invoke it via *p, Scala will parse it as if you’d written *.p, which is probably not what you had in mind!4 Postfix operators are methods that take no arguments, when they are in- voked without a dot or parentheses. In Scala, you can leave off empty paren- theses on method calls. The convention is that you include parentheses if the method has side effects, such as println(), but you can leave them off if the method has no side effects, such as toLowerCase invoked on a String: scala> val s = "Hello, world!" s: java.lang.String = Hello, world! scala> s.toLowerCase res4: java.lang.String = hello, world! In this latter case of a method that requires no arguments, you can alterna- tively leave off the dot and use postfix operator notation: scala> s toLowerCase res5: java.lang.String = hello, world! In this case, toLowerCase is used as a postfix operator on the operand s. To see what operators you can use with Scala’s basic types, therefore, all you really need to do is look at the methods declared in the type’s classes in the Scala API documentation. Given that this is a Scala tutorial, however, we’ll give you a quick tour of most of these methods in the next few sections. 4All is not necessarily lost, however. There is an extremely slight chance your program with the *p might compile as C++. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.4 Chapter 5 · Basic Types and Operations 128 Fast track for Java programmers Many aspects of Scala described in the remainder of this chapter are the same as in Java. If you’re a Java guru in a rush, you can safely skip to Section 5.7 on page 132, which describes how Scala differs from Java in the area of object equality. 5.4 Arithmetic operations You can invoke arithmetic methods via infix operator notation for addition (+), subtraction (-), multiplication (*), division (/), and remainder (%), on any numeric type. Here are some examples: scala> 1.2 + 2.3 res6: Double = 3.5 scala> 3 - 1 res7: Int = 2 scala> 'b' - 'a' res8: Int = 1 scala> 2L * 3L res9: Long = 6 scala> 11 / 4 res10: Int = 2 scala> 11 % 4 res11: Int = 3 scala> 11.0f / 4.0f res12: Float = 2.75 scala> 11.0 % 4.0 res13: Double = 3.0 When both the left and right operands are integral types (Int, Long, Byte, Short, or Char), the / operator will tell you the whole number por- tion of the quotient, excluding any remainder. The % operator indicates the remainder of an implied integer division. The floating-point remainder you get with % is not the one defined by the IEEE 754 standard. The IEEE 754 remainder uses rounding division, not truncating division, in calculating the remainder, so it is quite different from Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.5 Chapter 5 · Basic Types and Operations 129 the integer remainder operation. If you really want an IEEE 754 remainder, you can call IEEEremainder on scala.math, as in: scala> math.IEEEremainder(11.0, 4.0) res14: Double = -1.0 The numeric types also offer unary prefix operators + (method unary_+) and - (method unary_-), which allow you to indicate a literal number is positive or negative, as in -3 or +4.0. If you don’t specify a unary + or -, a literal number is interpreted as positive. Unary + exists solely for symmetry with unary -, but has no effect. The unary - can also be used to negate a variable. Here are some examples: scala> val neg = 1 + -3 neg: Int = -2 scala> val y = +3 y: Int = 3 scala> -neg res15: Int = 2 5.5 Relational and logical operations You can compare numeric types with relational methods greater than (>), less than (<), greater than or equal to (>=), and less than or equal to (<=), which yield a Boolean result. In addition, you can use the unary ‘!’ operator (the unary_! method) to invert a Boolean value. Here are a few examples: scala> 1 > 2 res16: Boolean = false scala> 1 < 2 res17: Boolean = true scala> 1.0 <= 1.0 res18: Boolean = true scala> 3.5f >= 3.6f res19: Boolean = false Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.5 Chapter 5 · Basic Types and Operations 130 scala> 'a' >= 'A' res20: Boolean = true scala> val thisIsBoring = !true thisIsBoring: Boolean = false scala> !thisIsBoring res21: Boolean = true The logical methods, logical-and (&&) and logical-or (||), take Boolean operands in infix notation and yield a Boolean result. For example: scala> val toBe = true toBe: Boolean = true scala> val question = toBe || !toBe question: Boolean = true scala> val paradox = toBe && !toBe paradox: Boolean = false The logical-and and logical-or operations are short-circuited as in Java: expressions built from these operators are only evaluated as far as needed to determine the result. In other words, the right-hand side of logical-and and logical-or expressions won’t be evaluated if the left-hand side determines the result. For example, if the left-hand side of a logical-and expression evaluates to false, the result of the expression will definitely be false, so the right-hand side is not evaluated. Likewise, if the left-hand side of a logical-or expression evaluates to true, the result of the expression will definitely be true, so the right-hand side is not evaluated. For example: scala> def salt() = { println("salt"); false } salt: ()Boolean scala> def pepper() = { println("pepper"); true } pepper: ()Boolean scala> pepper() && salt() pepper salt res22: Boolean = false Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.6 Chapter 5 · Basic Types and Operations 131 scala> salt() && pepper() salt res23: Boolean = false In the first expression, pepper and salt are invoked, but in the second, only salt is invoked. Given salt returns false, there’s no need to call pepper. Note You may be wondering how short-circuiting can work given operators are just methods. Normally, all arguments are evaluated before entering a method, so how can a method avoid evaluating its second argument? The answer is that all Scala methods have a facility for delaying the evaluation of their arguments, or even declining to evaluate them at all. The facility is called by-name parameters and is discussed in Section 9.5. 5.6 Bitwise operations Scala enables you to perform operations on individual bits of integer types with several bitwise methods. The bitwise methods are: bitwise-and (&), bitwise-or (|), and bitwise-xor (ˆ).5 The unary bitwise complement operator (~, the method unary_~), inverts each bit in its operand. For example: scala> 1 & 2 res24: Int = 0 scala> 1 | 2 res25: Int = 3 scala> 1 ˆ 3 res26: Int = 2 scala> ~1 res27: Int = -2 The first expression, 1 & 2, bitwise-ands each bit in 1 (0001) and 2 (0010), which yields 0 (0000). The second expression, 1 | 2, bitwise-ors each bit in 5The bitwise-xor method performs an exclusive or on its operands. Identical bits yield a 0. Different bits yield a 1. Thus 0011 ˆ 0101 yields 0110. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.7 Chapter 5 · Basic Types and Operations 132 the same operands, yielding 3 (0011). The third expression, 1 ˆ 3, bitwise- xors each bit in 1 (0001) and 3 (0011), yielding 2 (0010). The final expres- sion, ~1, inverts each bit in 1 (0001), yielding -2, which in binary looks like 11111111111111111111111111111110. Scala integer types also offer three shift methods: shift left (<<), shift right (>>), and unsigned shift right (>>>). The shift methods, when used in infix operator notation, shift the integer value on the left of the operator by the amount specified by the integer value on the right. Shift left and unsigned shift right fill with zeroes as they shift. Shift right fills with the highest bit (the sign bit) of the left-hand value as it shifts. Here are some examples: scala> -1 >> 31 res28: Int = -1 scala> -1 >>> 31 res29: Int = 1 scala> 1 << 2 res30: Int = 4 -1 in binary is 11111111111111111111111111111111. In the first ex- ample, -1 >> 31, -1 is shifted to the right 31 bit positions. Since an Int consists of 32 bits, this operation effectively moves the leftmost bit over un- til it becomes the rightmost bit.6 Since the >> method fills with ones as it shifts right, because the leftmost bit of -1 is 1, the result is identical to the original left operand, 32 one bits, or -1. In the second example, -1 >>> 31, the leftmost bit is again shifted right until it is in the rightmost position, but this time filling with zeroes along the way. Thus the result this time is binary 00000000000000000000000000000001, or 1. In the final example, 1 << 2, the left operand, 1, is shifted left two positions (filling in with zeroes), re- sulting in binary 00000000000000000000000000000100, or 4. 5.7 Object equality If you want to compare two objects for equality, you can use either ==, or its inverse !=. Here are a few simple examples: 6The leftmost bit in an integer type is the sign bit. If the leftmost bit is 1, the number is negative. If 0, the number is positive. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.7 Chapter 5 · Basic Types and Operations 133 scala> 1 == 2 res31: Boolean = false scala> 1 != 2 res32: Boolean = true scala> 2 == 2 res33: Boolean = true These operations actually apply to all objects, not just basic types. For ex- ample, you can use == to compare lists: scala> List(1, 2, 3) == List(1, 2, 3) res34: Boolean = true scala> List(1, 2, 3) == List(4, 5, 6) res35: Boolean = false Going further, you can compare two objects that have different types: scala> 1 == 1.0 res36: Boolean = true scala> List(1, 2, 3) == "hello" res37: Boolean = false You can even compare against null, or against things that might be null. No exception will be thrown: scala> List(1, 2, 3) == null res38: Boolean = false scala> null == List(1, 2, 3) res39: Boolean = false As you see, == has been carefully crafted so that you get just the equality comparison you want in most cases. This is accomplished with a very simple rule: first check the left side for null, and if it is not null, call the equals method. Since equals is a method, the precise comparison you get depends on the type of the left-hand argument. Since there is an automatic null check, you do not have to do the check yourself.7 7The automatic check does not look at the right-hand side, but any reasonable equals method should return false if its argument is null. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.8 Chapter 5 · Basic Types and Operations 134 This kind of comparison will yield true on different objects, so long as their contents are the same and their equals method is written to be based on contents. For example, here is a comparison between two strings that happen to have the same five letters in them: scala> ("he"+"llo") == "hello" res40: Boolean = true How Scala’s == differs from Java’s In Java, you can use == to compare both primitive and reference types. On primitive types, Java’s == compares value equality, as in Scala. On reference types, however, Java’s == compares reference equality, which means the two variables point to the same object on the JVM’s heap. Scala provides a facility for comparing reference equality, as well, under the name eq. However, eq and its opposite, ne, only apply to objects that directly map to Java objects. The full details about eq and ne are given in Sections 11.1 and 11.2. Also, see Chapter 30 on how to write a good equals method. 5.8 Operator precedence and associativity Operator precedence determines which parts of an expression are evaluated before the other parts. For example, the expression 2 + 2 * 7 evaluates to 16, not 28, because the * operator has a higher precedence than the + operator. Thus the multiplication part of the expression is evaluated before the addition part. You can of course use parentheses in expressions to clarify evaluation order or to override precedence. For example, if you really wanted the result of the expression above to be 28, you could write the expression like this: (2 + 2) * 7 Given that Scala doesn’t have operators, per se, just a way to use meth- ods in operator notation, you may be wondering how operator precedence works. Scala decides precedence based on the first character of the methods used in operator notation (there’s one exception to this rule, which will be discussed below). If the method name starts with a *, for example, it will Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.8 Chapter 5 · Basic Types and Operations 135 have a higher precedence than a method that starts with a +. Thus 2 + 2 * 7 will be evaluated as 2 + (2 * 7), and a +++ b *** c (in which a, b, and c are variables, and +++ and *** are methods) will be evaluated a +++ (b *** c), because the *** method has a higher precedence than the +++ method. Table 5.3 · Operator precedence (all other special characters) * / % + - : = ! < > & ˆ | (all letters) (all assignment operators) Table 5.3 shows the precedence given to the first character of a method in decreasing order of precedence, with characters on the same line having the same precedence. The higher a character is in this table, the higher the precedence of methods that start with that character. Here’s an example that illustrates the influence of precedence: scala>2 << 2 + 2 res41: Int = 32 The << method starts with the character <, which appears lower in Ta- ble 5.3 than the character +, which is the first and only character of the + method. Thus << will have lower precedence than +, and the expression will be evaluated by first invoking the + method, then the << method, as in 2 << (2 + 2). 2 + 2 is 4, by our math, and 2 << 4 yields 32. Here’s another example: scala> 2 + 2 << 2 res42: Int = 16 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.8 Chapter 5 · Basic Types and Operations 136 Since the first characters are the same as in the previous example, the methods will be invoked in the same order. First the + method will be in- voked, then the << method. So 2 + 2 will again yield 4, and 4 << 2 is 16. The one exception to the precedence rule, alluded to above, concerns assignment operators, which end in an equals character. If an operator ends in an equals character (=), and the operator is not one of the comparison operators <=, >=, ==, or !=, then the precedence of the operator is the same as that of simple assignment (=). That is, it is lower than the precedence of any other operator. For instance: x *= y + 1 means the same as: x *= (y + 1) because *= is classified as an assignment operator whose precedence is lower than +, even though the operator’s first character is *, which would suggest a precedence higher than +. When multiple operators of the same precedence appear side by side in an expression, the associativity of the operators determines the way operators are grouped. The associativity of an operator in Scala is determined by its last character. As mentioned on page 87 of Chapter 3, any method that ends in a ‘:’ character is invoked on its right operand, passing in the left operand. Methods that end in any other character are the other way around. They are invoked on their left operand, passing in the right operand. So a * b yields a.*(b), but a ::: b yields b.:::(a). No matter what associativity an operator has, however, its operands are always evaluated left to right. So if a is an expression that is not just a simple reference to an immutable value, then a ::: b is more precisely treated as the following block: { val x = a; b.:::(x) } In this block a is still evaluated before b, and then the result of this evaluation is passed as an operand to b’s ::: method. This associativity rule also plays a role when multiple operators of the same precedence appear side by side. If the methods end in ‘:’, they are grouped right to left; otherwise, they are grouped left to right. For example, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.9 Chapter 5 · Basic Types and Operations 137 a ::: b ::: c is treated as a ::: (b ::: c). But a * b * c, by contrast, is treated as (a * b) * c. Operator precedence is part of the Scala language. You needn’t be afraid to use it. Nevertheless, it is good style to use parentheses to clarify what operators are operating upon what expressions. Perhaps the only precedence you can truly count on other programmers knowing without looking up is that multiplicative operators, *, /, and %, have a higher precedence than the additive ones + and -. Thus even if a + b << c yields the result you want without parentheses, the extra clarity you get by writing (a + b) << c may reduce the frequency with which your peers utter your name in operator notation, for example, by shouting in disgust, “bills !*&ˆ%~ code!”.8 5.9 Rich wrappers You can invoke many more methods on Scala’s basic types than were de- scribed in the previous sections. A few examples are shown in Table 5.4. These methods are available via implicit conversions, a technique that will be described in detail in Chapter 21. All you need to know for now is that for each basic type described in this chapter, there is also a “rich wrapper” that provides several additional methods. To see all the available methods on the basic types, therefore, you should look at the API documentation on the rich wrapper for each basic type. Those classes are listed in Table 5.5. 5.10 Conclusion The main take-aways from this chapter are that operators in Scala are method calls, and that implicit conversions to rich variants exist for Scala’s basic types that add even more useful methods. In the next chapter, we’ll show you what it means to design objects in a functional style that gives new im- plementations of some of the operators that you have seen in this chapter. 8By now you should be able to figure out that given this code, the Scala compiler would invoke (bills.!*&ˆ%~(code)).!(). Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 5.10 Chapter 5 · Basic Types and Operations 138 Table 5.4 · Some rich operations Code Result 0 max5 5 0 min 5 0 -2.7 abs 2.7 -2.7 round -3L 1.5 isInfinity false (1.0 / 0) isInfinity true 4 to 6 Range(4, 5, 6) "bob" capitalize "Bob" "robert" drop 2 "bert" Table 5.5· Rich wrapper classes Basic type Rich wrapper Byte scala.runtime.RichByte Short scala.runtime.RichShort Int scala.runtime.RichInt Char scala.runtime.RichChar Float scala.runtime.RichFloat Double scala.runtime.RichDouble Boolean scala.runtime.RichBoolean String scala.collection.immutable.StringOps Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 6 Functional Objects With the understanding of Scala basics you gained in previous chapters, you’re ready to see how to design more full-featured classes in Scala. The emphasis in this chapter is on classes that define functional objects, that is, objects that do not have any mutable state. As a running example, we’ll create several variants of a class that models rational numbers as immutable objects. Along the way, we’ll show you more aspects of object-oriented programming in Scala: class parameters and constructors, methods and op- erators, private members, overriding, checking preconditions, overloading, and self references. 6.1 A specification for class Rational A rational number is a number that can be expressed as a ratio n d , where n and d are integers, except that d cannot be zero. n is called the numerator and d the denominator. Examples of rational numbers are 1 2, 2 3 , 112 239, and 2 1. Compared to floating-point numbers, rational numbers have the advantage that fractions are represented exactly, without rounding or approximation. The class we’ll design in this chapter must model the behavior of rational numbers, including allowing them to be added, subtracted, multiplied, and divided. To add two rationals, you must first obtain a common denominator, then add the two numerators. For example, to add 1 2 + 2 3 , you multiply both parts of the left operand by 3 and both parts of the right operand by 2, which gives you 3 6 + 4 6 . Adding the two numerators yields the result, 7 6 . To mul- tiply two rational numbers, you can simply multiply their numerators and multiply their denominators. Thus, 1 2 ∗ 2 5 gives 2 10 , which can be represented Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.2 Chapter 6 · Functional Objects 140 more compactly in its “normalized” form as 1 5. You divide by swapping the numerator and denominator of the right operand and then multiplying. For instance 1 2/3 5 is the same as 1 2 ∗ 5 3 , or 5 6 . One, maybe rather trivial, observation is that in mathematics, rational numbers do not have mutable state. You can add one rational number to another, but the result will be a new rational number. The original num- bers will not have “changed.” The immutable Rational class we’ll design in this chapter will have the same property. Each rational number will be represented by one Rational object. When you add two Rational objects, you’ll create a new Rational object to hold the sum. This chapter will give you a glimpse of some of the ways Scala enables you to write libraries that feel like native language support. For example, at the end of this chapter you’ll be able to do this with class Rational: scala> val oneHalf = new Rational(1, 2) oneHalf: Rational = 1/2 scala> val twoThirds = new Rational(2, 3) twoThirds: Rational = 2/3 scala> (oneHalf / 7) + (1 - twoThirds) res0: Rational = 17/42 6.2 Constructing a Rational A good place to start designing class Rational is to consider how client programmers will create a new Rational object. Given we’ve decided to make Rational objects immutable, we’ll require that clients provide all data needed by an instance (in this case, a numerator and a denominator) when they construct the instance. Thus, we will start the design with this: class Rational(n: Int, d: Int) One of the first things to note about this line of code is that if a class doesn’t have a body, you don’t need to specify empty curly braces (though you could, of course, if you wanted to). The identifiers n and d in the parentheses after the class name, Rational, are called class parameters. The Scala compiler will gather up these two class parameters and create a primary constructor that takes the same two parameters. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.2 Chapter 6 · Functional Objects 141 Immutable object trade-offs Immutable objects offer several advantages over mutable objects, and one potential disadvantage. First, immutable objects are often easier to reason about than mutable ones, because they do not have complex state spaces that change over time. Second, you can pass immutable objects around quite freely, whereas you may need to make defensive copies of mutable objects before passing them to other code. Third, there is no way for two threads concurrently accessing an immutable to corrupt its state once it has been properly constructed, because no thread can change the state of an immutable. Fourth, immutable objects make safe hash table keys. If a mutable object is mutated after it is placed into a HashSet, for example, that object may not be found the next time you look into the HashSet. The main disadvantage of immutable objects is that they sometimes require that a large object graph be copied where otherwise an update could be done in place. In some cases this can be awkward to express and might also cause a performance bottleneck. As a result, it is not uncommon for libraries to provide mutable alternatives to immutable classes. For example, class StringBuilder is a mutable alternative to the immutable String. We’ll give you more information on designing mutable objects in Scala in Chapter 18. Note This initial Rational example highlights a difference between Java and Scala. In Java, classes have constructors, which can take parameters, whereas in Scala, classes can take parameters directly. The Scala notation is more concise—class parameters can be used directly in the body of the class; there’s no need to define fields and write assignments that copy constructor parameters into fields. This can yield substantial savings in boilerplate code, especially for small classes. The Scala compiler will compile any code you place in the class body, which isn’t part of a field or a method definition, into the primary constructor. For example, you could print a debug message like this: class Rational(n: Int, d: Int){ println("Created "+ n +"/"+ d) } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.3 Chapter 6 · Functional Objects 142 Given this code, the Scala compiler would place the call to println into Rational’s primary constructor. The println call will, therefore, print its debug message whenever you create a new Rational instance: scala> new Rational(1, 2) Created 1/2 res0: Rational = Rational@90110a 6.3 Reimplementing the toString method When we created an instance of Rational in the previous example, the in- terpreter printed “Rational@90110a”. The interpreter obtained this some- what funny looking string by calling toString on the Rational object. By default, class Rational inherits the implementation of toString defined in class java.lang.Object, which just prints the class name, an @ sign, and a hexadecimal number. The result of toString is primarily intended to help programmers by providing information that can be used in debug print statements, log messages, test failure reports, and interpreter and de- bugger output. The result currently provided by toString is not especially helpful, because it doesn’t give any clue about the rational number’s value. A more useful implementation of toString would print out the values of the Rational’s numerator and denominator. You can override the default implementation by adding a method toString to class Rational, like this: class Rational(n: Int, d: Int){ override def toString = n +"/"+ d } The override modifier in front of a method definition signals that a previous method definition is overridden; more on this in Chapter 10. Since Rational numbers will display nicely now, we removed the debug println statement we put into the body of previous version of class Rational. You can test the new behavior of Rational in the interpreter: scala> val x = new Rational(1, 3) x: Rational = 1/3 scala> val y = new Rational(5, 7) y: Rational = 5/7 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.4 Chapter 6 · Functional Objects 143 6.4 Checking preconditions As a next step, we will turn our attention to a problem with the current behav- ior of the primary constructor. As mentioned at the beginning of this chapter, rational numbers may not have a zero in the denominator. Currently, how- ever, the primary constructor accepts a zero passed as d: scala> new Rational(5, 0) res1: Rational = 5/0 One of the benefits of object-oriented programming is that it allows you to encapsulate data inside objects so that you can ensure the data is valid throughout its lifetime. In the case of an immutable object such as Rational, this means that you should ensure the data is valid when the object is con- structed. Given that a zero denominator is an invalid state for a Rational number, you should not let a Rational be constructed if a zero is passed in the d parameter. The best way to approach this problem is to define as a precondition of the primary constructor that d must be non-zero. A precondition is a con- straint on values passed into a method or constructor, a requirement which callers must fulfill. One way to do that is to use require,1 like this: class Rational(n: Int, d: Int){ require(d != 0) override def toString = n +"/"+ d } The require method takes one boolean parameter. If the passed value is true, require will return normally. Otherwise, require will prevent the ob- ject from being constructed by throwing an IllegalArgumentException. 6.5 Adding fields Now that the primary constructor is properly enforcing its precondition, we will turn our attention to supporting addition. To do so, we’ll define a public add method on class Rational that takes another Rational as a parame- ter. To keep Rational immutable, the add method must not add the passed 1The require method is defined in standalone object, Predef. As mentioned in Sec- tion 4.4, Predef’s members are imported automatically into every Scala source file. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.5 Chapter 6 · Functional Objects 144 rational number to itself. Rather, it must create and return a new Rational that holds the sum. You might think you could write add this way: class Rational(n: Int, d: Int){// This won’t compile require(d != 0) override def toString = n +"/"+ d def add(that: Rational): Rational = new Rational(n * that.d + that.n * d, d * that.d) } However, given this code the compiler will complain: :11: error: value d is not a member of Rational new Rational(n * that.d + that.n * d, d * that.d) ˆ :11: error: value d is not a member of Rational new Rational(n * that.d + that.n * d, d * that.d) ˆ Although class parameters n and d are in scope in the code of your add method, you can only access their value on the object on which add was invoked. Thus, when you say n or d in add’s implementation, the compiler is happy to provide you with the values for these class parameters. But it won’t let you say that.n or that.d, because that does not refer to the Rational object on which add was invoked.2 To access the numerator and denominator on that, you’ll need to make them into fields. Listing 6.1 shows how you could add these fields to class Rational.3 In the version of Rational shown in Listing 6.1, we added two fields named numer and denom, and initialized them with the values of class pa- rameters n and d.4 We also changed the implementation of toString and add so that they use the fields, not the class parameters. This version of class Rational compiles. You can test it by adding some rational numbers: 2Actually, you could add a Rational to itself, in which case that would refer to the object on which add was invoked. But because you can pass any Rational object to add, the compiler still won’t let you say that.n. 3In Section 10.6 you’ll find out about parametric fields, which provide a shorthand for writing the same code. 4Even though n and d are used in the body of the class, given they are only used inside constructors, the Scala compiler will not emit fields for them. Thus, given this code the Scala compiler will generate a class with two Int fields, one for numer and one for denom. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.6 Chapter 6 · Functional Objects 145 class Rational(n: Int, d: Int){ require(d != 0) val numer: Int = n val denom: Int = d override def toString = numer +"/"+ denom def add(that: Rational): Rational = new Rational( numer * that.denom + that.numer * denom, denom * that.denom ) } Listing 6.1· Rational with fields. scala> val oneHalf = new Rational(1, 2) oneHalf: Rational = 1/2 scala> val twoThirds = new Rational(2, 3) twoThirds: Rational = 2/3 scala> oneHalf add twoThirds res3: Rational = 7/6 One other thing you can do now that you couldn’t do before is access the numerator and denominator values from outside the object. Simply access the public numer and denom fields, like this: scala> val r = new Rational(1, 2) r: Rational = 1/2 scala> r.numer res4: Int = 1 scala> r.denom res5: Int = 2 6.6 Self references The keyword this refers to the object instance on which the currently exe- cuting method was invoked, or if used in a constructor, the object instance Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.7 Chapter 6 · Functional Objects 146 being constructed. As an example, consider adding a method, lessThan, which tests whether the given Rational is smaller than a parameter: def lessThan(that: Rational) = this.numer * that.denom < that.numer * this.denom Here, this.numer refers to the numerator of the object on which lessThan was invoked. You can also leave off the this prefix and write just numer; the two notations are equivalent. As an example where you can’t do without this, consider adding a max method to class Rational that returns the greater of the given rational num- ber and an argument: def max(that: Rational) = if (this.lessThan(that)) that else this Here, the first this is redundant. You could have equally well left it off and written: lessThan(that). But the second this represents the result of the method in the case where the test returns false; were you to omit it, there would be nothing left to return! 6.7 Auxiliary constructors Sometimes you need multiple constructors in a class. In Scala, construc- tors other than the primary constructor are called auxiliary constructors. For example, a rational number with a denominator of 1 can be written more suc- cinctly as simply the numerator. Instead of 5 1 , for example, you can just write 5. It might be nice, therefore, if instead of writing new Rational(5, 1), client programmers could simply write new Rational(5). This would re- quire adding an auxiliary constructor to Rational that takes only one argu- ment, the numerator, with the denominator predefined to be 1. Listing 6.2 shows what that would look like. Auxiliary constructors in Scala start with def this(...). The body of Rational’s auxiliary constructor merely invokes the primary constructor, passing along its lone argument, n, as the numerator and 1 as the denomina- tor. You can see the auxiliary constructor in action by typing the following into the interpreter: scala> val y = new Rational(3) y: Rational = 3/1 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.7 Chapter 6 · Functional Objects 147 class Rational(n: Int, d: Int){ require(d != 0) val numer: Int = n val denom: Int = d def this(n: Int) = this(n, 1) // auxiliary constructor override def toString = numer +"/"+ denom def add(that: Rational): Rational = new Rational( numer * that.denom + that.numer * denom, denom * that.denom ) } Listing 6.2· Rational with an auxiliary constructor. In Scala, every auxiliary constructor must invoke another constructor of the same class as its first action. In other words, the first statement in every auxiliary constructor in every Scala class will have the form “this(...)”. The invoked constructor is either the primary constructor (as in the Rational example), or another auxiliary constructor that comes textually before the calling constructor. The net effect of this rule is that every constructor invo- cation in Scala will end up eventually calling the primary constructor of the class. The primary constructor is thus the single point of entry of a class. Note If you’re familiar with Java, you may wonder why Scala’s rules for constructors are a bit more restrictive than Java’s. In Java, a constructor must either invoke another constructor of the same class, or directly invoke a constructor of the superclass, as its first action. In a Scala class, only the primary constructor can invoke a superclass constructor. The increased restriction in Scala is really a design trade-off that needed to be paid in exchange for the greater conciseness and simplicity of Scala’s constructors compared to Java’s. Superclasses and the details of how constructor invocation and inheritance interact will be explained in Chapter 10. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.8 Chapter 6 · Functional Objects 148 6.8 Private fields and methods In the previous version of Rational, we simply initialized numer with n and denom with d. As a result, the numerator and denominator of a Rational can be larger than needed. For example, the fraction 66 42 could be normalized to an equivalent reduced form, 11 7 , but Rational’s primary constructor doesn’t currently do this: scala> new Rational(66, 42) res6: Rational = 66/42 To normalize in this way, you need to divide the numerator and denominator by their greatest common divisor. For example, the greatest common divisor of 66 and 42 is 6. (In other words, 6 is the largest integer that divides evenly into both 66 and 42.) Dividing both the numerator and denominator of 66 42 by 6 yields its reduced form, 11 7 . Listing 6.3 shows one way to do this: class Rational(n: Int, d: Int){ require(d != 0) private val g = gcd(n.abs, d.abs) val numer = n / g val denom = d / g def this(n: Int) = this(n, 1) def add(that: Rational): Rational = new Rational( numer * that.denom + that.numer * denom, denom * that.denom ) override def toString = numer +"/"+ denom private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b) } Listing 6.3· Rational with a private field and method. In this version of Rational, we added a private field, g, and modified the initializers for numer and denom. (An initializer is the code that initializes Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.9 Chapter 6 · Functional Objects 149 a variable, for example, the “n / g” that initializes numer.) Because g is private, it can be accessed inside the body of the class, but not outside. We also added a private method, gcd, which calculates the greatest common divisor of two passed Ints. For example, gcd(12, 8) is 4. As you saw in Section 4.1, to make a field or method private you simply place the private keyword in front of its definition. The purpose of the private “helper method” gcd is to factor out code needed by some other part of the class, in this case, the primary constructor. To ensure g is always positive, we pass the absolute value of n and d, which we obtain by invoking abs on them, a method you can invoke on any Int to get its absolute value. The Scala compiler will place the code for the initializers of Rational’s three fields into the primary constructor in the order in which they appear in the source code. Thus, g’s initializer, gcd(n.abs, d.abs), will execute before the other two, because it appears first in the source. Field g will be initialized with the result, the greatest common divisor of the absolute value of the class parameters, n and d. Field g is then used in the initializers of numer and denom. By dividing n and d by their greatest common divisor, g, every Rational will be constructed in its normalized form: scala> new Rational(66, 42) res7: Rational = 11/7 6.9 Defining operators The current implementation of Rational addition is OK, but could be made more convenient to use. You might ask yourself why you can write: x + y if x and y are integers or floating-point numbers, but you have to write: x.add(y) or at least: x add y if they are rational numbers. There’s no convincing reason why this should be so. Rational numbers are numbers just like other numbers. In a mathe- matical sense they are even more natural than, say, floating-point numbers. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.9 Chapter 6 · Functional Objects 150 Why should you not use the natural arithmetic operators on them? In Scala you can do this. In the rest of this chapter, we’ll show you how. The first step is to replace add by the usual mathematical symbol. This is straightforward, as + is a legal identifier in Scala. We can simply define a method with + as its name. While we’re at it, you may as well imple- ment a method named * that performs multiplication. The result is shown in Listing 6.4: class Rational(n: Int, d: Int){ require(d != 0) private val g = gcd(n.abs, d.abs) val numer = n / g val denom = d / g def this(n: Int) = this(n, 1) def + (that: Rational): Rational = new Rational( numer * that.denom + that.numer * denom, denom * that.denom ) def * (that: Rational): Rational = new Rational(numer * that.numer, denom * that.denom) override def toString = numer +"/"+ denom private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b) } Listing 6.4· Rational with operator methods. With class Rational defined in this manner, you can now write: scala> valx= new Rational(1, 2) x: Rational = 1/2 scala> val y = new Rational(2, 3) y: Rational = 2/3 scala> x + y res8: Rational = 7/6 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.10 Chapter 6 · Functional Objects 151 As always, the operator syntax on the last input line is equivalent to a method call. You could also write: scala> x.+(y) res9: Rational = 7/6 but this is not as readable. Another thing to note is that given Scala’s rules for operator precedence, which were described in Section 5.8, the * method will bind more tightly than the + method for Rationals. In other words, expressions involving + and * operations on Rationals will behave as expected. For example, x + x * y will execute as x + (x * y), not (x + x) * y: scala> x + x * y res10: Rational = 5/6 scala> (x + x) * y res11: Rational = 2/3 scala> x + (x * y) res12: Rational = 5/6 6.10 Identifiers in Scala You have now seen the two most important ways to form an identifier in Scala: alphanumeric and operator. Scala has very flexible rules for forming identifiers. Besides the two forms you have seen there are also two others. All four forms of identifier formation are described in this section. An alphanumeric identifier starts with a letter or underscore, which can be followed by further letters, digits, or underscores. The ‘$’ character also counts as a letter, however it is reserved for identifiers generated by the Scala compiler. Identifiers in user programs should not contain ‘$’ characters, even though it will compile; if they do this might lead to name clashes with iden- tifiers generated by the Scala compiler. Scala follows Java’s convention of using camel-case5 identifiers, such as toString and HashSet. Although underscores are legal in identifiers, they are not used that often in Scala programs, in part to be consistent with Java, 5This style of naming identifiers is called camel case because the identifiersHaveHumps consisting of the embedded capital letters. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.10 Chapter 6 · Functional Objects 152 but also because underscores have many other non-identifier uses in Scala code. As a result, it is best to avoid identifiers like to_string, __init__, or name_. Camel-case names of fields, method parameters, local variables, and functions should start with lower case letter, for example: length, flatMap, and s. Camel-case names of classes and traits should start with an upper case letter, for example: BigInt, List, and UnbalancedTreeMap.6 Note One consequence of using a trailing underscore in an identifier is that if you attempt, for example, to write a declaration like this, “val name_: Int = 1”, you’ll get a compiler error. The compiler will think you are trying to declare a val named “name_:”. To get this to compile, you would need to insert an extra space before the colon, as in: “val name_ : Int = 1”. One way in which Scala’s conventions depart from Java’s involves con- stant names. In Scala, the word constant does not just mean val. Even though a val does remain constant after it is initialized, it is still a variable. For example, method parameters are vals, but each time the method is called those vals can hold different values. A constant is more permanent. For ex- ample, scala.math.Pi is defined to be the double value closest to the real value of π, the ratio of a circle’s circumference to its diameter. This value is unlikely to change ever, thus, Pi is clearly a constant. You can also use constants to give names to values that would otherwise be magic numbers in your code: literal values with no explanation, which in the worst case appear in multiple places. You may also want to define constants for use in pattern matching, a use case that will be described in Section 15.2. In Java, the con- vention is to give constants names that are all upper case, with underscores separating the words, such as MAX_VALUE or PI. In Scala, the convention is merely that the first character should be upper case. Thus, constants named in the Java style, such as X_OFFSET, will work as Scala constants, but the Scala convention is to use camel case for constants, such as XOffset. An operator identifier consists of one or more operator characters. Oper- ator characters are printable ASCII characters such as +, :, ?, ~ or #.7 Here 6In Section 16.5, you’ll see that sometimes you may want to give a special kind of class known as a case class a name consisting solely of operator characters. For example, the Scala API contains a class named ::, which facilitates pattern matching on Lists. 7More precisely, an operator character belongs to the Unicode set of mathematical sym- bols(Sm) or other symbols(So), or to the 7-bit ASCII characters that are not letters, digits, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.10 Chapter 6 · Functional Objects 153 are some examples of operator identifiers: + ++ ::: :-> The Scala compiler will internally “mangle” operator identifiers to turn them into legal Java identifiers with embedded $ characters. For instance, the identifier :-> would be represented internally as $colon$minus$greater. If you ever wanted to access this identifier from Java code, you’d need to use this internal representation. Because operator identifiers in Scala can become arbitrarily long, there is a small difference between Java and Scala. In Java, the input x<-y would be parsed as four lexical symbols, so it would be equivalent to x < - y. In Scala, <- would be parsed as a single identifier, giving x <- y. If you want the first interpretation, you need to separate the < and the - characters by a space. This is unlikely to be a problem in practice, as very few people would write x<-y in Java without inserting spaces or parentheses between the operators. A mixed identifier consists of an alphanumeric identifier, which is fol- lowed by an underscore and an operator identifier. For example, unary_+ used as a method name defines a unary + operator. Or, myvar_= used as method name defines an assignment operator. In addition, the mixed identi- fier form myvar_= is generated by the Scala compiler to support properties; more on that in Chapter 18. A literal identifier is an arbitrary string enclosed in back ticks (` ... `). Some examples of literal identifiers are: `x` `` `yield` The idea is that you can put any string that’s accepted by the runtime as an identifier between back ticks. The result is always a Scala identifier. This works even if the name contained in the back ticks would be a Scala reserved word. A typical use case is accessing the static yield method in Java’s Thread class. You cannot write Thread.yield() because yield is a reserved word in Scala. However, you can still name the method in back ticks, e.g., Thread.`yield`(). parentheses, square brackets, curly braces, single or double quote, or an underscore, period, semi-colon, comma, or back tick character. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.11 Chapter 6 · Functional Objects 154 6.11 Method overloading Back to class Rational. With the latest changes, you can now do addition and multiplication operations in a natural style on rational numbers. But one thing still missing is mixed arithmetic. For instance, you cannot multiply a rational number by an integer, because the operands of * always have to be Rationals. So for a rational number r you can’t write r * 2. You must write r * new Rational(2), which is not as nice. To make Rational even more convenient, we’ll add new methods to the class that perform mixed addition and multiplication on rational numbers and integers. While we’re at it, we’ll add methods for subtraction and division too. The result is shown in Listing 6.5. There are now two versions each of the arithmetic methods: one that takes a rational as its argument and another that takes an integer. In other words, each of these method names is overloaded, because each name is now being used by multiple methods. For example, the name + is used by one method that takes a Rational and another that takes an Int. In a method call, the compiler picks the version of an overloaded method that correctly matches the types of the arguments. For instance, if the argument y in x.+(y) is a Rational, the compiler will pick the method + that takes a Rational parameter. But if the argument is an integer, the compiler will pick the method + that takes an Int parameter instead. If you try this: scala> val x = new Rational(2, 3) x: Rational = 2/3 scala> x * x res13: Rational = 4/9 scala> x * 2 res14: Rational = 4/3 You’ll see that the * method invoked is determined in each case by the type of the right operand. Note Scala’s process of overloaded method resolution is very similar to Java’s. In every case, the chosen overloaded version is the one that best matches the static types of the arguments. Sometimes there is no unique best matching version; in that case the compiler will give you an “ambiguous reference” error. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.11 Chapter 6 · Functional Objects 155 class Rational(n: Int, d: Int){ require(d != 0) private val g = gcd(n.abs, d.abs) val numer = n / g val denom = d / g def this(n: Int) = this(n, 1) def + (that: Rational): Rational = new Rational( numer * that.denom + that.numer * denom, denom * that.denom ) def + (i: Int): Rational = new Rational(numer + i * denom, denom) def - (that: Rational): Rational = new Rational( numer * that.denom - that.numer * denom, denom * that.denom ) def - (i: Int): Rational = new Rational(numer - i * denom, denom) def * (that: Rational): Rational = new Rational(numer * that.numer, denom * that.denom) def * (i: Int): Rational = new Rational(numer * i, denom) def / (that: Rational): Rational = new Rational(numer * that.denom, denom * that.numer) def / (i: Int): Rational = new Rational(numer, denom * i) override def toString = numer +"/"+ denom private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b) } Listing 6.5· Rational with overloaded methods. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.12 Chapter 6 · Functional Objects 156 6.12 Implicit conversions Now that you can write r * 2, you might also want to swap the operands, as in 2 * r. Unfortunately this does not work yet: scala> 2 * r :7: error: overloaded method value * with alternatives (Double)Double (Float)Float (Long)Long (Int)Int (Char)Int (Short)Int (Byte)Int cannot be applied to (Rational) 2 * r ˆ The problem here is that 2 * r is equivalent to 2.*(r), so it is a method call on the number 2, which is an integer. But the Int class contains no multiplication method that takes a Rational argument—it couldn’t because class Rational is not a standard class in the Scala library. However, there is another way to solve this problem in Scala: You can create an implicit conversion that automatically converts integers to rational numbers when needed. Try adding this line in the interpreter: scala> implicit def intToRational(x: Int) = new Rational(x) This defines a conversion method from Int to Rational. The implicit modifier in front of the method tells the compiler to apply it automatically in a number of situations. With the conversion defined, you can now retry the example that failed before: scala> val r = new Rational(2,3) r: Rational = 2/3 scala> 2 * r res16: Rational = 4/3 Note that for an implicit conversion to work, it needs to be in scope. If you place the implicit method definition inside class Rational, it won’t be in scope in the interpreter. For now, you’ll need to define it directly in the interpreter. As you can glimpse from this example, implicit conversions are a very powerful technique for making libraries more flexible and more convenient to use. Because they are so powerful, they can also be easily misused. You’ll Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.13 Chapter 6 · Functional Objects 157 find out more on implicit conversions, including ways to bring them into scope where they are needed, in Chapter 21. 6.13 A word of caution As this chapter has demonstrated, creating methods with operator names and defining implicit conversions can help you design libraries for which client code is concise and easy to understand. Scala gives you a great deal of power to design such easy-to-use libraries, but please bear in mind that with power comes responsibility. If used unartfully, both operator methods and implicit conversions can give rise to client code that is hard to read and understand. Because im- plicit conversions are applied implicitly by the compiler, not explicitly writ- ten down in the source code, it can be non-obvious to client programmers what implicit conversions are being applied. And although operator meth- ods will usually make client code more concise, they will only make it more readable to the extent client programmers will be able to recognize and re- member the meaning of each operator. The goal you should keep in mind as you design libraries is not merely enabling concise client code, but readable, understandable client code. Con- ciseness will often be a big part of that readability, but you can take concise- ness too far. By designing libraries that enable tastefully concise and at the same time understandable client code, you can help those client program- mers work productively. 6.14 Conclusion In this chapter, you saw more aspects of classes in Scala. You saw how to add parameters to a class, define several constructors, define operators as methods, and customize classes so that they are natural to use. Maybe most importantly, you saw that defining and using immutable objects is a quite natural way to code in Scala. Although the final version of Rational shown in this chapter fulfills the requirements set forth at the beginning of the chapter, it could still be im- proved. We will in fact return to this example later in the book. For example, in Chapter 30, you’ll learn how to override equals and hashcode to allow Rationals to behave better when compared with == or placed into hash ta- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 6.14 Chapter 6 · Functional Objects 158 bles. In Chapter 21, you’ll learn how to place implicit method definitions in a companion object for Rational, so they can be more easily placed into scope when client programmers are working with Rationals. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 7 Built-in Control Structures Scala has only a handful of built-in control structures. The only control struc- tures are if, while, for, try, match, and function calls. The reason Scala has so few is that it has included function literals since its inception. Instead of accumulating one higher-level control structure after another in the base syntax, Scala accumulates them in libraries. Chapter 9 will show precisely how that is done. This chapter will show those few control structures that are built in. One thing you will notice is that almost all of Scala’s control structures result in some value. This is the approach taken by functional languages, in which programs are viewed as computing a value, thus the components of a program should also compute values. You can also view this approach as the logical conclusion of a trend already present in imperative languages. In im- perative languages, function calls can return a value, even though having the called function update an output variable passed as an argument would work just as well. In addition, imperative languages often have a ternary operator (such as the ?: operator of C, C++, and Java), which behaves exactly like if, but results in a value. Scala adopts this ternary operator model, but calls it if. In other words, Scala’s if can result in a value. Scala then continues this trend by having for, try, and match also result in values. Programmers can use these result values to simplify their code, just as they use return values of functions. Without this facility, the programmer must create temporary variables just to hold results that are calculated inside a control structure. Removing these temporary variables makes the code a little simpler, and it also prevents many bugs where you set the variable in one branch but forget to set it in another. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.1 Chapter 7 · Built-in Control Structures 160 Overall, Scala’s basic control structures, minimal as they are, are suffi- cient to provide all of the essentials from imperative languages. Further, they allow you to shorten your code by consistently having result values. To show you how all of this works, this chapter takes a closer look at each of Scala’s basic control structures. 7.1 If expressions Scala’s if works just like in many other languages. It tests a condition and then executes one of two code branches depending on whether the condition holds true. Here is a common example, written in an imperative style: var filename = "default.txt" if (!args.isEmpty) filename = args(0) This code declares a variable, filename, and initializes it to a default value. It then uses an if expression to check whether any arguments were supplied to the program. If so, it changes the variable to hold the value specified in the argument list. If no arguments were supplied, it leaves the variable set to the default value. This code can be written more nicely, because as mentioned in Step 3 in Chapter 2, Scala’s if is an expression that results in a value. Listing 7.1 shows how you can accomplish the same effect as the previous example, but without using any vars: val filename = if (!args.isEmpty) args(0) else "default.txt" Listing 7.1· Scala’s idiom for conditional initialization. This time, the if has two branches. If args is not empty, the initial element, args(0), is chosen. Else, the default value is chosen. The if ex- pression results in the chosen value, and the filename variable is initialized with that value. This code is slightly shorter, but its real advantage is that it uses a val instead of a var. Using a val is the functional style, and it helps you in much the same way as a final variable in Java. It tells readers of the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.2 Chapter 7 · Built-in Control Structures 161 code that the variable will never change, saving them from scanning all code in the variable’s scope to see if it ever changes. A second advantage to using a val instead of a var is that it better sup- ports equational reasoning. The introduced variable is equal to the expres- sion that computes it, assuming that expression has no side effects. Thus, any time you are about to write the variable name, you could instead write the expression. Instead of println(filename), for example, you could just as well write this: println(if (!args.isEmpty) args(0) else "default.txt") The choice is yours. You can write it either way. Using vals helps you safely make this kind of refactoring as your code evolves over time. Look for opportunities to use vals. They can make your code both easier to read and easier to refactor. 7.2 While loops Scala’s while loop behaves as in other languages. It has a condition and a body, and the body is executed over and over as long as the condition holds true. Listing 7.2 shows an example: def gcdLoop(x: Long, y: Long): Long = { var a = x var b = y while (a != 0){ val temp = a a = b % a b = temp } b } Listing 7.2· Calculating greatest common divisor with a while loop. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.2 Chapter 7 · Built-in Control Structures 162 Scala also has a do-while loop. This works like the while loop except that it tests the condition after the loop body instead of before. Listing 7.3 shows a Scala script that uses a do-while to echo lines read from the stan- dard input, until an empty line is entered: var line = "" do { line = readLine() println("Read: "+ line) } while (line != "") Listing 7.3· Reading from the standard input with do-while. The while and do-while constructs are called “loops,” not expressions, because they don’t result in an interesting value. The type of the result is Unit. It turns out that a value (and in fact, only one value) exists whose type is Unit. It is called the unit value and is written (). The existence of () is how Scala’s Unit differs from Java’s void. Try this in the interpreter: scala> def greet() { println("hi")} greet: ()Unit scala> greet() == () hi res0: Boolean = true Because no equals sign precedes its body, greet is defined to be a proce- dure with a result type of Unit. Therefore, greet returns the unit value, (). This is confirmed in the next line: comparing the greet’s result for equality with the unit value, (), yields true. One other construct that results in the unit value, which is relevant here, is reassignment to vars. For example, were you to attempt to read lines in Scala using the following while loop idiom from Java (and C and C++), you’ll run into trouble: var line = "" while ((line = readLine()) != "") // This doesn’t work! println("Read: "+ line) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.2 Chapter 7 · Built-in Control Structures 163 When you compile this code, Scala will give you a warning that comparing values of type Unit and String using != will always yield true. Whereas in Java, assignment results in the value assigned, in this case a line from the standard input, in Scala assignment always results in the unit value, (). Thus, the value of the assignment “line = readLine()” will always be () and never be "". As a result, this while loop’s condition will never be false, and the loop will, therefore, never terminate. Because the while loop results in no value, it is often left out of pure functional languages. Such languages have expressions, not loops. Scala includes the while loop nonetheless, because sometimes an imperative solu- tion can be more readable, especially to programmers with a predominantly imperative background. For example, if you want to code an algorithm that repeats a process until some condition changes, a while loop can express it directly while the functional alternative, which likely uses recursion, may be less obvious to some readers of the code. For example, Listing 7.4 shows an alternate way to determine a greatest common divisor of two numbers.1 Given the same two values for x and y, the gcd function shown in Listing 7.4 will return the same result as the gcdLoop function, shown in Listing 7.2. The difference between these two approaches is that gcdLoop is written in an imperative style, using vars and and a while loop, whereas gcd is written in a more functional style that involves recursion (gcd calls itself) and requires no vars. def gcd(x: Long, y: Long): Long = if (y == 0) x else gcd(y, x % y) Listing 7.4· Calculating greatest common divisor with recursion. In general, we recommend you challenge while loops in your code in the same way you challenge vars. In fact, while loops and vars often go hand in hand. Because while loops don’t result in a value, to make any kind of difference to your program, a while loop will usually either need to update vars or perform I/O. You can see this in action in the gcdLoop example shown previously. As that while loop does its business, it updates vars a and b. Thus, we suggest you be a bit suspicious of while loops in your code. 1The gcd function shown in Listing 7.4 uses the same approach used by the like-named function, first shown in Listing 6.3, to calculate greatest common divisors for class Rational. The main difference is that instead of Ints the gcd of Listing 7.4 works with Longs. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.3 Chapter 7 · Built-in Control Structures 164 If there isn’t a good justification for a particular while or do-while loop, try to find a way to do the same thing without it. 7.3 For expressions Scala’s for expression is a Swiss army knife of iteration. It lets you combine a few simple ingredients in different ways to express a wide variety of itera- tions. Simple uses enable common tasks such as iterating through a sequence of integers. More advanced expressions can iterate over multiple collections of different kinds, can filter out elements based on arbitrary conditions, and can produce new collections. Iteration through collections The simplest thing you can do with for is to iterate through all the elements of a collection. For example, Listing 7.5 shows some code that prints out all files in the current directory. The I/O is performed using the Java API. First, we create a java.io.File on the current directory, ".", and call its listFiles method. This method returns an array of File objects, one per directory and file contained in the current directory. We store the resulting array in the filesHere variable. val filesHere = (new java.io.File(".")).listFiles for (file <- filesHere) println(file) Listing 7.5· Listing files in a directory with a for expression. With the “file <- filesHere” syntax, which is called a generator, we iterate through the elements of filesHere. In each iteration, a new val named file is initialized with an element value. The compiler infers the type of file to be File, because filesHere is an Array[File]. For each iteration, the body of the for expression, println(file), will be executed. Because File’s toString method yields the name of the file or directory, the names of all the files and directories in the current directory will be printed. The for expression syntax works for any kind of collection, not just arrays.2 One convenient special case is the Range type, which you briefly 2To be precise, the expression to the right of the <- symbol in a for expression can be Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.3 Chapter 7 · Built-in Control Structures 165 saw in Table 5.4 on page 138. You can create Ranges using syntax like “1 to 5” and can iterate through them with a for. Here is a simple example: scala> for (i <- 1 to 4) println("Iteration "+ i) Iteration 1 Iteration 2 Iteration 3 Iteration 4 If you don’t want to include the upper bound of the range in the values that are iterated over, use until instead of to: scala> for (i <- 1 until 4) println("Iteration "+ i) Iteration 1 Iteration 2 Iteration 3 Iterating through integers like this is common in Scala, but not nearly as much as in other languages. In other languages, you might use this facility to iterate through an array, like this: // Not common in Scala... for (i <- 0 to filesHere.length - 1) println(filesHere(i)) This for expression introduces a variable i, sets it in turn to each integer between 0 and filesHere.length - 1, and executes the body of the for expression for each setting of i. For each setting of i, the i’th element of filesHere is extracted and processed. The reason this kind of iteration is less common in Scala is that you can just as well iterate over the collection directly. If you do, your code becomes shorter and you sidestep many of the off-by-one errors that can arise when iterating through arrays. Should you start at 0 or 1? Should you add -1, +1, or nothing to the final index? Such questions are easily answered, but easily answered wrongly. It is safer to avoid such questions entirely. any type that has certain methods, in this case foreach, with appropriate signatures. The details on how the Scala compiler processes for expressions are described in Chapter 23. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.3 Chapter 7 · Built-in Control Structures 166 Filtering Sometimes you do not want to iterate through a collection in its entirety. You want to filter it down to some subset. You can do this with a for expression by adding a filter: an if clause inside the for’s parentheses. For example, the code shown in Listing 7.6 lists only those files in the current directory whose names end with “.scala”: val filesHere = (new java.io.File(".")).listFiles for (file <- filesHere if file.getName.endsWith(".scala")) println(file) Listing 7.6· Finding .scala files using a for with a filter. You could alternatively accomplish the same goal with this code: for (file <- filesHere) if (file.getName.endsWith(".scala")) println(file) This code yields the same output as the previous code, and likely looks more familiar to programmers with an imperative background. The imperative form, however, is only an option because this particular for expression is executed for its printing side-effects and results in the unit value (). As will be demonstrated later in this section, the for expression is called an “expression” because it can result in an interesting value, a collection whose type is determined by the for expression’s <- clauses. You can include more filters if you want. Just keep adding if clauses. For example, to be extra defensive, the code in Listing 7.7 prints only files and not directories. It does so by adding a filter that checks the file’s isFile method. for( file <- filesHere if file.isFile if file.getName.endsWith(".scala") ) println(file) Listing 7.7· Using multiple filters in a for expression. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.3 Chapter 7 · Built-in Control Structures 167 Nested iteration If you add multiple <- clauses, you will get nested “loops.” For exam- ple, the for expression shown in Listing 7.8 has two nested loops. The outer loop iterates through filesHere, and the inner loop iterates through fileLines(file) for any file that ends with .scala. def fileLines(file: java.io.File) = scala.io.Source.fromFile(file).getLines().toList def grep(pattern: String) = for( file <- filesHere if file.getName.endsWith(".scala"); line <- fileLines(file) if line.trim.matches(pattern) ) println(file +": "+ line.trim) grep(".*gcd.*") Listing 7.8· Using multiple generators in a for expression. If you prefer, you can use curly braces instead of parentheses to surround the generators and filters. One advantage to using curly braces is that you can leave off some of the semicolons that are needed when you use parentheses, because as explained in Section 4.2, the Scala compiler will not infer semi- colons while inside parentheses. Mid-stream variable bindings Note that the previous code repeats the expression line.trim. This is a non-trivial computation, so you might want to only compute it once. You can do this by binding the result to a new variable using an equals sign (=). The bound variable is introduced and used just like a val, only with the val keyword left out. Listing 7.9 shows an example. In Listing 7.9, a variable named trimmed is introduced halfway through the for expression. That variable is initialized to the result of line.trim. The rest of the for expression then uses the new variable in two places, once in an if and once in println. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.3 Chapter 7 · Built-in Control Structures 168 def grep(pattern: String) = for{ file <- filesHere if file.getName.endsWith(".scala") line <- fileLines(file) trimmed = line.trim if trimmed.matches(pattern) } println(file +": "+ trimmed) grep(".*gcd.*") Listing 7.9· Mid-stream assignment in a for expression. Producing a new collection While all of the examples so far have operated on the iterated values and then forgotten them, you can also generate a value to remember for each iteration. To do so, you prefix the body of the for expression by the keyword yield. For example, here is a function that identifies the .scala files and stores them in an array: def scalaFiles = for { file <- filesHere if file.getName.endsWith(".scala") } yield file Each time the body of the for expression executes it produces one value, in this case simply file. When the for expression completes, the result will include all of the yielded values contained in a single collection. The type of the resulting collection is based on the kind of collections processed in the iteration clauses. In this case the result is an Array[File], because filesHere is an array and the type of the yielded expression is File. Be careful, by the way, where you place the yield keyword. The syntax of a for-yield expression is like this: for clauses yield body The yield goes before the entire body. Even if the body is a block sur- rounded by curly braces, put the yield before the first curly brace, not be- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.4 Chapter 7 · Built-in Control Structures 169 fore the last expression of the block. Avoid the temptation to write things like this: for (file <- filesHere if file.getName.endsWith(".scala")) { yield file // Syntax error! } For example, the for expression shown in Listing 7.10 first transforms the Array[File] named filesHere, which contains all files in the current directory, to one that contains only .scala files. For each of these it gen- erates an Iterator[String] (the result of the fileLines method, whose definition is shown in Listing 7.8). An Iterator offers methods next and hasNext that allow you to iterate over a collection of elements. This ini- tial iterator is transformed into another Iterator[String] containing only trimmed lines that include the substring "for". Finally, for each of these, an integer length is yielded. The result of this for expression is an Array[Int] containing those lengths. val forLineLengths = for{ file <- filesHere if file.getName.endsWith(".scala") line <- fileLines(file) trimmed = line.trim if trimmed.matches(".*for.*") } yield trimmed.length Listing 7.10· Transforming an Array[File] to Array[Int] with a for. At this point, you have seen all the major features of Scala’s for ex- pression. This section went through them rather quickly, however. A more thorough coverage of for expressions is given in Chapter 23. 7.4 Exception handling with try expressions Scala’s exceptions behave just like in many other languages. Instead of re- turning a value in the normal way, a method can terminate by throwing an exception. The method’s caller can either catch and handle that exception, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.4 Chapter 7 · Built-in Control Structures 170 or it can itself simply terminate, in which case the exception propagates to the caller’s caller. The exception propagates in this way, unwinding the call stack, until a method handles it or there are no more methods left. Throwing exceptions Throwing an exception looks the same as in Java. You create an exception object and then you throw it with the throw keyword: throw new IllegalArgumentException Although it may seem somewhat paradoxical, in Scala, throw is an ex- pression that has a result type. Here is an example in which that result type matters: val half = if (n % 2 == 0) n / 2 else throw new RuntimeException("n must be even") What happens here is that if n is even, half will be initialized to half of n. If n is not even, an exception will be thrown before half can be initialized to anything at all. Because of this, it is safe to treat a thrown exception as any kind of value whatsoever. Any context that tries to use the return from a throw will never get to do so, and thus no harm will come. Technically, an exception throw has type Nothing. You can use a throw as an expression even though it will never actually evaluate to anything. This little bit of technical gymnastics might sound weird, but is frequently useful in cases like the previous example. One branch of an if computes a value, while the other throws an exception and computes Nothing. The type of the whole if expression is then the type of that branch which does compute something. Type Nothing is discussed further in Section 11.3. Catching exceptions You catch exceptions using the syntax shown in Listing 7.11 The syntax for catch clauses was chosen for its consistency with an important part of Scala: pattern matching. Pattern matching, a powerful feature, is described briefly in this chapter and in more detail in Chapter 15. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.4 Chapter 7 · Built-in Control Structures 171 import java.io.FileReader import java.io.FileNotFoundException import java.io.IOException try{ valf= new FileReader("input.txt") // Use and close file } catch { case ex: FileNotFoundException => // Handle missing file case ex: IOException => // Handle other I/O error } Listing 7.11· A try-catch clause in Scala. The behavior of this try-catch expression is the same as in other lan- guages with exceptions. The body is executed, and if it throws an exception, each catch clause is tried in turn. In this example, if the exception is of type FileNotFoundException, the first clause will execute. If it is of type IOException, the second clause will execute. If the exception is of neither type, the try-catch will terminate and the exception will propagate further. Note One difference from Java that you’ll quickly notice in Scala is that unlike Java, Scala does not require you to catch checked exceptions, or declare them in a throws clause. You can declare a throws clause if you wish with the @throws annotation, but it is not required. See Section 31.2 for more information on @throws. The finally clause You can wrap an expression with a finally clause if you want to cause some code to execute no matter how the expression terminates. For example, you might want to be sure an open file gets closed even if a method exits by throwing an exception. Listing 7.12 shows an example. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.4 Chapter 7 · Built-in Control Structures 172 import java.io.FileReader val file = new FileReader("input.txt") try { // Use the file } finally { file.close() // Be sure to close the file } Listing 7.12· A try-finally clause in Scala. Note Listing 7.12 shows the idiomatic way to ensure a non-memory resource, such as a file, socket, or database connection is closed. First you acquire the resource. Then you start a try block in which you use the resource. Lastly, you close the resource in a finally block. This idiom is the same in Scala as in Java, however, in Scala you can alternatively employ a technique called the loan pattern to achieve the same goal more concisely. The loan pattern will be described in Section 9.4. Yielding a value As with most other Scala control structures, try-catch-finally results in a value. For example, Listing 7.13 shows how you can try to parse a URL but use a default value if the URL is badly formed. The result is that of the try clause if no exception is thrown, or the relevant catch clause if an exception is thrown and caught. If an exception is thrown but not caught, the expression has no result at all. The value computed in the finally clause, if there is one, is dropped. Usually finally clauses do some kind of clean up such as closing a file; they should not normally change the value computed in the main body or a catch clause of the try. If you’re familiar with Java, it’s worth noting that Scala’s behavior differs from Java only because Java’s try-finally does not result in a value. As in Java, if a finally clause includes an explicit return statement, or throws an exception, that return value or exception will “overrule” any previous one that originated in the try block or one of its catch clauses. For example, given this, rather contrived, function definition: def f(): Int = try { return 1 } finally { return 2 } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.5 Chapter 7 · Built-in Control Structures 173 import java.net.URL import java.net.MalformedURLException def urlFor(path: String) = try{ new URL(path) } catch{ case e: MalformedURLException => new URL("http://www.scala-lang.org") } Listing 7.13· A catch clause that yields a value. calling f() results in 2. By contrast, given: def g(): Int = try { 1 } finally { 2 } calling g() results in 1. Both of these functions exhibit behavior that could surprise most programmers, thus it’s usually best to avoid returning values from finally clauses. The best way to think of finally clauses is as a way to ensure some side effect happens, such as closing an open file. 7.5 Match expressions Scala’s match expression lets you select from a number of alternatives, just like switch statements in other languages. In general a match expression lets you select using arbitrary patterns, which will be described in Chap- ter 15. The general form can wait. For now, just consider using match to select among a number of alternatives. As an example, the script in Listing 7.14 reads a food name from the argument list and prints a companion to that food. This match expression examines firstArg, which has been set to the first argument out of the ar- gument list. If it is the string "salt", it prints "pepper", while if it is the string "chips", it prints "salsa", and so on. The default case is speci- fied with an underscore (_), a wildcard symbol frequently used in Scala as a placeholder for a completely unknown value. There are a few important differences from Java’s switch statement. One is that any kind of constant, as well as other things, can be used in Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.5 Chapter 7 · Built-in Control Structures 174 val firstArg = if (args.length > 0) args(0) else "" firstArg match { case "salt" => println("pepper") case "chips" => println("salsa") case "eggs" => println("bacon") case _ => println("huh?") } Listing 7.14· A match expression with side effects. cases in Scala, not just the integer-type and enum constants of Java’s case statements. In Listing 7.14, the alternatives are strings. Another difference is that there are no breaks at the end of each alternative. Instead the break is implicit, and there is no fall through from one alternative to the next. The common case—not falling through—becomes shorter, and a source of errors is avoided because programmers can no longer fall through by accident. The most significant difference from Java’s switch, however, may be that match expressions result in a value. In the previous example, each al- ternative in the match expression prints out a value. It would work just as well to yield the value rather than printing it, as shown in Listing 7.15. The value that results from this match expression is stored in the friend vari- able. Aside from the code getting shorter (in number of tokens, anyway), the code now disentangles two separate concerns: first it chooses a food, and then it prints it. val firstArg = if (!args.isEmpty) args(0) else "" val friend = firstArg match { case "salt" => "pepper" case "chips" => "salsa" case "eggs" => "bacon" case _ => "huh?" } println(friend) Listing 7.15· A match expression that yields a value. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.6 Chapter 7 · Built-in Control Structures 175 7.6 Living without break and continue You may have noticed that there has been no mention of break or continue. Scala leaves out these commands because they do not mesh well with func- tion literals, a feature described in the next chapter. It is clear what continue means inside a while loop, but what would it mean inside a function literal? While Scala supports both imperative and functional styles of programming, in this case it leans slightly towards functional programming in exchange for simplifying the language. Do not worry, though. There are many ways to program without break and continue, and if you take advantage of function literals, those alternatives can often be shorter than the original code. The simplest approach is to replace every continue by an if and ev- ery break by a boolean variable. The boolean variable indicates whether the enclosing while loop should continue. For example, suppose you are searching through an argument list for a string that ends with “.scala” but does not start with a hyphen. In Java you could—if you were quite fond of while loops, break, and continue—write the following: int i = 0; // This is Java boolean foundIt = false; while (i < args.length) { if (args[i].startsWith("-")) { i = i + 1; continue; } if (args[i].endsWith(".scala")) { foundIt = true; break; } i = i + 1; } To transliterate this Java code directly to Scala, instead of doing an if and then a continue, you could write an if that surrounds the entire re- mainder of the while loop. To get rid of the break, you would normally add a boolean variable indicating whether to keep going, but in this case you can reuse foundIt. Using both of these tricks, the code ends up looking as shown in Listing 7.16. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.6 Chapter 7 · Built-in Control Structures 176 vari= 0 var foundIt = false while (i < args.length && !foundIt) { if (!args(i).startsWith("-")) { if (args(i).endsWith(".scala")) foundIt = true } i = i + 1 } Listing 7.16· Looping without break or continue. This Scala code in Listing 7.16 is quite similar to the original Java code. All the basic pieces are still there and in the same order. There are two reassignable variables and a while loop. Inside the loop, there is a test that i is less than args.length, a check for "-", and a check for ".scala". If you wanted to get rid of the vars in Listing 7.16, one approach you could try is to rewrite the loop as a recursive function. You could, for exam- ple, define a searchFrom function that takes an integer as an input, searches forward from there, and then returns the index of the desired argument. Us- ing this technique the code would look as shown in Listing 7.17: def searchFrom(i: Int): Int = if (i >= args.length) -1 else if (args(i).startsWith("-")) searchFrom(i + 1) else if (args(i).endsWith(".scala")) i else searchFrom(i + 1) val i = searchFrom(0) Listing 7.17· A recursive alternative to looping with vars. The version in Listing 7.17 gives a human-meaningful name to what the function does, and it uses recursion to substitute for looping. Each continue is replaced by a recursive call with i + 1 as the argument, effectively skipping to the next integer. Many people find this style of programming easier to understand, once they get used to the recursion. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.7 Chapter 7 · Built-in Control Structures 177 Note The Scala compiler will not actually emit a recursive function for the code shown in Listing 7.17. Because all of the recursive calls are in tail-call position, the compiler will generate code similar to a while loop. Each recursive call will be implemented as a jump back to the beginning of the function. Tail-call optimization will be discussed in Section 8.9. If after all this discussion you still feel the need to use break, there’s help in Scala’s standard library. Class Breaks in package scala.util.control offers a break method, which can be used to exit the an enclosing block that’s marked with breakable. Here an example how this library-supplied break method could be applied: import scala.util.control.Breaks._ import java.io._ val in = new BufferedReader(new InputStreamReader(System.in)) breakable { while (true){ println("? ") if (in.readLine() == "") break } } This will repeatedly read non-empty lines from the standard input. Once the user enters an empty line, control flow exits from the enclosing breakable, and with it the while loop. The Breaks class implements break by throwing an exception that is caught by an enclosing application of the breakable method. Therefore, the call to break does not need to be in the same method as the call to breakable. 7.7 Variable scope Now that you’ve seen Scala’s built-in control structures, we’ll use them in this section to explain how scoping works in Scala. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.7 Chapter 7 · Built-in Control Structures 178 Fast track for Java programmers If you’re a Java programmer, you’ll find that Scala’s scoping rules are almost identical to Java’s. One difference between Java and Scala exists, however, in that Scala allows you to define variables of the same name in nested scopes. If you’re a Java programmer, therefore, you may wish to at least skim this section. Variable declarations in Scala programs have a scope that defines where you can use the name. The most common example of scoping is that curly braces generally introduce a new scope, so anything defined inside curly braces leaves scope after the final closing brace.3 As an illustration, consider the function shown in Listing 7.18. The printMultiTable function shown in Listing 7.18 prints out a mul- tiplication table.4 The first statement of this function introduces a variable named i and initializes it to the integer 1. You can then use the name i for the remainder of the function. The next statement in printMultiTable is a while loop: while (i <= 10){ var j = 1 ... } You can use i here because it is still in scope. In the first statement inside that while loop, you introduce another variable, this time named j, and again initialize it to 1. Because the variable j was defined inside the open curly brace of the while loop, it can be used only within that while loop. If you were to attempt to do something with j after the closing curly brace of this while loop, after the comment that says j, prod, and k are out of scope, your program would not compile. All variables defined in this example—i, j, prod, and k—are local vari- ables. Such variables are “local” to the function in which they are defined. Each time a function is invoked, a new set of its local variables is used. 3There are a few exceptions to this rule, because in Scala you can sometimes use curly braces in place of parentheses. One example of this kind of curly-brace use is the alternative for expression syntax described in Section 7.3. 4The printMultiTable function shown in Listing 7.18 is written in an imperative style. We’ll refactor it into a functional style in the next section. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.7 Chapter 7 · Built-in Control Structures 179 def printMultiTable() { vari= 1 // only i in scope here while (i <= 10){ var j = 1 // both i and j in scope here while (j <= 10){ val prod = (i * j).toString // i, j, and prod in scope here var k = prod.length // i, j, prod, and k in scope here while (k < 4){ print("") k += 1 } print(prod) j += 1 } // i and j still in scope; prod and k out of scope println() i += 1 } // i still in scope; j, prod, and k out of scope } Listing 7.18· Variable scoping when printing a multiplication table. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.7 Chapter 7 · Built-in Control Structures 180 Once a variable is defined, you can’t define a new variable with the same name in the same scope. For example, the following script with two variables named a in the same scope would not compile: val a = 1 val a = 2 // Does not compile println(a) You can, on the other hand, define a variable in an inner scope that has the same name as a variable in an outer scope. The following script would com- pile and run: val a = 1; { val a = 2 // Compiles just fine println(a) } println(a) When executed, the script shown previously would print 2 then 1, because the a defined inside the curly braces is a different variable, which is in scope only until the closing curly brace.5 One difference to note between Scala and Java is that unlike Scala, Java will not let you create a variable in an inner scope that has the same name as a variable in an outer scope. In a Scala program, an inner variable is said to shadow a like-named outer variable, because the outer variable becomes invisible in the inner scope. You might have already noticed something that looks like shadowing in the interpreter: scala> val a = 1 a: Int = 1 scala> val a = 2 a: Int = 2 scala> println(a) 2 5By the way, the semicolon is required in this case after the first definition of a because Scala’s semicolon inference mechanism will not place one there. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.8 Chapter 7 · Built-in Control Structures 181 In the interpreter, you can reuse variable names to your heart’s content. Among other things, this allows you to change your mind if you made a mistake when you defined a variable the first time in the interpreter. The rea- son you can do this is that, conceptually, the interpreter creates a new nested scope for each new statement you type in. Thus, you could visualize the previous interpreted code like this: val a = 1; { val a = 2; { println(a) } } This code will compile and run as a Scala script, and like the code typed into the interpreter, will print 2. Keep in mind that such code can be very confusing to readers, because variable names adopt new meanings in nested scopes. It is usually better to choose a new, meaningful variable name rather than to shadow an outer variable. 7.8 Refactoring imperative-style code To help you gain insight into the functional style, in this section we’ll refac- tor the imperative approach to printing a multiplication table shown in List- ing 7.18. Our functional alternative is shown in Listing 7.19. The imperative style reveals itself in Listing 7.18 in two ways. First, invoking printMultiTable has a side effect: printing a multiplication ta- ble to the standard output. In Listing 7.19, we refactored the function so that it returns the multiplication table as a string. Since the function no longer prints, we renamed it multiTable. As mentioned previously, one advantage of side-effect-free functions is they are easier to unit test. To test printMultiTable, you would need to somehow redefine print and println so you could check the output for correctness. You could test multiTable more easily, by checking its string result. The other telltale sign of the imperative style in printMultiTable is its while loop and vars. By contrast, the multiTable function uses vals, for expressions, helper functions, and calls to mkString. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.8 Chapter 7 · Built-in Control Structures 182 // Returns a row as a sequence def makeRowSeq(row: Int) = for (col <- 1 to 10) yield { val prod = (row * col).toString val padding = ""* (4 - prod.length) padding + prod } // Returns a row as a string def makeRow(row: Int) = makeRowSeq(row).mkString // Returns table as a string with one row per line def multiTable() = { val tableSeq = // a sequence of row strings for (row <- 1 to 10) yield makeRow(row) tableSeq.mkString("\n") } Listing 7.19· A functional way to create a multiplication table. We factored out the two helper functions, makeRow and makeRowSeq, to make the code easier to read. Function makeRowSeq uses a for expression whose generator iterates through column numbers 1 through 10. The body of this for calculates the product of row and column, determines the padding needed for the product, and yields the result of concatenating the padding and product strings. The result of the for expression will be a sequence (some subclass of scala.Seq) containing these yielded strings as elements. The other helper function, makeRow, simply invokes mkString on the re- sult returned by makeRowSeq. mkString will concatenate the strings in the sequence and return them as one string. The multiTable method first initializes tableSeq with the result of a for expression whose generator iterates through row numbers 1 to 10, and for each calls makeRow to get the string for that row. This string is yielded, thus the result of this for expression will be a sequence of row strings. The only remaining task is to convert the sequence of strings into a single string. The call to mkString accomplishes this, and because we pass "\n", we get an end of line character inserted between each string. If you pass the string Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 7.9 Chapter 7 · Built-in Control Structures 183 returned by multiTable to println, you’ll see the same output that’s pro- duced by calling printMultiTable: 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100 7.9 Conclusion Scala’s built-in control structures are minimal, but they do the job. They act much like their imperative equivalents, but because they tend to result in a value, they support a functional style, too. Just as important, they are careful in what they omit, thus leaving room for one of Scala’s most powerful features, the function literal, which will be described in the next chapter. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 8 Functions and Closures When programs get larger, you need some way to divide them into smaller, more manageable pieces. For dividing up control flow, Scala offers an ap- proach familiar to all experienced programmers: divide the code into func- tions. In fact, Scala offers several ways to define functions that are not present in Java. Besides methods, which are functions that are members of some object, there are also functions nested within functions, function lit- erals, and function values. This chapter takes you on a tour through all of these flavors of functions in Scala. 8.1 Methods The most common way to define a function is as a member of some object. Such a function is called a method. As an example, Listing 8.1 shows two methods that together read a file with a given name and print out all lines whose length exceeds a given width. Every printed line is prefixed with the name of the file it appears in. The processFile method takes a filename and width as parameters. It creates a Source object from the file name and, in the generator of the for expression, calls getLines on the source. As mentioned in Step 12 of Chapter 3, getLines returns an iterator that provides one line from the file on each iteration, excluding the end-of-line character. The for expression processes each of these lines by calling the helper method, processLine. The processLine method takes three parameters: a filename, a width, and a line. It tests whether the length of the line is greater than the given width, and, if so, it prints the filename, a colon, and the line. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.1 Chapter 8 · Functions and Closures 185 import scala.io.Source object LongLines{ def processFile(filename: String, width: Int){ val source = Source.fromFile(filename) for (line <- source.getLines()) processLine(filename, width, line) } private def processLine(filename: String, width: Int, line: String){ if (line.length > width) println(filename +": "+ line.trim) } } Listing 8.1· LongLines with a private processLine method. To use LongLines from the command line, we’ll create an application that expects the line width as the first command-line argument, and interprets subsequent arguments as filenames:1 object FindLongLines{ def main(args: Array[String]){ val width = args(0).toInt for (arg <- args.drop(1)) LongLines.processFile(arg, width) } } Here’s how you’d use this application to find the lines in LongLines.scala that are over 45 characters in length (there’s just one): $ scala FindLongLines 45 LongLines.scala LongLines.scala: def processFile(filename: String, width: Int) { 1In this book, we usually won’t check command-line arguments for validity in example applications, both to save trees and reduce boilerplate code that can obscure the example’s important code. The trade-off is that instead of producing a helpful error message when given bad input, our example applications will throw an exception. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.2 Chapter 8 · Functions and Closures 186 So far, this is very similar to what you would do in any object-oriented language. However, the concept of a function in Scala is more general than a method. Scala’s other ways to express functions will be explained in the following sections. 8.2 Local functions The construction of the processFile method in the previous section demon- strated an important design principle of the functional programming style: programs should be decomposed into many small functions that each do a well-defined task. Individual functions are often quite small. The advantage of this style is that it gives a programmer many building blocks that can be flexibly composed to do more difficult things. Each building block should be simple enough to be understood individually. One problem with this approach is that all the helper function names can pollute the program namespace. In the interpreter this is not so much of a problem, but once functions are packaged in reusable classes and objects, it’s desirable to hide the helper functions from clients of a class. They often do not make sense individually, and you often want to keep enough flexibility to delete the helper functions if you later rewrite the class a different way. In Java, your main tool for this purpose is the private method. This private-method approach works in Scala as well, as is demonstrated in List- ing 8.1, but Scala offers an additional approach: you can define functions inside other functions. Just like local variables, such local functions are vis- ible only in their enclosing block. Here’s an example: def processFile(filename: String, width: Int){ def processLine(filename: String, width: Int, line: String){ if (line.length > width) println(filename +": "+ line) } val source = Source.fromFile(filename) for (line <- source.getLines()) { processLine(filename, width, line) } } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.2 Chapter 8 · Functions and Closures 187 In this example, we refactored the original LongLines version, shown in Listing 8.1, by transforming private method, processLine, into a local func- tion of processFile. To do so we removed the private modifier, which can only be applied (and is only needed) for methods, and placed the definition of processLine inside the definition of processFile. As a local function, processLine is in scope inside processFile, but inaccessible outside. Now that processLine is defined inside processFile, however, an- other improvement becomes possible. Notice how filename and width are passed unchanged into the helper function? This is not necessary, because local functions can access the parameters of their enclosing function. You can just use the parameters of the outer processLine function, as shown in Listing 8.2: import scala.io.Source object LongLines{ def processFile(filename: String, width: Int){ def processLine(line: String){ if (line.length > width) println(filename +": "+ line) } val source = Source.fromFile(filename) for (line <- source.getLines()) processLine(line) } } Listing 8.2· LongLines with a local processLine function. Simpler, isn’t it? This use of an enclosing function’s parameters is a common and useful example of the general nesting Scala provides. The nesting and scoping described in Section 7.7 applies to all Scala constructs, including functions. It’s a simple principle, but very powerful, especially in a language with first-class functions. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.3 Chapter 8 · Functions and Closures 188 8.3 First-class functions Scala has first-class functions. Not only can you define functions and call them, but you can write down functions as unnamed literals and then pass them around as values. We introduced function literals in Chapter 2 and showed the basic syntax in Figure 2.2 on page 79. A function literal is compiled into a class that when instantiated at run- time is a function value.2 Thus the distinction between function literals and values is that function literals exist in the source code, whereas function val- ues exist as objects at runtime. The distinction is much like that between classes (source code) and objects (runtime). Here is a simple example of a function literal that adds one to a number: (x: Int) => x + 1 The => designates that this function converts the thing on the left (any integer x) to the thing on the right (x + 1). So, this is a function mapping any integer x to x + 1. Function values are objects, so you can store them in variables if you like. They are functions, too, so you can invoke them using the usual parentheses function-call notation. Here is an example of both activities: scala> var increase = (x: Int) => x + 1 increase: (Int) => Int = scala> increase(10) res0: Int = 11 Because increase, in this example, is a var, you can reassign it a different function value later on. scala> increase = (x: Int) => x + 9999 increase: (Int) => Int = scala> increase(10) res1: Int = 10009 2Every function value is an instance of some class that extends one of several FunctionN traits in package scala, such as Function0 for functions with no parameters, Function1 for functions with one parameter, and so on. Each FunctionN trait has an apply method used to invoke the function. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.3 Chapter 8 · Functions and Closures 189 If you want to have more than one statement in the function literal, surround its body by curly braces and put one statement per line, thus forming a block. Just like a method, when the function value is invoked, all of the statements will be executed, and the value returned from the function is whatever the expression on the last line generates. scala> increase = (x: Int) => { println("We") println("are") println("here!") x + 1 } increase: (Int) => Int = scala> increase(10) We are here! res2: Int = 11 So now you have seen the nuts and bolts of function literals and function val- ues. Many Scala libraries give you opportunities to use them. For example, a foreach method is available for all collections.3 It takes a function as an argument and invokes that function on each of its elements. Here is how it can be used to print out all of the elements of a list: scala> val someNumbers = List(-11,-10,-5, 0, 5, 10) someNumbers: List[Int] = List(-11, -10, -5, 0, 5, 10) scala> someNumbers.foreach((x: Int) => println(x)) -11 -10 -5 0 5 10 As another example, collection types also have a filter method. This method selects those elements of a collection that pass a test the user sup- 3A foreach method is defined in trait Traversable, a common supertrait of List, Set, Array, and Map. See Chapter 17 for the details. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.4 Chapter 8 · Functions and Closures 190 plies. That test is supplied using a function. For example, the function (x: Int) => x > 0 could be used for filtering. This function maps positive integers to true and all others to false. Here is how to use it with filter: scala> someNumbers.filter((x: Int) => x > 0) res4: List[Int] = List(5, 10) Methods like foreach and filter are described further later in the book. Chapter 16 talks about their use in class List. Chapter 17 discusses their use with other collection types. 8.4 Short forms of function literals Scala provides a number of ways to leave out redundant information and write function literals more briefly. Keep your eyes open for these opportu- nities, because they allow you to remove clutter from your code. One way to make a function literal more brief is to leave off the parameter types. Thus, the previous example with filter could be written like this: scala> someNumbers.filter((x) => x > 0) res5: List[Int] = List(5, 10) The Scala compiler knows that x must be an integer, because it sees that you are immediately using the function to filter a list of integers (referred to by someNumbers). This is called target typing, because the targeted usage of an expression—in this case an argument to someNumbers.filter()—is allowed to influence the typing of that expression—in this case to determine the type of the x parameter. The precise details of target typing are not important to study. You can simply start by writing a function literal without the argument type, and, if the compiler gets confused, add in the type. Over time you’ll get a feel for which situations the compiler can and cannot puzzle out. A second way to remove useless characters is to leave out parentheses around a parameter whose type is inferred. In the previous example, the parentheses around x are unnecessary: scala> someNumbers.filter(x => x > 0) res6: List[Int] = List(5, 10) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.5 Chapter 8 · Functions and Closures 191 8.5 Placeholder syntax To make a function literal even more concise, you can use underscores as placeholders for one or more parameters, so long as each parameter appears only one time within the function literal. For example, _ > 0 is very short notation for a function that checks whether a value is greater than zero: scala> someNumbers.filter(_ > 0) res7: List[Int] = List(5, 10) You can think of the underscore as a “blank” in the expression that needs to be “filled in.” This blank will be filled in with an argument to the function each time the function is invoked. For example, given that someNumbers was initialized on page 189 to the value List(-11, -10, -5, 0, 5, 10), the filter method will replace the blank in _ > 0 first with -11, as in -11 > 0, then with -10, as in -10 > 0, then with -5, as in -5 > 0, and so on to the end of the List. The function literal _ > 0, therefore, is equivalent to the slightly more verbose x => x > 0, as demonstrated here: scala> someNumbers.filter(x => x > 0) res8: List[Int] = List(5, 10) Sometimes when you use underscores as placeholders for parameters, the compiler might not have enough information to infer missing parameter types. For example, suppose you write _ + _ by itself: scala> val f = _ + _ :4: error: missing parameter type for expanded function ((x$1, x$2) => x$1.$plus(x$2)) val f = _ + _ ˆ In such cases, you can specify the types using a colon, like this: scala> val f = (_: Int) + (_: Int) f: (Int, Int) => Int = scala> f(5, 10) res9: Int = 15 Note that _ + _ expands into a literal for a function that takes two parame- ters. This is why you can use this short form only if each parameter appears Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.6 Chapter 8 · Functions and Closures 192 in the function literal at most once. Multiple underscores mean multiple pa- rameters, not reuse of a single parameter repeatedly. The first underscore represents the first parameter, the second underscore the second parameter, the third underscore the third parameter, and so on. 8.6 Partially applied functions Although the previous examples substitute underscores in place of individual parameters, you can also replace an entire parameter list with an underscore. For example, rather than writing println(_), you could write println _. Here’s an example: someNumbers.foreach(println _) Scala treats this short form exactly as if you had written the following: someNumbers.foreach(x => println(x)) Thus, the underscore in this case is not a placeholder for a single parameter. It is a placeholder for an entire parameter list. Remember that you need to leave a space between the function name and the underscore, because otherwise the compiler will think you are referring to a different symbol, such as for example, a method named println_, which likely does not exist. When you use an underscore in this way, you are writing a partially ap- plied function. In Scala, when you invoke a function, passing in any needed arguments, you apply that function to the arguments. For example, given the following function: scala> def sum(a: Int, b: Int, c: Int) = a + b + c sum: (a: Int,b: Int,c: Int)Int You could apply the function sum to the arguments 1, 2, and 3 like this: scala> sum(1, 2, 3) res10: Int = 6 A partially applied function is an expression in which you don’t supply all of the arguments needed by the function. Instead, you supply some, or none, of the needed arguments. For example, to create a partially applied function expression involving sum, in which you supply none of the three required Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.6 Chapter 8 · Functions and Closures 193 arguments, you just place an underscore after “sum”. The resulting function can then be stored in a variable. Here’s an example: scala> val a = sum _ a: (Int, Int, Int) => Int = Given this code, the Scala compiler instantiates a function value that takes the three integer parameters missing from the partially applied function ex- pression, sum _, and assigns a reference to that new function value to the variable a. When you apply three arguments to this new function value, it will turn around and invoke sum, passing in those same three arguments: scala> a(1, 2, 3) res11: Int = 6 Here’s what just happened: The variable named a refers to a function value object. This function value is an instance of a class generated automatically by the Scala compiler from sum _, the partially applied function expression. The class generated by the compiler has an apply method that takes three arguments.4 The generated class’s apply method takes three arguments be- cause three is the number of arguments missing in the sum _ expression. The Scala compiler translates the expression a(1, 2, 3) into an invocation of the function value’s apply method, passing in the three arguments 1, 2, and 3. Thus, a(1, 2, 3) is a short form for: scala> a.apply(1, 2, 3) res12: Int = 6 This apply method, defined in the class generated automatically by the Scala compiler from the expression sum _, simply forwards those three miss- ing parameters to sum, and returns the result. In this case apply invokes sum(1, 2, 3), and returns what sum returns, which is 6. Another way to think about this kind of expression, in which an under- score is used to represent an entire parameter list, is as a way to transform a def into a function value. For example, if you have a local function, such as sum(a: Int, b: Int, c: Int): Int, you can “wrap” it in a function value whose apply method has the same parameter list and result types. When you apply this function value to some arguments, it in turn applies sum to 4The generated class extends trait Function3, which declares a three-arg apply method. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.6 Chapter 8 · Functions and Closures 194 those same arguments, and returns the result. Although you can’t assign a method or nested function to a variable, or pass it as an argument to another function, you can do these things if you wrap the method or nested function in a function value by placing an underscore after its name. Now, although sum _ is indeed a partially applied function, it may not be obvious to you why it is called this. It has this name because you are not applying that function to all of its arguments. In the case of sum _, you are applying it to none of its arguments. But you can also express a partially applied function by supplying some but not all of the required arguments. Here’s an example: scala> val b = sum(1, _: Int, 3) b: (Int) => Int = In this case, you’ve supplied the first and last argument to sum, but the mid- dle argument is missing. Since only one argument is missing, the Scala compiler generates a new function class whose apply method takes one ar- gument. When invoked with that one argument, this generated function’s apply method invokes sum, passing in 1, the argument passed to the func- tion, and 3. Here are some examples: scala> b(2) res13: Int = 6 In this case, b.apply invoked sum(1, 2, 3). scala> b(5) res14: Int = 9 And in this case, b.apply invoked sum(1, 5, 3). If you are writing a partially applied function expression in which you leave off all parameters, such as println _ or sum _, you can express it more concisely by leaving off the underscore if a function is required at that point in the code. For example, instead of printing out each of the numbers in someNumbers (defined on page 189) like this: someNumbers.foreach(println _) You could just write: someNumbers.foreach(println) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.7 Chapter 8 · Functions and Closures 195 This last form is allowed only in places where a function is required, such as the invocation of foreach in this example. The compiler knows a function is required in this case, because foreach requires that a function be passed as an argument. In situations where a function is not required, attempting to use this form will cause a compilation error. Here’s an example: scala> val c = sum :5: error: missing arguments for method sum... follow this method with `_' if you want to treat it as a partially applied function val c = sum ˆ scala> val d = sum _ d: (Int, Int, Int) => Int = scala> d(10, 20, 30) res15: Int = 60 8.7 Closures So far in this chapter, all the examples of function literals have referred only to passed parameters. For example, in (x: Int) => x > 0, the only variable used in the function body, x > 0, is x, which is defined as a parameter to the function. You can, however, refer to variables defined elsewhere: (x: Int) => x + more // how much more? This function adds “more” to its argument, but what is more? From the point of view of this function, more is a free variable, because the function literal does not itself give a meaning to it. The x variable, by contrast, is a bound variable, because it does have a meaning in the context of the function: it is defined as the function’s lone parameter, an Int. If you try using this function literal by itself, without any more defined in its scope, the compiler will complain: scala> (x: Int) => x + more :5: error: not found: value more (x: Int) => x + more ˆ Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.7 Chapter 8 · Functions and Closures 196 Why the trailing underscore? Scala’s syntax for partially applied functions highlights a difference in the design trade-offs of Scala and classical functional languages such as Haskell or ML. In these languages, partially applied functions are considered the normal case. Furthermore, these languages have a fairly strict static type system that will usually highlight every error with partial applications that you can make. Scala bears a much closer relation to imperative languages such as Java, where a method that’s not applied to all its arguments is considered an error. Furthermore, the object-oriented tradition of subtyping and a universal root type accepts some programs that would be considered erroneous in classical functional languages. For instance, say you mistook the drop(n: Int) method of List for tail(), and you therefore forgot you need to pass a number to drop. You might write, “println(drop)”. Had Scala adopted the classical functional tradition that partially applied functions are OK everywhere, this code would type check. However, you might be surprised to find out that the output printed by this println statement would always be ! What would have happened is that the expression drop would have been treated as a function object. Because println takes objects of any type, this would have compiled OK, but it would have given an unexpected result. To avoid situations like this, Scala normally requires you to specify function arguments that are left out explicitly, even if the indication is as simple as a ‘_’. Scala allows you to leave off even the _ only when a function type is expected. On the other hand, the same function literal will work fine so long as there is something available named more: scala> var more = 1 more: Int = 1 scala> val addMore = (x: Int) => x + more addMore: (Int) => Int = scala> addMore(10) res17: Int = 11 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.7 Chapter 8 · Functions and Closures 197 The function value (the object) that’s created at runtime from this function literal is called a closure. The name arises from the act of “closing” the func- tion literal by “capturing” the bindings of its free variables. A function literal with no free variables, such as (x: Int) => x + 1, is called a closed term, where a term is a bit of source code. Thus a function value created at run- time from this function literal is not a closure in the strictest sense, because (x: Int) => x + 1 is already closed as written. But any function literal with free variables, such as (x: Int) => x + more, is an open term. Therefore, any function value created at runtime from (x: Int) => x + more will by definition require that a binding for its free variable, more, be captured. The resulting function value, which will contain a reference to the captured more variable, is called a closure, therefore, because the function value is the end product of the act of closing the open term, (x: Int) => x + more. This example brings up a question: what happens if more changes af- ter the closure is created? In Scala, the answer is that the closure sees the change. For example: scala> more = 9999 more: Int = 9999 scala> addMore(10) res18: Int = 10009 Intuitively, Scala’s closures capture variables themselves, not the value to which variables refer.5 As the previous example demonstrates, the closure created for (x: Int) => x + more sees the change to more made outside the closure. The same is true in the opposite direction. Changes made by a closure to a captured variable are visible outside the closure. Here’s an example: scala> val someNumbers = List(-11,-10,-5, 0, 5, 10) someNumbers: List[Int] = List(-11, -10, -5, 0, 5, 10) scala> var sum = 0 sum: Int = 0 scala> someNumbers.foreach(sum += _) 5By contrast, Java’s inner classes do not allow you to access modifiable variables in surrounding scopes at all, so there is no difference between capturing a variable and capturing its currently held value. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.7 Chapter 8 · Functions and Closures 198 scala> sum res20: Int = -11 This example uses a roundabout way to sum the numbers in a List. Variable sum is in a surrounding scope from the function literal sum += _, which adds numbers to sum. Even though it is the closure modifying sum at runtime, the resulting total, -11, is still visible outside the closure. What if a closure accesses some variable that has several different copies as the program runs? For example, what if a closure uses a local variable of some function, and the function is invoked many times? Which instance of that variable gets used at each access? Only one answer is consistent with the rest of the language: the instance used is the one that was active at the time the closure was created. For example, here is a function that creates and returns “increase” closures: def makeIncreaser(more: Int) = (x: Int) => x + more Each time this function is called it will create a new closure. Each closure will access the more variable that was active when the closure was created. scala> val inc1 = makeIncreaser(1) inc1: (Int) => Int = scala> val inc9999 = makeIncreaser(9999) inc9999: (Int) => Int = When you call makeIncreaser(1), a closure is created and returned that captures the value 1 as the binding for more. Similarly, when you call makeIncreaser(9999), a closure that captures the value 9999 for more is returned. When you apply these closures to arguments (in this case, there’s just one argument, x, which must be passed in), the result that comes back depends on how more was defined when the closure was created: scala> inc1(10) res21: Int = 11 scala> inc9999(10) res22: Int = 10009 It makes no difference that the more in this case is a parameter to a method call that has already returned. The Scala compiler rearranges things in cases like this so that the captured parameter lives out on the heap, instead of the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.8 Chapter 8 · Functions and Closures 199 stack, and thus can outlive the method call that created it. This rearrangement is all taken care of automatically, so you don’t have to worry about it. Capture any variable you like: val, var, or parameter. 8.8 Special function call forms Most functions and function calls you encounter will be as you have seen so far in this chapter. The function will have a fixed number of parameters, the call will have an equal number of arguments, and the arguments will be specified in the same order and number as the parameters. Since function calls are so central to programming in Scala, however, a few special forms of function definitions and function calls have been added to the language to address some special needs. Scala supports repeated pa- rameters, named arguments, and default arguments. Repeated parameters Scala allows you to indicate that the last parameter to a function may be repeated. This allows clients to pass variable length argument lists to the function. To denote a repeated parameter, place an asterisk after the type of the parameter. For example: scala> def echo(args: String*) = for (arg <- args) println(arg) echo: (args: String*)Unit Defined this way, echo can be called with zero to many String arguments: scala> echo() scala> echo("one") one scala> echo("hello", "world!") hello world! Inside the function, the type of the repeated parameter is an Array of the declared type of the parameter. Thus, the type of args inside the echo function, which is declared as type “String*” is actually Array[String]. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.8 Chapter 8 · Functions and Closures 200 Nevertheless, if you have an array of the appropriate type, and you attempt to pass it as a repeated parameter, you’ll get a compiler error: scala> val arr = Array("What's", "up", "doc?") arr: Array[java.lang.String] = Array(What's, up, doc?) scala> echo(arr) :7: error: type mismatch; found : Array[java.lang.String] required: String echo(arr) ˆ To accomplish this, you’ll need to append the array argument with a colon and an _* symbol, like this: scala> echo(arr: _*) What's up doc? This notation tells the compiler to pass each element of arr as its own argu- ment to echo, rather than all of it as a single argument. Named arguments In a normal function call, the arguments in the call are matched one by one in the order of the parameters of the called function: scala> def speed(distance: Float, time: Float): Float = distance / time speed: (distance: Float,time: Float)Float scala> speed(100, 10) res28: Float = 10.0 In this call, the 100 is matched to distance and the 10 to time. The 100 and 10 are matched in the same order as the formal parameters are listed. Named arguments allow you to pass arguments to a function in a differ- ent order. The syntax is simply that each argument is preceded by a param- eter name and an equals sign. For example, the following call to speed is equivalent to speed(100,10): Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.8 Chapter 8 · Functions and Closures 201 scala> speed(distance = 100, time = 10) res29: Float = 10.0 Called with named arguments, the arguments can be reversed without changing the meaning: scala> speed(time = 10, distance = 100) res30: Float = 10.0 It is also possible to mix positional and named arguments. In that case, the positional arguments come first. Named arguments are most frequently used in combination with default parameter values. Default parameter values Scala lets you specify default values for function parameters. The argument for such a parameter can optionally be omitted from a function call, in which case the corresponding argument will be filled in with the default. An example is shown in Listing 8.3. Function printTime has one pa- rameter, out, and it has a default value of Console.out. def printTime(out: java.io.PrintStream = Console.out) = out.println("time = "+ System.currentTimeMillis()) Listing 8.3· A parameter with a default value. If you call the function as printTime(), thus specifying no argument to be used for out, then out will be set to its default value of Console.out. You could also call the function with an explicit output stream. For example, you could send logging to the standard error output by calling the function as printTime(Console.err). Default parameters are especially helpful when used in combination with named parameters. In Listing 8.4, function printTime2 has two optional parameters. The out parameter has a default of Console.out, and the divisor parameter has a default value of 1. Function printTime2 can be called as printTime2() to have both pa- rameters filled in with their default values. Using named arguments, how- ever, either one of the parameters can be specified while leaving the other as the default. To specify the output stream, call it like this: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.9 Chapter 8 · Functions and Closures 202 def printTime2(out: java.io.PrintStream = Console.out, divisor: Int = 1) = out.println("time = "+ System.currentTimeMillis()/divisor) Listing 8.4· A function with two parameters that have defaults. printTime2(out = Console.err) To specify the time divisor, call it like this: printTime2(divisor = 1000) 8.9 Tail recursion In Section 7.2, we mentioned that to transform a while loop that updates vars into a more functional style that uses only vals, you may sometimes need to use recursion. Here’s an example of a recursive function that approx- imates a value by repeatedly improving a guess until it is good enough: def approximate(guess: Double): Double = if (isGoodEnough(guess)) guess else approximate(improve(guess)) A function like this is often used in search problems, with appropriate imple- mentations for isGoodEnough and improve. If you want the approximate function to run faster, you might be tempted to write it with a while loop to try and speed it up, like this: def approximateLoop(initialGuess: Double): Double = { var guess = initialGuess while (!isGoodEnough(guess)) guess = improve(guess) guess } Which of the two versions of approximate is preferable? In terms of brevity and var avoidance, the first, functional one wins. But is the imperative ap- proach perhaps more efficient? In fact, if we measure execution times it turns Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.9 Chapter 8 · Functions and Closures 203 out that they are almost exactly the same! This might seem surprising, be- cause a recursive call looks much more expensive than a simple jump from the end of a loop to its beginning. However, in the case of approximate above, the Scala compiler is able to apply an important optimization. Note that the recursive call is the last thing that happens in the evaluation of function approximate’s body. Func- tions like approximate, which call themselves as their last action, are called tail recursive. The Scala compiler detects tail recursion and replaces it with a jump back to the beginning of the function, after updating the function parameters with the new values. The moral is that you should not shy away from using recursive algo- rithms to solve your problem. Often, a recursive solution is more elegant and concise than a loop-based one. If the solution is tail recursive, there won’t be any runtime overhead to be paid. Tracing tail-recursive functions A tail-recursive function will not build a new stack frame for each call; all calls will execute in a single frame. This may surprise a programmer inspect- ing a stack trace of a program that failed. For example, this function calls itself some number of times then throws an exception: def boom(x: Int): Int = if (x == 0) throw new Exception("boom!") else boom(x - 1) + 1 This function is not tail recursive, because it performs an increment operation after the recursive call. You’ll get what you expect when you run it: scala> boom(3) java.lang.Exception: boom! at .boom(:5) at .boom(:6) at .boom(:6) at .boom(:6) at .(:6) ... If you now modify boom so that it does become tail recursive: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.9 Chapter 8 · Functions and Closures 204 Tail call optimization The compiled code for approximate is essentially the same as the compiled code for approximateLoop. Both functions compile down to the same thirteen instructions of Java bytecodes. If you look through the bytecodes generated by the Scala compiler for the tail recursive method, approximate, you’ll see that although both isGoodEnough and improve are invoked in the body of the method, approximate is not. The Scala compiler optimized away the recursive call: public double approximate(double); Code: 0: aload_0 1: astore_3 2: aload_0 3: dload_1 4: invokevirtual #24; //Method isGoodEnough:(D)Z 7: ifeq 12 10: dload_1 11: dreturn 12: aload_0 13: dload_1 14: invokevirtual #27; //Method improve:(D)D 17: dstore_1 18: goto 2 def bang(x: Int): Int = if (x == 0) throw new Exception("bang!") else bang(x - 1) You’ll get: scala> bang(5) java.lang.Exception: bang! at .bang(:5) at .(:6) ... Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.9 Chapter 8 · Functions and Closures 205 This time, you see only a single stack frame for bang. You might think that bang crashed before it called itself, but this is not the case. If you think you might be confused by tail-call optimizations when looking at a stack trace, you can turn them off by giving the following argument to the scala shell or to the scalac compiler: -g:notailcalls With that option specified, you will get a longer stack trace: scala> bang(5) java.lang.Exception: bang! at .bang(:5) at .bang(:5) at .bang(:5) at .bang(:5) at .bang(:5) at .bang(:5) at .(:6) ... Limits of tail recursion The use of tail recursion in Scala is fairly limited, because the JVM instruc- tion set makes implementing more advanced forms of tail recursion very difficult. Scala only optimizes directly recursive calls back to the same func- tion making the call. If the recursion is indirect, as in the following example of two mutually recursive functions, no optimization is possible: def isEven(x: Int): Boolean = if (x == 0) true else isOdd(x - 1) def isOdd(x: Int): Boolean = if (x == 0) false else isEven(x - 1) You also won’t get a tail-call optimization if the final call goes to a function value. Consider for instance the following recursive code: val funValue = nestedFun _ def nestedFun(x: Int){ if (x != 0) { println(x); funValue(x - 1)} } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 8.10 Chapter 8 · Functions and Closures 206 The funValue variable refers to a function value that essentially wraps a call to nestedFun. When you apply the function value to an argument, it turns around and applies nestedFun to that same argument, and returns the result. You might hope, therefore, the Scala compiler would perform a tail-call opti- mization, but in this case it would not. Thus, tail-call optimization is limited to situations in which a method or nested function calls itself directly as its last operation, without going through a function value or some other inter- mediary. (If you don’t fully understand tail recursion yet, see Section 8.9). 8.10 Conclusion This chapter has given you a grand tour of functions in Scala. In addition to methods, Scala provides local functions, function literals, and function values. In addition to normal function calls, Scala provides partially applied functions and functions with repeated parameters. When possible, function calls are implemented as optimized tail calls, and thus many nice-looking recursive functions run just as quickly as hand-optimized versions that use while loops. The next chapter will build on these foundations and show how Scala’s rich support for functions helps you abstract over control. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 9 Control Abstraction In Chapter 7, we pointed out that Scala doesn’t have many built-in control abstractions, because it gives you the ability to create your own. In the pre- vious chapter, you learned about function values. In this chapter, we’ll show you how to apply function values to create new control abstractions. Along the way, you’ll also learn about currying and by-name parameters. 9.1 Reducing code duplication All functions are separated into common parts, which are the same in every invocation of the function, and non-common parts, which may vary from one function invocation to the next. The common parts are in the body of the function, while the non-common parts must be supplied via arguments. When you use a function value as an argument, the non-common part of the algorithm is itself some other algorithm! At each invocation of such a function, you can pass in a different function value as an argument, and the invoked function will, at times of its choosing, invoke the passed func- tion value. These higher-order functions—functions that take functions as parameters—give you extra opportunities to condense and simplify code. One benefit of higher-order functions is they enable you to create control abstractions that allow you to reduce code duplication. For example, suppose you are writing a file browser, and you want to provide an API that allows users to search for files matching some criterion. First, you add a facility to search for files whose names end in a particular string. This would enable your users to find, for example, all files with a “.scala” extension. You could provide such an API by defining a public filesEnding method inside Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.1 Chapter 9 · Control Abstraction 208 a singleton object like this: object FileMatcher { private def filesHere = (new java.io.File(".")).listFiles def filesEnding(query: String) = for (file <- filesHere; if file.getName.endsWith(query)) yield file } The filesEnding method obtains the list of all files in the current direc- tory using the private helper method filesHere, then filters them based on whether each file name ends with the user-specified query. Given filesHere is private, the filesEnding method is the only accessible method defined in FileMatcher, the API you provide to your users. So far so good, and there is no repeated code yet. Later on, though, you decide to let people search based on any part of the file name. This is good for when your users cannot remember if they named a file phb-important.doc, stupid-phb-report.doc, may2003salesdoc.phb, or something entirely different, but they think that “phb” appears in the name somewhere. You go back to work and add this function to your FileMatcher API: def filesContaining(query: String) = for (file <- filesHere; if file.getName.contains(query)) yield file This function works just like filesEnding. It searches filesHere, checks the name, and returns the file if the name matches. The only difference is that this function uses contains instead of endsWith. The months go by, and the program becomes more successful. Eventu- ally, you give in to the requests of a few power users who want to search based on regular expressions. These sloppy guys have immense directories with thousands of files, and they would like to do things like find all “pdf” files that have “oopsla” in the title somewhere. To support them, you write this function: def filesRegex(query: String) = for (file <- filesHere; if file.getName.matches(query)) yield file Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.1 Chapter 9 · Control Abstraction 209 Experienced programmers will notice all of this repetition and wonder if it can be factored into a common helper function. Doing it the obvious way does not work, however. You would like to be able to do the following: def filesMatching(query: String, method) = for (file <- filesHere; if file.getName.method(query)) yield file This approach would work in some dynamic languages, but Scala does not allow pasting together code at runtime like this. So what do you do? Function values provide an answer. While you cannot pass around a method name as a value, you can get the same effect by passing around a function value that calls the method for you. In this case, you could add a matcher parameter to the method whose sole purpose is to check a file name against a query: def filesMatching(query: String, matcher: (String, String) => Boolean) = { for (file <- filesHere; if matcher(file.getName, query)) yield file } In this version of the method, the if clause now uses matcher to check the file name against the query. Precisely what this check does depends on what is specified as the matcher. Take a look, now, at the type of matcher itself. It is a function, and thus has a => in the type. This function takes two string arguments—the file name and the query—and returns a boolean, so the type of this function is (String, String) => Boolean. Given this new filesMatching helper method, you can simplify the three searching methods by having them call the helper method, passing in an appropriate function: def filesEnding(query: String) = filesMatching(query, _.endsWith(_)) def filesContaining(query: String) = filesMatching(query, _.contains(_)) def filesRegex(query: String) = filesMatching(query, _.matches(_)) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.1 Chapter 9 · Control Abstraction 210 The function literals shown in this example use the placeholder syntax, in- troduced in the previous chapter, which may not as yet feel very natural to you. Thus, here’s a clarification of how placeholders are used in this exam- ple. The function literal _.endsWith(_), used in the filesEnding method, means the same thing as: (fileName: String, query: String) => fileName.endsWith(query) Because filesMatching takes a function that requires two String argu- ments, however, you need not specify the types of the arguments. Thus you could also write (fileName, query) => fileName.endsWith(query). Since the parameters are each used only once in the body of the function, and since the first parameter, fileName, is used first in the body, and the sec- ond parameter, query, is used second, you can use the placeholder syntax: _.endsWith(_). The first underscore is a placeholder for the first param- eter, the file name, and the second underscore a placeholder for the second parameter, the query string. This code is already simplified, but it can actually be even shorter. No- tice that the query gets passed to filesMatching, but filesMatching does nothing with the query except to pass it back to the passed matcher func- tion. This passing back and forth is unnecessary, because the caller already knew the query to begin with! You might as well simply remove the query parameter from filesMatching and matcher, thus simplifying the code as shown in Listing 9.1. This example demonstrates the way in which first-class functions can help you eliminate code duplication where it would be very difficult to do so without them. In Java, for example, you could create an interface con- taining a method that takes one String and returns a Boolean, then create and pass anonymous inner class instances that implement this interface to filesMatching. Although this approach would remove the code duplica- tion you are trying to eliminate, it would at the same time add as much or more new code. Thus the benefit is not worth the cost, and you may as well live with the duplication. Moreover, this example demonstrates how closures can help you reduce code duplication. The function literals used in the previous example, such as _.endsWith(_) and _.contains(_), are instantiated at runtime into func- tion values that are not closures, because they don’t capture any free vari- ables. Both variables used in the expression, _.endsWith(_), for example, are represented by underscores, which means they are taken from arguments Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.2 Chapter 9 · Control Abstraction 211 object FileMatcher{ private def filesHere = (new java.io.File(".")).listFiles private def filesMatching(matcher: String => Boolean) = for (file <- filesHere; if matcher(file.getName)) yield file def filesEnding(query: String) = filesMatching(_.endsWith(query)) def filesContaining(query: String) = filesMatching(_.contains(query)) def filesRegex(query: String) = filesMatching(_.matches(query)) } Listing 9.1· Using closures to reduce code duplication. to the function. Thus, _.endsWith(_) uses two bound variables, and no free variables. By contrast, the function literal _.endsWith(query), used in the most recent example, contains one bound variable, the argument represented by the underscore, and one free variable named query. It is only because Scala supports closures that you were able to remove the query parameter from filesMatching in the most recent example, thereby simplifying the code even further. 9.2 Simplifying client code The previous example demonstrated that higher-order functions can help re- duce code duplication as you implement an API. Another important use of higher-order functions is to put them in an API itself to make client code more concise. A good example is provided by the special-purpose looping methods of Scala’s collection types.1 Many of these are listed in Table 3.1 in Chapter 3, but take a look at just one example for now to see why these methods are so useful. 1These special-purpose looping methods are defined in trait Traversable, which is ex- tended by List, Set, and Map. See Chapter 17 for a discussion. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.2 Chapter 9 · Control Abstraction 212 Consider exists, a method that determines whether a passed value is contained in a collection. You could of course search for an element by having a var initialized to false, looping through the collection checking each item, and setting the var to true if you find what you are looking for. Here’s a method that uses this approach to determine whether a passed List contains a negative number: def containsNeg(nums: List[Int]): Boolean = { var exists = false for (num <- nums) if (num < 0) exists = true exists } If you define this method in the interpreter, you can call it like this: scala> containsNeg(List(1, 2, 3, 4)) res0: Boolean = false scala> containsNeg(List(1, 2,-3, 4)) res1: Boolean = true A more concise way to define the method, though, is by calling the higher- order function exists on the passed List, like this: def containsNeg(nums: List[Int]) = nums.exists(_ < 0) This version of containsNeg yields the same results as the previous: scala> containsNeg(Nil) res2: Boolean = false scala> containsNeg(List(0,-1,-2)) res3: Boolean = true The exists method represents a control abstraction. It is a special-purpose looping construct provided by the Scala library rather than being built into the Scala language like while or for. In the previous section, the higher- order function, filesMatching, reduces code duplication in the implemen- tation of the object FileMatcher. The exists method provides a similar benefit, but because exists is public in Scala’s collections API, the code Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.3 Chapter 9 · Control Abstraction 213 duplication it reduces is client code of that API. If exists didn’t exist, and you wanted to write a containsOdd method, to test whether a list contains odd numbers, you might write it like this: def containsOdd(nums: List[Int]): Boolean = { var exists = false for (num <- nums) if (num % 2 == 1) exists = true exists } If you compare the body of containsNeg with that of containsOdd, you’ll find that everything is repeated except the test condition of an if expression. Using exists, you could write this instead: def containsOdd(nums: List[Int]) = nums.exists(_ % 2 == 1) The body of the code in this version is again identical to the body of the cor- responding containsNeg method (the version that uses exists), except the condition for which to search is different. Yet the amount of code duplication is much smaller because all of the looping infrastructure is factored out into the exists method itself. There are many other looping methods in Scala’s standard library. As with exists, they can often shorten your code if you recognize opportunities to use them. 9.3 Currying In Chapter 1, we said that Scala allows you to create new control abstrac- tions that “feel like native language support.” Although the examples you’ve seen so far are indeed control abstractions, it is unlikely anyone would mis- take them for native language support. To understand how to make control abstractions that feel more like language extensions, you first need to under- stand the functional programming technique called currying. A curried function is applied to multiple argument lists, instead of just one. Listing 9.2 shows a regular, non-curried function, which adds two Int parameters, x and y. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.3 Chapter 9 · Control Abstraction 214 scala> def plainOldSum(x: Int, y: Int) = x + y plainOldSum: (x: Int,y: Int)Int scala> plainOldSum(1, 2) res4: Int = 3 Listing 9.2· Defining and invoking a “plain old” function. By contrast, Listing 9.3 shows a similar function that’s curried. Instead of one list of two Int parameters, you apply this function to two lists of one Int parameter each. scala> def curriedSum(x: Int)(y: Int) = x + y curriedSum: (x: Int)(y: Int)Int scala> curriedSum(1)(2) res5: Int = 3 Listing 9.3· Defining and invoking a curried function. What’s happening here is that when you invoke curriedSum, you actu- ally get two traditional function invocations back to back. The first function invocation takes a single Int parameter named x, and returns a function value for the second function. This second function takes the Int parameter y. Here’s a function named first that does in spirit what the first traditional function invocation of curriedSum would do: scala> def first(x: Int) = (y: Int) => x + y first: (x: Int)(Int) => Int Applying 1 to the first function—in other words, invoking the first function and passing in 1—yields the second function: scala> val second = first(1) second: (Int) => Int = Applying 2 to the second function yields the result: scala> second(2) res6: Int = 3 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.4 Chapter 9 · Control Abstraction 215 These first and second functions are just an illustration of the currying process. They are not directly connected to the curriedSum function. Nev- ertheless, there is a way to get an actual reference to curriedSum’s “second” function. You can use the placeholder notation to use curriedSum in a par- tially applied function expression, like this: scala> val onePlus = curriedSum(1)_ onePlus: (Int) => Int = The underscore in curriedSum(1)_ is a placeholder for the second parame- ter list.2 The result is a reference to a function that, when invoked, adds one to its sole Int argument and returns the result: scala> onePlus(2) res7: Int = 3 And here’s how you’d get a function that adds two to its sole Int argument: scala> val twoPlus = curriedSum(2)_ twoPlus: (Int) => Int = scala> twoPlus(2) res8: Int = 4 9.4 Writing new control structures In languages with first-class functions, you can effectively make new control structures even though the syntax of the language is fixed. All you need to do is create methods that take functions as arguments. For example, here is the “twice” control structure, which repeats an op- eration two times and returns the result: scala> def twice(op: Double => Double, x: Double) = op(op(x)) twice: (op: (Double) => Double,x: Double)Double scala> twice(_ + 1, 5) res9: Double = 7.0 2In the previous chapter, when the placeholder notation was used on traditional methods, like println _, you had to leave a space between the name and the underscore. In this case you don’t, because whereas println_ is a legal identifier in Scala, curriedSum(1)_ is not. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.4 Chapter 9 · Control Abstraction 216 The type of op in this example is Double => Double, which means it is a function that takes one Double as an argument and returns another Double. Any time you find a control pattern repeated in multiple parts of your code, you should think about implementing it as a new control structure. Earlier in the chapter you saw filesMatching, a very specialized control pattern. Consider now a more widely used coding pattern: open a resource, operate on it, and then close the resource. You can capture this in a control abstraction using a method like the following: def withPrintWriter(file: File, op: PrintWriter => Unit){ val writer = new PrintWriter(file) try { op(writer) } finally { writer.close() } } Given such a method, you can use it like this: withPrintWriter( new File("date.txt"), writer => writer.println(new java.util.Date) ) The advantage of using this method is that it’s withPrintWriter, not user code, that assures the file is closed at the end. So it’s impossible to for- get to close the file. This technique is called the loan pattern, because a control-abstraction function, such as withPrintWriter, opens a resource and “loans” it to a function. For instance, withPrintWriter in the previ- ous example loans a PrintWriter to the function, op. When the function completes, it signals that it no longer needs the “borrowed” resource. The resource is then closed in a finally block, to ensure it is indeed closed, re- gardless of whether the function completes by returning normally or throw- ing an exception. One way in which you can make the client code look a bit more like a built-in control structure is to use curly braces instead of parentheses to sur- round the argument list. In any method invocation in Scala in which you’re passing in exactly one argument, you can opt to use curly braces to surround the argument instead of parentheses. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.4 Chapter 9 · Control Abstraction 217 For example, instead of: scala> println("Hello, world!") Hello, world! You could write: scala> println { "Hello, world!" } Hello, world! In the second example, you used curly braces instead of parentheses to sur- round the arguments to println. This curly braces technique will work, however, only if you’re passing in one argument. Here’s an attempt at vio- lating that rule: scala> val g = "Hello, world!" g: java.lang.String = Hello, world! scala> g.substring { 7, 9 } :1: error: ';' expected but ',' found. g.substring { 7, 9 } ˆ Because you are attempting to pass in two arguments to substring, you get an error when you try to surround those arguments with curly braces. Instead, you’ll need to use parentheses: scala> g.substring(7, 9) res12: java.lang.String = wo The purpose of this ability to substitute curly braces for parentheses for passing in one argument is to enable client programmers to write function literals between curly braces. This can make a method call feel more like a control abstraction. Take the withPrintWriter method defined previously as an example. In its most recent form, withPrintWriter takes two ar- guments, so you can’t use curly braces. Nevertheless, because the function passed to withPrintWriter is the last argument in the list, you can use cur- rying to pull the first argument, the File, into a separate argument list. This will leave the function as the lone parameter of the second argument list. Listing 9.4 shows how you’d need to redefine withPrintWriter. The new version differs from the old one only in that there are now two parameter lists with one parameter each instead of one parameter list with Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.5 Chapter 9 · Control Abstraction 218 def withPrintWriter(file: File)(op: PrintWriter => Unit){ val writer = new PrintWriter(file) try { op(writer) } finally { writer.close() } } Listing 9.4· Using the loan pattern to write to a file. two parameters. Look between the two parameters. In the previous version of withPrintWriter, shown on page 216, you see . . . File, op. . . . But in this version, you see . . . File)(op. . . . Given the above definition, you can call the method with a more pleasing syntax: val file = new File("date.txt") withPrintWriter(file) { writer => writer.println(new java.util.Date) } In this example, the first argument list, which contains one File argument, is written surrounded by parentheses. The second argument list, which contains one function argument, is surrounded by curly braces. 9.5 By-name parameters The withPrintWriter method shown in the previous section differs from built-in control structures of the language, such as if and while, in that the code between the curly braces takes an argument. The withPrintWriter method requires one argument of type PrintWriter. This argument shows up as the “writer =>” in: withPrintWriter(file) { writer => writer.println(new java.util.Date) } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.5 Chapter 9 · Control Abstraction 219 What if you want to implement something more like if or while, however, where there is no value to pass into the code between the curly braces? To help with such situations, Scala provides by-name parameters. As a concrete example, suppose you want to implement an assertion con- struct called myAssert.3 The myAssert function will take a function value as input and consult a flag to decide what to do. If the flag is set, myAssert will invoke the passed function and verify that it returns true. If the flag is turned off, myAssert will quietly do nothing at all. Without using by-name parameters, you could write myAssert like this: var assertionsEnabled = true def myAssert(predicate: () => Boolean) = if (assertionsEnabled && !predicate()) throw new AssertionError The definition is fine, but using it is a little bit awkward: myAssert(() => 5 > 3) You would really prefer to leave out the empty parameter list and => symbol in the function literal and write the code like this: myAssert(5 > 3) // Won’t work, because missing () => By-name parameters exist precisely so that you can do this. To make a by- name parameter, you give the parameter a type starting with => instead of () =>. For example, you could change myAssert’s predicate parame- ter into a by-name parameter by changing its type, “() => Boolean”, into “=> Boolean”. Listing 9.5 shows how that would look: def byNameAssert(predicate: => Boolean) = if (assertionsEnabled && !predicate) throw new AssertionError Listing 9.5· Using a by-name parameter. Now you can leave out the empty parameter in the property you want to assert. The result is that using byNameAssert looks exactly like using a built-in control structure: 3You’ll call this myAssert, not assert, because Scala provides an assert of its own, which will be described in Section 14.1. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.5 Chapter 9 · Control Abstraction 220 byNameAssert(5 > 3) A by-name type, in which the empty parameter list, (), is left out, is only allowed for parameters. There is no such thing as a by-name variable or a by-name field. Now, you may be wondering why you couldn’t simply write myAssert using a plain old Boolean for the type of its parameter, like this: def boolAssert(predicate: Boolean) = if (assertionsEnabled && !predicate) throw new AssertionError This formulation is also legal, of course, and the code using this version of boolAssert would still look exactly as before: boolAssert(5 > 3) Nevertheless, one difference exists between these two approaches that is im- portant to note. Because the type of boolAssert’s parameter is Boolean, the expression inside the parentheses in boolAssert(5 > 3) is evaluated be- fore the call to boolAssert. The expression 5 > 3 yields true, which is passed to boolAssert. By contrast, because the type of byNameAssert’s predicate parameter is => Boolean, the expression inside the parentheses in byNameAssert(5 > 3) is not evaluated before the call to byNameAssert. Instead a function value will be created whose apply method will evaluate 5 > 3, and this function value will be passed to byNameAssert. The difference between the two approaches, therefore, is that if asser- tions are disabled, you’ll see any side effects that the expression inside the parentheses may have in boolAssert, but not in byNameAssert. For exam- ple, if assertions are disabled, attempting to assert on “x / 0 == 0” will yield an exception in boolAssert’s case: scala> var assertionsEnabled = false assertionsEnabled: Boolean = false scala> boolAssert(x / 0 == 0) java.lang.ArithmeticException: / by zero at .(:9) at .() at RequestResult$.(:9) at RequestResult$.() Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 9.6 Chapter 9 · Control Abstraction 221 But attempting to assert on the same code in byNameAssert’s case will not yield an exception: scala> byNameAssert(x / 0 == 0) 9.6 Conclusion This chapter has shown you how to build on Scala’s rich function support to build control abstractions. You can use functions within your code to factor out common control patterns, and you can take advantage of higher- order functions in the Scala library to reuse control patterns that are common across all programmers’ code. This chapter has also shown how to use cur- rying and by-name parameters so that your own higher-order functions can be used with a concise syntax. In the previous chapter and this one, you have seen quite a lot of infor- mation about functions. The next few chapters will go back to discussing more object-oriented features of the language. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 10 Composition and Inheritance Chapter 6 introduced some basic object-oriented aspects of Scala. This chap- ter will pick up where Chapter 6 left off and dive with much greater detail into Scala’s support for object-oriented programming. We’ll compare two fundamental relationships between classes: composition and inheritance. Composition means one class holds a reference to another, using the refer- enced class to help it fulfill its mission. Inheritance is the superclass/subclass relationship. In addition to these topics, we’ll discuss abstract classes, pa- rameterless methods, extending classes, overriding methods and fields, para- metric fields, invoking superclass constructors, polymorphism and dynamic binding, final members and classes, and factory objects and methods. 10.1 A two-dimensional layout library As a running example in this chapter, we’ll create a library for building and rendering two-dimensional layout elements. Each element will represent a rectangle filled with text. For convenience, the library will provide factory methods named “elem” that construct new elements from passed data. For example, you’ll be able to create a layout element containing a string using a factory method with the following signature: elem(s: String): Element As you can see, elements will be modeled with a type named Element. You’ll be able to call above or beside on an element, passing in a sec- ond element, to get a new element that combines the two. For example, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.2 Chapter 10 · Composition and Inheritance 223 the following expression would construct a larger element consisting of two columns, each with a height of two: val column1 = elem("hello") above elem("***") val column2 = elem("***") above elem("world") column1 beside column2 Printing the result of this expression would give: hello *** *** world Layout elements are a good example of a system in which objects can be constructed from simple parts with the aid of composing operators. In this chapter, we’ll define classes that enable element objects to be constructed from arrays, lines, and rectangles—the simple parts. We’ll also define com- posing operators above and beside. Such composing operators are also often called combinators because they combine elements of some domain into new elements. Thinking in terms of combinators is generally a good way to approach library design: it pays to think about the fundamental ways to construct ob- jects in an application domain. What are the simple objects? In what ways can more interesting objects be constructed out of simpler ones? How do combinators hang together? What are the most general combinations? Do they satisfy any interesting laws? If you have good answers to these ques- tions, your library design is on track. 10.2 Abstract classes Our first task is to define type Element, which represents layout elements. Since elements are two dimensional rectangles of characters, it makes sense to include a member, contents, that refers to the contents of a layout el- ement. The contents can be represented as an array of strings, where each string represents a line. Hence, the type of the result returned by contents will be Array[String]. Listing 10.1 shows what it will look like. In this class, contents is declared as a method that has no implementa- tion. In other words, the method is an abstract member of class Element.A class with abstract members must itself be declared abstract, which is done by writing an abstract modifier in front of the class keyword: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.3 Chapter 10 · Composition and Inheritance 224 abstract class Element { def contents: Array[String] } Listing 10.1· Defining an abstract method and class. abstract class Element ... The abstract modifier signifies that the class may have abstract members that do not have an implementation. As a result, you cannot instantiate an abstract class. If you try to do so, you’ll get a compiler error: scala> new Element :5: error: class Element is abstract; cannot be instantiated new Element ˆ Later in this chapter you’ll see how to create subclasses of class Element, which you’ll be able to instantiate because they fill in the missing definition for contents. Note that the contents method in class Element does not carry an abstract modifier. A method is abstract if it does not have an implemen- tation (i.e., no equals sign or body). Unlike Java, no abstract modifier is necessary (or allowed) on method declarations. Methods that do have an implementation are called concrete. Another bit of terminology distinguishes between declarations and defi- nitions. Class Element declares the abstract method contents, but currently defines no concrete methods. In the next section, however, we’ll enhance Element by defining some concrete methods. 10.3 Defining parameterless methods As a next step, we’ll add methods to Element that reveal its width and height, as shown in Listing 10.2. The height method returns the number of lines in contents. The width method returns the length of the first line, or, if there are no lines in the element, zero. (This means you cannot define an element with a height of zero and a non-zero width.) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.3 Chapter 10 · Composition and Inheritance 225 abstract class Element { def contents: Array[String] def height: Int = contents.length def width: Int = if (height == 0) 0 else contents(0).length } Listing 10.2· Defining parameterless methods width and height. Note that none of Element’s three methods has a parameter list, not even an empty one. For example, instead of: def width(): Int the method is defined without parentheses: def width: Int Such parameterless methods are quite common in Scala. By contrast, meth- ods defined with empty parentheses, such as def height(): Int, are called empty-paren methods. The recommended convention is to use a parame- terless method whenever there are no parameters and the method accesses mutable state only by reading fields of the containing object (in particular, it does not change mutable state). This convention supports the uniform access principle,1 which says that client code should not be affected by a decision to implement an attribute as a field or method. For instance, we could have chosen to implement width and height as fields instead of methods, simply by changing the def in each definition to a val: abstract class Element { def contents: Array[String] val height = contents.length val width = if (height == 0) 0 else contents(0).length } The two pairs of definitions are completely equivalent from a client’s point of view. The only difference is that field accesses might be slightly faster than method invocations, because the field values are pre-computed when the 1Meyer, Object-Oriented Software Construction [Mey00] Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.3 Chapter 10 · Composition and Inheritance 226 class is initialized, instead of being computed on each method call. On the other hand, the fields require extra memory space in each Element object. So it depends on the usage profile of a class whether an attribute is better represented as a field or method, and that usage profile might change over time. The point is that clients of the Element class should not be affected when its internal implementation changes. In particular, a client of class Element should not need to be rewritten if a field of that class gets changed into an access function so long as the access function is pure, i.e., it does not have any side effects and does not depend on mutable state. The client should not need to care either way. So far so good. But there’s still a slight complication that has to do with the way Java handles things. The problem is that Java does not imple- ment the uniform access principle. So it’s string.length() in Java, not string.length (even though it’s array.length, not array.length()). Needless to say, this is very confusing. To bridge that gap, Scala is very liberal when it comes to mixing param- eterless and empty-paren methods. In particular, you can override a param- eterless method with an empty-paren method, and vice versa. You can also leave off the empty parentheses on an invocation of any function that takes no arguments. For instance, the following two lines are both legal in Scala: Array(1, 2, 3).toString "abc".length In principle it’s possible to leave out all empty parentheses in Scala func- tion calls. However, it is recommended to still write the empty parentheses when the invoked method represents more than a property of its receiver ob- ject. For instance, empty parentheses are appropriate if the method performs I/O, or writes reassignable variables (vars), or reads vars other than the re- ceiver’s fields, either directly or indirectly by using mutable objects. That way, the parameter list acts as a visual clue that some interesting computa- tion is triggered by the call. For instance: "hello".length // no () because no side-effect println() // better to not drop the () To summarize, it is encouraged style in Scala to define methods that take no parameters and have no side effects as parameterless methods, i.e., leaving off the empty parentheses. On the other hand, you should never define a Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.4 Chapter 10 · Composition and Inheritance 227 method that has side-effects without parentheses, because then invocations of that method would look like a field selection. So your clients might be surprised to see the side effects. Similarly, whenever you invoke a function that has side effects, be sure to include the empty parentheses when you write the invocation. Another way to think about this is if the function you’re calling performs an operation, use the parentheses, but if it merely provides access to a property, leave the parentheses off. 10.4 Extending classes We still need to be able to create new element objects. You have already seen that “new Element” cannot be used for this because class Element is abstract. To instantiate an element, therefore, we will need to create a sub- class that extends Element and implements the abstract contents method. Listing 10.3 shows one possible way to do that: class ArrayElement(conts: Array[String]) extends Element { def contents: Array[String] = conts } Listing 10.3· Defining ArrayElement as a subclass of Element. Class ArrayElement is defined to extend class Element. Just like in Java, you use an extends clause after the class name to express this: ... extends Element ... Such an extends clause has two effects: it makes class ArrayElement in- herit all non-private members from class Element, and it makes the type ArrayElement a subtype of the type Element. Given ArrayElement ex- tends Element, class ArrayElement is called a subclass of class Element. Conversely, Element is a superclass of ArrayElement. If you leave out an extends clause, the Scala compiler implicitly as- sumes your class extends from scala.AnyRef, which on the Java platform is the same as class java.lang.Object. Thus, class Element implicitly extends class AnyRef. You can see these inheritance relationships in Fig- ure 10.1. Inheritance means that all members of the superclass are also members of the subclass, with two exceptions. First, private members of the super- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.4 Chapter 10 · Composition and Inheritance 228 scala AnyRef «java.lang.Object» ArrayElement Array[String] Element «abstract» Figure 10.1· Class diagram for ArrayElement. class are not inherited in a subclass. Second, a member of a superclass is not inherited if a member with the same name and parameters is already im- plemented in the subclass. In that case we say the member of the subclass overrides the member of the superclass. If the member in the subclass is concrete and the member of the superclass is abstract, we also say that the concrete member implements the abstract one. For example, the contents method in ArrayElement overrides (or, al- ternatively: implements) abstract method contents in class Element.2 By contrast, class ArrayElement inherits the width and height methods from class Element. For example, given an ArrayElement ae, you can query its width using ae.width, as if width were defined in class ArrayElement: scala> val ae = new ArrayElement(Array("hello", "world")) ae: ArrayElement = ArrayElement@d94e60 scala> ae.width res1: Int = 5 2One flaw with this design is that because the returned array is mutable, clients could change it. For the book we’ll keep things simple, but were ArrayElement part of a real project, you might consider returning a defensive copy of the array instead. Another problem is we aren’t currently ensuring that every String element of the contents array has the same length. This could be solved by checking the precondition in the primary constructor, and throwing an exception if it is violated. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.5 Chapter 10 · Composition and Inheritance 229 Subtyping means that a value of the subclass can be used wherever a value of the superclass is required. For example: val e: Element = new ArrayElement(Array("hello")) Variable e is defined to be of type Element, so its initializing value should also be an Element. In fact, the initializing value’s type is ArrayElement. This is OK, because class ArrayElement extends class Element, and as a result, the type ArrayElement is compatible with the type Element.3 Figure 10.1 also shows the composition relationship that exists between ArrayElement and Array[String]. This relationship is called composition because class ArrayElement is “composed” out of class Array[String], in that the Scala compiler will place into the binary class it generates for ArrayElement a field that holds a reference to the passed conts array. We’ll discuss some design considerations concerning composition and inheritance later in this chapter, in Section 10.11. 10.5 Overriding methods and fields The uniform access principle is just one aspect where Scala treats fields and methods more uniformly than Java. Another difference is that in Scala, fields and methods belong to the same namespace. This makes it possible for a field to override a parameterless method. For instance, you could change the implementation of contents in class ArrayElement from a method to a field without having to modify the abstract method definition of contents in class Element, as shown in Listing 10.4: class ArrayElement(conts: Array[String]) extends Element { val contents: Array[String] = conts } Listing 10.4· Overriding a parameterless method with a field. Field contents (defined with a val) in this version of ArrayElement is a perfectly good implementation of the parameterless method contents (declared with a def) in class Element. 3For more perspective on the difference between subclass and subtype, see the glossary entry for subtype. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.6 Chapter 10 · Composition and Inheritance 230 On the other hand, in Scala it is forbidden to define a field and method with the same name in the same class, whereas it is allowed in Java. For example, this Java class would compile just fine: // This is Java class CompilesFine { private int f = 0; public int f() { return 1; } } But the corresponding Scala class would not compile: class WontCompile{ private varf= 0 // Won’t compile, because a field def f = 1 // and method have the same name } Generally, Scala has just two namespaces for definitions in place of Java’s four. Java’s four namespaces are fields, methods, types, and packages. By contrast, Scala’s two namespaces are: • values (fields, methods, packages, and singleton objects) • types (class and trait names) The reason Scala places fields and methods into the same namespace is pre- cisely so you can override a parameterless method with a val, something you can’t do with Java.4 10.6 Defining parametric fields Consider again the definition of class ArrayElement shown in the previous section. It has a parameter conts whose sole purpose is to be copied into the contents field. The name conts of the parameter was chosen just so that 4The reason that packages share the same namespace as fields and methods in Scala is to enable you to import packages in addition to just importing the names of types, and the fields and methods of singleton objects. This is also something you can’t do in Java. It will be described in Section 13.3. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.6 Chapter 10 · Composition and Inheritance 231 it would look similar to the field name contents without actually clashing with it. This is a “code smell,” a sign that there may be some unnecessary redundancy and repetition in your code. You can avoid the code smell by combining the parameter and the field in a single parametric field definition, as shown in Listing 10.5: class ArrayElement( val contents: Array[String] ) extends Element Listing 10.5· Defining contents as a parametric field. Note that now the contents parameter is prefixed by val. This is a shorthand that defines at the same time a parameter and field with the same name. Specifically, class ArrayElement now has an (unreassignable) field contents, which can be accessed from outside the class. The field is initial- ized with the value of the parameter. It’s as if the class had been written as follows, where x123 is an arbitrary fresh name for the parameter: class ArrayElement(x123: Array[String]) extends Element { val contents: Array[String] = x123 } You can also prefix a class parameter with var, in which case the correspond- ing field would be reassignable. Finally, it is possible to add modifiers such as private, protected,5 or override to these parametric fields, just as you can do for any other class member. Consider, for instance, the following class definitions: class Cat { val dangerous = false } class Tiger( override val dangerous: Boolean, private var age: Int ) extends Cat 5The protected modifier, which grants access to subclasses, will be covered in detail in Chapter 13. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.7 Chapter 10 · Composition and Inheritance 232 Tiger’s definition is a shorthand for the following alternate class definition with an overriding member dangerous and a private member age: class Tiger(param1: Boolean, param2: Int) extends Cat { override val dangerous = param1 private var age = param2 } Both members are initialized from the corresponding parameters. We chose the names of those parameters, param1 and param2, arbitrarily. The impor- tant thing was that they not clash with any other name in scope. 10.7 Invoking superclass constructors You now have a complete system consisting of two classes: an abstract class Element, which is extended by a concrete class ArrayElement. You might also envision other ways to express an element. For example, clients might want to create a layout element consisting of a single line given by a string. Object-oriented programming makes it easy to extend a system with new data-variants. You can simply add subclasses. For example, Listing 10.6 shows a LineElement class that extends ArrayElement: class LineElement(s: String) extends ArrayElement(Array(s)) { override def width = s.length override def height = 1 } Listing 10.6· Invoking a superclass constructor. Since LineElement extends ArrayElement, and ArrayElement’s con- structor takes a parameter (an Array[String]), LineElement needs to pass an argument to the primary constructor of its superclass. To invoke a super- class constructor, you simply place the argument or arguments you want to pass in parentheses following the name of the superclass. For example, class LineElement passes Array(s) to ArrayElement’s primary constructor by placing it in parentheses after the superclass ArrayElement’s name: ... extends ArrayElement(Array(s)) ... Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.8 Chapter 10 · Composition and Inheritance 233 Element «abstract» ArrayElement Array[String] LineElement Figure 10.2· Class diagram for LineElement. With the new subclass, the inheritance hierarchy for layout elements now looks as shown in Figure 10.2. 10.8 Using override modifiers Note that the definitions of width and height in LineElement carry an override modifier. In Section 6.3, you saw this modifier in the definition of a toString method. Scala requires such a modifier for all members that override a concrete member in a parent class. The modifier is optional if a member implements an abstract member with the same name. The modifier is forbidden if a member does not override or implement some other member in a base class. Since height and width in class LineElement override concrete definitions in class Element, override is required. This rule provides useful information for the compiler that helps avoid some hard-to-catch errors and makes system evolution safer. For instance, if you happen to misspell the method or accidentally give it a different param- eter list, the compiler will respond with an error message: $ scalac LineElement.scala .../LineElement.scala:50: error: method hight overrides nothing override def hight = 1 ˆ Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.8 Chapter 10 · Composition and Inheritance 234 The override convention is even more important when it comes to system evolution. Say you defined a library of 2D drawing methods. You made it publicly available, and it is widely used. In the next version of the library you want to add to your base class Shape a new method with this signature: def hidden(): Boolean Your new method will be used by various drawing methods to determine whether a shape needs to be drawn. This could lead to a significant speedup, but you cannot do this without the risk of breaking client code. After all, a client could have defined a subclass of Shape with a different implementation of hidden. Perhaps the client’s method actually makes the receiver object disappear instead of testing whether the object is hidden. Because the two versions of hidden override each other, your drawing methods would end up making objects disappear, which is certainly not what you want! These “ac- cidental overrides” are the most common manifestation of what is called the “fragile base class” problem. The problem is that if you add new members to base classes (which we usually call superclasses) in a class hierarchy, you risk breaking client code. Scala cannot completely solve the fragile base class problem, but it im- proves on the situation compared to Java.6 If the drawing library and its clients were written in Scala, then the client’s original implementation of hidden could not have had an override modifier, because at the time there was no other method with that name. Once you add the hidden method to the second version of your shape class, a recompile of the client would give an error like the following: .../Shapes.scala:6: error: error overriding method hidden in class Shape of type ()Boolean; method hidden needs `override' modifier def hidden(): Boolean = ˆ That is, instead of wrong behavior your client would get a compile-time error, which is usually much preferable. 6In Java 1.5, an @Override annotation was introduced that works similarly to Scala’s override modifier, but unlike Scala’s override, is not required. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.9 Chapter 10 · Composition and Inheritance 235 10.9 Polymorphism and dynamic binding You saw in Section 10.4 that a variable of type Element could refer to an object of type ArrayElement. The name for this phenomenon is poly- morphism, which means “many shapes” or “many forms.” In this case, Element objects can have many forms.7 So far, you’ve seen two such forms: ArrayElement and LineElement. You can create more forms of Element by defining new Element subclasses. For example, here’s how you could define a new form of Element that has a given width and height and is filled everywhere with a given character: class UniformElement( ch: Char, override val width: Int, override val height: Int ) extends Element { private val line = ch.toString * width def contents = Array.fill(height)(line) } The inheritance hierarchy for class Element now looks as shown in Fig- ure 10.3. As a result, Scala will accept all of the following assignments, because the assigning expression’s type conforms to the type of the defined variable: val e1: Element = new ArrayElement(Array("hello", "world")) val ae: ArrayElement = new LineElement("hello") val e2: Element = ae val e3: Element = new UniformElement('x', 2, 3) If you check the inheritance hierarchy, you’ll find that in each of these four val definitions, the type of the expression to the right of the equals sign is below the type of the val being initialized to the left of the equals sign. The other half of the story, however, is that method invocations on vari- ables and expressions are dynamically bound. This means that the actual method implementation invoked is determined at run time based on the class of the object, not the type of the variable or expression. To demonstrate this 7This kind of polymorphism is called subtyping polymorphism. Another kind of poly- morphism in Scala, called universal polymorphism, is discussed in Chapter 19. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.9 Chapter 10 · Composition and Inheritance 236 Element «abstract» UniformElement ArrayElement LineElement Figure 10.3· Class hierarchy of layout elements. behavior, we’ll temporarily remove all existing members from our Element classes and add a method named demo to Element. We’ll override demo in ArrayElement and LineElement, but not in UniformElement: abstract class Element { def demo() { println("Element's implementation invoked") } } class ArrayElement extends Element { override def demo() { println("ArrayElement's implementation invoked") } } class LineElement extends ArrayElement { override def demo() { println("LineElement's implementation invoked") } } // UniformElement inherits Element’s demo class UniformElement extends Element If you enter this code into the interpreter, you can then define this method Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.10 Chapter 10 · Composition and Inheritance 237 that takes an Element and invokes demo on it: def invokeDemo(e: Element){ e.demo() } If you pass an ArrayElement to invokeDemo, you’ll see a message indicat- ing ArrayElement’s implementation of demo was invoked, even though the type of the variable, e, on which demo was invoked is Element: scala> invokeDemo(new ArrayElement) ArrayElement's implementation invoked Similarly, if you pass a LineElement to invokeDemo, you’ll see a message that indicates LineElement’s demo implementation was invoked: scala> invokeDemo(new LineElement) LineElement's implementation invoked The behavior when passing a UniformElement may at first glance look sus- picious, but it is correct: scala> invokeDemo(new UniformElement) Element's implementation invoked Because UniformElement does not override demo, it inherits the implemen- tation of demo from its superclass, Element. Thus, Element’s implementa- tion is the correct implementation of demo to invoke when the class of the object is UniformElement. 10.10 Declaring final members Sometimes when designing an inheritance hierarchy, you want to ensure that a member cannot be overridden by subclasses. In Scala, as in Java, you do this by adding a final modifier to the member. For example, you could place a final modifier on ArrayElement’s demo method, as shown in List- ing 10.7. Given this version of ArrayElement, an attempt to override demo in its subclass, LineElement, would not compile: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.10 Chapter 10 · Composition and Inheritance 238 class ArrayElement extends Element { final override def demo() { println("ArrayElement's implementation invoked") } } Listing 10.7· Declaring a final method. elem.scala:18: error: error overriding method demo in class ArrayElement of type ()Unit; method demo cannot override final member override def demo() { ˆ You may also at times want to ensure that an entire class not be sub- classed. To do this you simply declare the entire class final by adding a final modifier to the class declaration. For example, Listing 10.8 shows how you would declare ArrayElement final: final class ArrayElement extends Element { override def demo() { println("ArrayElement's implementation invoked") } } Listing 10.8· Declaring a final class. With this version of ArrayElement, any attempt at defining a subclass would fail to compile: elem.scala: 18: error: illegal inheritance from final class ArrayElement class LineElement extends ArrayElement { ˆ We’ll now remove the final modifiers and demo methods, and go back to the earlier implementation of the Element family. We’ll focus our atten- tion in the remainder of this chapter to completing a working version of the layout library. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.11 Chapter 10 · Composition and Inheritance 239 10.11 Using composition and inheritance Composition and inheritance are two ways to define a new class in terms of another existing class. If what you’re after is primarily code reuse, you should in general prefer composition to inheritance. Only inheritance suffers from the fragile base class problem, in which you can inadvertently break subclasses by changing a superclass. One question you can ask yourself about an inheritance relationship is whether it models an is-a relationship.8 For example, it would be reasonable to say that ArrayElement is-an Element. Another question you can ask is whether clients will want to use the subclass type as a superclass type.9 In the case of ArrayElement, we do indeed expect clients will want to use an ArrayElement as an Element. If you ask these questions about the inheritance relationships shown in Figure 10.3, do any of the relationships seem suspicious? In particular, does it seem obvious to you that a LineElement is-an ArrayElement? Do you think clients would ever need to use a LineElement as an ArrayElement? In fact, we defined LineElement as a subclass of ArrayElement primarily to reuse ArrayElement’s definition of contents. Perhaps it would be better, therefore, to define LineElement as a direct subclass of Element, like this: class LineElement(s: String) extends Element { val contents = Array(s) override def width = s.length override def height = 1 } In the previous version, LineElement had an inheritance relationship with ArrayElement, from which it inherited contents. It now has a composition relationship with Array: it holds a reference to an array of strings from its own contents field.10 Given this implementation of LineElement, the inheritance hierarchy for Element now looks as shown in Figure 10.4. 8Meyers, Effective C++ [Mey91] 9Eckel, Thinking in Java [Eck98] 10Class ArrayElement also has a composition relationship with Array, because its para- metric contents field holds a reference to an array of strings. The code for ArrayElement is shown in Listing 10.5 on page 231. Its composition relationship is represented in class diagrams by a diamond, as shown, for example, in Figure 10.1 on page 228. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.12 Chapter 10 · Composition and Inheritance 240 Element «abstract» LineElementArrayElement UniformElement Figure 10.4· Class hierarchy with revised LineElement. 10.12 Implementing above, beside, and toString As a next step, we’ll implement method above in class Element. Putting one element above another means concatenating the two contents values of the elements. So a first draft of method above could look like this: def above(that: Element): Element = new ArrayElement(this.contents ++ that.contents) The ++ operation concatenates two arrays. Arrays in Scala are represented as Java arrays, but support many more methods. Specifically, arrays in Scala can be converted to instances of a class scala.Seq, which represents sequence-like structures and contains a number of methods for accessing and transforming sequences. Some other array methods will be explained in this chapter, and a comprehensive discussion will be given in Chapter 17. In fact, the code shown previously is not quite sufficient, because it does not permit you to put elements of different widths on top of each other. To keep things simple in this section, however, we’ll leave this as is and only pass elements of the same length to above. In Section 10.14, we’ll make an enhancement to above so that clients can use it to combine elements of different widths. The next method to implement is beside. To put two elements beside each other, we’ll create a new element in which every line results from con- catenating corresponding lines of the two elements. As before, to keep things simple we’ll start by assuming the two elements have the same height. This leads to the following design of method beside: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.12 Chapter 10 · Composition and Inheritance 241 def beside(that: Element): Element = { val contents = new Array[String](this.contents.length) for (i <- 0 until this.contents.length) contents(i) = this.contents(i) + that.contents(i) new ArrayElement(contents) } The beside method first allocates a new array, contents, and fills it with the concatenation of the corresponding array elements in this.contents and that.contents. It finally produces a new ArrayElement containing the new contents. Although this implementation of beside works, it is in an imperative style, the telltale sign of which is the loop in which we index through arrays. The method could alternatively be abbreviated to one expression: new ArrayElement( for ( (line1, line2) <- this.contents zip that.contents ) yield line1 + line2 ) Here, the two arrays this.contents and that.contents are transformed into an array of pairs (as Tuple2s are called) using the zip operator. The zip method picks corresponding elements in its two arguments and forms an array of pairs. For instance, this expression: Array(1, 2, 3) zip Array("a", "b") will evaluate to: Array((1, "a"), (2, "b")) If one of the two operand arrays is longer than the other, zip will drop the remaining elements. In the expression above, the third element of the left operand, 3, does not form part of the result, because it does not have a cor- responding element in the right operand. The zipped array is then iterated over by a for expression. Here, the syntax “for ((line1, line2) <- ...)” allows you to name both elements of a pair in one pattern, i.e., line1 stands now for the first element of the pair, and line2 stands for the second. Scala’s pattern-matching system will Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.13 Chapter 10 · Composition and Inheritance 242 be described in detail in Chapter 15. For now, you can just think of this as a way to define two vals, line1 and line2, for each step of the iteration. The for expression has a yield part and therefore yields a result. The result is of the same kind as the expression iterated over, i.e., it is an array. Each element of the array is the result of concatenating the corresponding lines, line1 and line2. So the end result of this code is the same as in the first version of beside, but because it avoids explicit array indexing, the result is obtained in a less error-prone way. You still need a way to display elements. As usual, this is done by defin- ing a toString method that returns an element formatted as a string. Here is its definition: override def toString = contents mkString "\n" The implementation of toString makes use of mkString, which is defined for all sequences, including arrays. As you saw in Section 7.8, an expression like “arr mkString sep” returns a string consisting of all elements of the ar- ray arr. Each element is mapped to a string by calling its toString method. A separator string sep is inserted between consecutive element strings. So the expression, “contents mkString "\n"” formats the contents array as a string, where each array element appears on a line by itself. Note that toString does not carry an empty parameter list. This follows the recommendations for the uniform access principle, because toString is a pure method that does not take any parameters. With the addition of these three methods, class Element now looks as shown in Listing 10.9. 10.13 Defining a factory object You now have a hierarchy of classes for layout elements. This hierarchy could be presented to your clients “as is.” But you might also choose to hide the hierarchy behind a factory object. A factory object contains methods that construct other objects. Clients would then use these factory methods for object construction rather than constructing the objects directly with new. An advantage of this approach is that object creation can be centralized and the details of how objects are represented with classes can be hidden. This hiding will both make your library simpler for clients to understand, because Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.13 Chapter 10 · Composition and Inheritance 243 abstract class Element { def contents: Array[String] def width: Int = if (height == 0) 0 else contents(0).length def height: Int = contents.length def above(that: Element): Element = new ArrayElement(this.contents ++ that.contents) def beside(that: Element): Element = new ArrayElement( for ( (line1, line2) <- this.contents zip that.contents ) yield line1 + line2 ) override def toString = contents mkString "\n" } Listing 10.9· Class Element with above, beside, and toString. less detail is exposed, and provide you with more opportunities to change your library’s implementation later without breaking client code. The first task in constructing a factory for layout elements is to choose where the factory methods should be located. Should they be members of a singleton object or of a class? What should the containing object or class be called? There are many possibilities. A straightforward solution is to create a companion object of class Element and make this be the factory ob- ject for layout elements. That way, you need to expose only the class/object combo of Element to your clients, and you can hide the three implementa- tion classes ArrayElement, LineElement, and UniformElement. Listing 10.10 is a design of the Element object that follows this scheme. The Element companion object contains three overloaded variants of an elem method. Each variant constructs a different kind of layout object. With the advent of these factory methods, it makes sense to change the implementation of class Element so that it goes through the elem factory methods rather than creating new ArrayElement instances explicitly. To call the factory methods without qualifying them with Element, the name of the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.14 Chapter 10 · Composition and Inheritance 244 object Element{ def elem(contents: Array[String]): Element = new ArrayElement(contents) def elem(chr: Char, width: Int, height: Int): Element = new UniformElement(chr, width, height) def elem(line: String): Element = new LineElement(line) } Listing 10.10· A factory object with factory methods. singleton object, we will import Element.elem at the top of the source file. In other words, instead of invoking the factory methods with Element.elem inside class Element, we’ll import Element.elem so we can just call the factory methods by their simple name, elem. Listing 10.11 shows what class Element will look like after these changes. In addition, given the factory methods, the subclasses ArrayElement, LineElement and UniformElement could now be private, because they need no longer be accessed directly by clients. In Scala, you can define classes and singleton objects inside other classes and singleton objects. One way to make the Element subclasses private, therefore, is to place them in- side the Element singleton object and declare them private there. The classes will still be accessible to the three elem factory methods, where they are needed. Listing 10.12 shows how that will look. 10.14 Heighten and widen We need one last enhancement. The version of Element shown in List- ing 10.11 is not quite sufficient, because it does not allow clients to place el- ements of different widths on top of each other, or place elements of different heights beside each other. For example, evaluating the following expression would not work correctly, because the second line in the combined element is longer than the first: new ArrayElement(Array("hello")) above new ArrayElement(Array("world!")) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.14 Chapter 10 · Composition and Inheritance 245 import Element.elem abstract class Element { def contents: Array[String] def width: Int = if (height == 0) 0 else contents(0).length def height: Int = contents.length def above(that: Element): Element = elem(this.contents ++ that.contents) def beside(that: Element): Element = elem( for ( (line1, line2) <- this.contents zip that.contents ) yield line1 + line2 ) override def toString = contents mkString "\n" } Listing 10.11· Class Element refactored to use factory methods. Similarly, evaluating the following expression would not work properly, be- cause the first ArrayElement has a height of two, and the second a height of only one: new ArrayElement(Array("one", "two")) beside new ArrayElement(Array("one")) Listing 10.13 shows a private helper method, widen, which takes a width and returns an Element of that width. The result contains the contents of this Element, centered, padded to the left and right by any spaces needed to achieve the required width. Listing 10.13 also shows a similar method, heighten, which performs the same function in the vertical direction. The widen method is invoked by above to ensure that Elements placed above each other have the same width. Similarly, the heighten method is invoked by beside to ensure that elements placed beside each other have the same height. With these changes, the layout library is ready for use. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.14 Chapter 10 · Composition and Inheritance 246 object Element{ private class ArrayElement( val contents: Array[String] ) extends Element private class LineElement(s: String) extends Element { val contents = Array(s) override def width = s.length override def height = 1 } private class UniformElement( ch: Char, override val width: Int, override val height: Int ) extends Element { private val line = ch.toString * width def contents = Array.fill(height)(line) } def elem(contents: Array[String]): Element = new ArrayElement(contents) def elem(chr: Char, width: Int, height: Int): Element = new UniformElement(chr, width, height) def elem(line: String): Element = new LineElement(line) } Listing 10.12· Hiding implementation with private classes. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.14 Chapter 10 · Composition and Inheritance 247 import Element.elem abstract class Element { def contents: Array[String] def width: Int = contents(0).length def height: Int = contents.length def above(that: Element): Element = { val this1 = this widen that.width val that1 = that widen this.width elem(this1.contents ++ that1.contents) } def beside(that: Element): Element = { val this1 = this heighten that.height val that1 = that heighten this.height elem( for ((line1, line2) <- this1.contents zip that1.contents) yield line1 + line2) } def widen(w: Int): Element = if (w <= width) this else { val left = elem('', (w - width) / 2, height) var right = elem('', w - width - left.width, height) left beside this beside right } def heighten(h: Int): Element = if (h <= height) this else { val top = elem('', width, (h - height) / 2) var bot = elem('', width, h - height - top.height) top above this above bot } override def toString = contents mkString "\n" } Listing 10.13· Element with widen and heighten methods. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.15 Chapter 10 · Composition and Inheritance 248 10.15 Putting it all together A fun way to exercise almost all elements of the layout library is to write a program that draws a spiral with a given number of edges. This Spiral program, shown in Listing 10.14, will do just that: import Element.elem object Spiral{ val space = elem("") val corner = elem("+") def spiral(nEdges: Int, direction: Int): Element = { if (nEdges == 1) elem("+") else { val sp = spiral(nEdges - 1, (direction + 3) % 4) def verticalBar = elem('|', 1, sp.height) def horizontalBar = elem('-', sp.width, 1) if (direction == 0) (corner beside horizontalBar) above (sp beside space) else if (direction == 1) (sp above space) beside (corner above verticalBar) else if (direction == 2) (space beside sp) above (horizontalBar beside corner) else (verticalBar above corner) beside (space above sp) } } def main(args: Array[String]){ val nSides = args(0).toInt println(spiral(nSides, 0)) } } Listing 10.14· The Spiral application. Because Spiral is a standalone object with a main method with the proper signature, it is a Scala application. Spiral takes one command-line Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 10.16 Chapter 10 · Composition and Inheritance 249 argument, an integer, and draws a spiral with the specified number of edges. For example, you could draw a six-edge spiral as shown below on the left, and larger spirals as shown to the right: $ scala Spiral 6 $ scala Spiral 11 $ scala Spiral 17 +----- +---------- +---------------- | | | | +-+ | +------+ | +------------+ | + | | | | | | | | | | | +--+ | | | +--------+ | +---+ | | | | | | | | | | | | ++ | | | | | +----+ | | | | | | | | | | | | | | +----+ | | | | | ++ | | | | | | | | | | | | | +--------+ | | | +--+ | | | | | | | | | | | +------+ | | | | | | | +----------+ | | | +--------------+ 10.16 Conclusion In this section, you saw more concepts related to object-oriented program- ming in Scala. Among others, you encountered abstract classes, inheritance and subtyping, class hierarchies, parametric fields, and method overriding. You should have developed a feel for constructing a non-trivial class hierar- chy in Scala. We’ll work with the layout library again in Chapter 14. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 11 Scala’s Hierarchy Now that you’ve seen the details of class inheritance in the previous chapter, it is a good time to take a step back and look at Scala’s class hierarchy as a whole. In Scala, every class inherits from a common superclass named Any. Because every class is a subclass of Any, the methods defined in Any are “universal” methods: they may be invoked on any object. Scala also defines some interesting classes at the bottom of the hierarchy, Null and Nothing, which essentially act as common subclasses. For example, just as Any is a superclass of every other class, Nothing is a subclass of every other class. In this chapter, we’ll give you a tour of Scala’s class hierarchy. 11.1 Scala’s class hierarchy Figure 11.1 shows an outline of Scala’s class hierarchy. At the top of the hierarchy is class Any, which defines methods that include the following: final def ==(that: Any): Boolean final def !=(that: Any): Boolean def equals(that: Any): Boolean def ##: Int def hashCode: Int def toString: String Because every class inherits from Any, every object in a Scala program can be compared using ==, !=, or equals; hashed using ## or hashCode; and formatted using toString. The equality and inequality methods, == and !=, are declared final in class Any, so they cannot be overridden in subclasses. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 11.1 Chapter 11 · Scala’s Hierarchy 251 The == method is essentially the same as equals and != is always the negation of equals.1 So individual classes can tailor what == or != means by overriding the equals method. We’ll show an example later in this chapter. The root class Any has two subclasses: AnyVal and AnyRef. AnyVal is the parent class of every built-in value class in Scala. There are nine such value classes: Byte, Short, Char, Int, Long, Float, Double, Boolean, and Unit. The first eight of these correspond to Java’s primitive types, and their values are represented at run time as Java’s primitive values. The instances of these classes are all written as literals in Scala. For example, 42 is an instance of Int, 'x' is an instance of Char, and false an instance of Boolean. You cannot create instances of these classes using new. This is enforced by the “trick” that value classes are all defined to be both abstract and final. So if you were to write: scala> new Int you would get: :5: error: class Int is abstract; cannot be instantiated new Int ˆ The other value class, Unit, corresponds roughly to Java’s void type; it is used as the result type of a method that does not otherwise return an interest- ing result. Unit has a single instance value, which is written (), as discussed in Section 7.2. As explained in Chapter 5, the value classes support the usual arithmetic and boolean operators as methods. For instance, Int has methods named + and *, and Boolean has methods named || and &&. Value classes also inherit all methods from class Any. You can test this in the interpreter: 1The only cases where == is does not directly call equals is for Java’s boxed numeric classes such as Integer or Long. In Java, a new Integer(1) does not equal a new Long(1) even though for primitive values 1 == 1L. Since Scala is a more regular language than Java it was necessary correct this discrepancy by special-casing the == method for these classes. Likewise, the ## method provides a Scala version of hashing that is the same as Java’s hashCode, except for boxed numeric types, where it works consistently with ==. For in- stance new Integer(1) and new Long(1) hash the same with ## even though their Java hashCodes are different. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 11.1 Chapter 11 · Scala’s Hierarchy 252 java.lang String scala Boolean scala Iterable scala Any scala AnyVal scala Unit scala Double scala Float scala Char scala Long scala Int scala Short scala Byte scala Nothing scala ScalaObject scala Seq scala List scala Null scala AnyRef «java.lang.Object» ... (other Scala classes) ... ... (other Java classes) ... Implicit Conversion Subtype Figure 11.1 · Class hierarchy of Scala. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 11.1 Chapter 11 · Scala’s Hierarchy 253 scala> 42.toString res1: java.lang.String = 42 scala> 42.hashCode res2: Int = 42 scala> 42 equals 42 res3: Boolean = true Note that the value class space is flat; all value classes are subtypes of scala.AnyVal, but they do not subclass each other. Instead there are im- plicit conversions between different value class types. For example, an in- stance of class scala.Int is automatically widened (by an implicit conver- sion) to an instance of class scala.Long when required. As mentioned in Section 5.9, implicit conversions are also used to add more functionality to value types. For instance, the type Int supports all of the operations below: scala> 42 max 43 res4: Int = 43 scala> 42 min 43 res5: Int = 42 scala> 1 until 5 res6: Range = Range(1, 2, 3, 4) scala> 1 to 5 res7: Range.Inclusive = Range(1, 2, 3, 4, 5) scala> 3.abs res8: Int = 3 scala> (-3).abs res9: Int = 3 Here’s how this works: The methods min, max, until, to, and abs are all defined in a class scala.runtime.RichInt, and there is an implicit con- version from class Int to RichInt. The conversion is applied whenever a method is invoked on an Int that is undefined in Int but defined in RichInt. Similar “booster classes” and implicit conversions exist for the other value classes. Implicit conversions will be discussed in detail in Chapter 21. The other subclass of the root class Any is class AnyRef. This is the base class of all reference classes in Scala. As mentioned previously, on the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 11.2 Chapter 11 · Scala’s Hierarchy 254 Java platform AnyRef is in fact just an alias for class java.lang.Object. So classes written in Java as well as classes written in Scala all inherit from AnyRef.2 One way to think of java.lang.Object, therefore, is as the way AnyRef is implemented on the Java platform. Thus, although you can use Object and AnyRef interchangeably in Scala programs on the Java platform, the recommended style is to use AnyRef everywhere. Scala classes are different from Java classes in that they also inherit from a special marker trait called ScalaObject. 11.2 How primitives are implemented How is all this implemented? In fact, Scala stores integers in the same way as Java: as 32-bit words. This is important for efficiency on the JVM and also for interoperability with Java libraries. Standard operations like addition or multiplication are implemented as primitive operations. However, Scala uses the “backup” class java.lang.Integer whenever an integer needs to be seen as a (Java) object. This happens for instance when invoking the toString method on an integer number or when assigning an integer to a variable of type Any. Integers of type Int are converted transparently to “boxed integers” of type java.lang.Integer whenever necessary. All this sounds a lot like auto-boxing in Java 5 and it is indeed quite similar. There’s one crucial difference, though, in that boxing in Scala is much less visible than boxing in Java. Try the following in Java: // This is Java boolean isEqual(int x, int y) { return x == y; } System.out.println(isEqual(421, 421)); You will surely get true. Now, change the argument types of isEqual to java.lang.Integer (or Object, the result will be the same): 2The reason the AnyRef alias exists, instead of just using the name java.lang.Object, is because Scala was designed to work on both the Java and .NET platforms. On .NET, AnyRef is an alias for System.Object. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 11.2 Chapter 11 · Scala’s Hierarchy 255 // This is Java boolean isEqual(Integer x, Integer y) { return x == y; } System.out.println(isEqual(421, 421)); You will find that you get false! What happens is that the number 421 gets boxed twice, so that the arguments for x and y are two different objects. Because == means reference equality on reference types, and Integer is a reference type, the result is false. This is one aspect where it shows that Java is not a pure object-oriented language. There is a difference between primitive types and reference types that can be clearly observed. Now try the same experiment in Scala: scala> def isEqual(x: Int, y: Int) = x == y isEqual: (Int,Int)Boolean scala> isEqual(421, 421) res10: Boolean = true scala> def isEqual(x: Any, y: Any) = x == y isEqual: (Any,Any)Boolean scala> isEqual(421, 421) res11: Boolean = true In fact, the equality operation == in Scala is designed to be transparent with respect to the type’s representation. For value types, it is the natural (numeric or boolean) equality. For reference types other than Java’s boxed numeric types, == is treated as an alias of the equals method inherited from Object. That method is originally defined as reference equality, but is over- ridden by many subclasses to implement their natural notion of equality. This also means that in Scala you never fall into Java’s well-known trap concern- ing string comparisons. In Scala, string comparison works as it should: scala> val x = "abcd".substring(2) x: java.lang.String = cd scala> val y = "abcd".substring(2) y: java.lang.String = cd scala> x == y res12: Boolean = true Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 11.3 Chapter 11 · Scala’s Hierarchy 256 In Java, the result of comparing x with y would be false. The programmer should have used equals in this case, but it is easy to forget. However, there are situations where you need reference equality instead of user-defined equality. For example, in some situations where efficiency is paramount, you would like to hash cons with some classes and compare their instances with reference equality.3 For these cases, class AnyRef defines an additional eq method, which cannot be overridden and is implemented as reference equality (i.e., it behaves like == in Java for reference types). There’s also the negation of eq, which is called ne. For example: scala> val x = new String("abc") x: java.lang.String = abc scala> val y = new String("abc") y: java.lang.String = abc scala> x == y res13: Boolean = true scala> x eq y res14: Boolean = false scala> x ne y res15: Boolean = true Equality in Scala is discussed further in Chapter 30. 11.3 Bottom types At the bottom of the type hierarchy in Figure 11.1 you see the two classes scala.Null and scala.Nothing. These are special types that handle some “corner cases” of Scala’s object-oriented type system in a uniform way. Class Null is the type of the null reference; it is a subclass of every reference class (i.e., every class that itself inherits from AnyRef). Null is not compatible with value types. You cannot, for example, assign a null value to an integer variable: 3You hash cons instances of a class by caching all instances you have created in a weak collection. Then, any time you want a new instance of the class, you first check the cache. If the cache already has an element equal to the one you are about to create, you can reuse the existing instance. As a result of this arrangement, any two instances that are equal with equals() are also equal with reference equality. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 11.4 Chapter 11 · Scala’s Hierarchy 257 scala> val i: Int = null :4: error: type mismatch; found : Null(null) required: Int Type Nothing is at the very bottom of Scala’s class hierarchy; it is a sub- type of every other type. However, there exist no values of this type whatso- ever. Why does it make sense to have a type without values? As discussed in Section 7.4, one use of Nothing is that it signals abnormal termination. For instance there’s the error method in the Predef object of Scala’s standard library, which is defined like this: def error(message: String): Nothing = throw new RuntimeException(message) The return type of error is Nothing, which tells users that the method will not return normally (it throws an exception instead). Because Nothing is a subtype of every other type, you can use methods like error in very flexible ways. For instance: def divide(x: Int, y: Int): Int = if (y != 0) x / y else error("can't divide by zero") The “then” branch of the conditional, x / y, has type Int, whereas the else branch, the call to error, has type Nothing. Because Nothing is a subtype of Int, the type of the whole conditional is Int, as required. 11.4 Conclusion In this chapter we showed you the classes at the top and bottom of Scala’s class hierarchy. Now that you’ve gotten a good foundation on class inher- itance in Scala, you’re ready to understand mixin composition. In the next chapter, you’ll learn about traits. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 12 Traits Traits are a fundamental unit of code reuse in Scala. A trait encapsulates method and field definitions, which can then be reused by mixing them into classes. Unlike class inheritance, in which each class must inherit from just one superclass, a class can mix in any number of traits. This chapter shows you how traits work and shows two of the most common ways they are use- ful: widening thin interfaces to rich ones, and defining stackable modifica- tions. It also shows how to use the Ordered trait and compares traits to the multiple inheritance of other languages. 12.1 How traits work A trait definition looks just like a class definition except that it uses the key- word trait. An example is shown in Listing 12.1: trait Philosophical{ def philosophize() { println("I consume memory, therefore I am!") } } Listing 12.1· The definition of trait Philosophical. This trait is named Philosophical. It does not declare a superclass, so like a class, it has the default superclass of AnyRef. It defines one method, named philosophize, which is concrete. It’s a simple trait, just enough to show how traits work. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.1 Chapter 12 · Traits 259 Once a trait is defined, it can be mixed in to a class using either the extends or with keywords. Scala programmers “mix in” traits rather than inherit from them, because mixing in a trait has important differences from the multiple inheritance found in many other languages. This issue is dis- cussed in Section 12.6. For example, Listing 12.2 shows a class that mixes in the Philosophical trait using extends: class Frog extends Philosophical { override def toString = "green" } Listing 12.2· Mixing in a trait using extends. You can use the extends keyword to mix in a trait; in that case you implicitly inherit the trait’s superclass. For instance, in Listing 12.2, class Frog subclasses AnyRef (the superclass of Philosophical) and mixes in Philosophical. Methods inherited from a trait can be used just like meth- ods inherited from a superclass. Here’s an example: scala> val frog = new Frog frog: Frog = green scala> frog.philosophize() I consume memory, therefore I am! A trait also defines a type. Here’s an example in which Philosophical is used as a type: scala> val phil: Philosophical = frog phil: Philosophical = green scala> phil.philosophize() I consume memory, therefore I am! The type of phil is Philosophical, a trait. Thus, variable phil could have been initialized with any object whose class mixes in Philosophical. If you wish to mix a trait into a class that explicitly extends a superclass, you use extends to indicate the superclass and with to mix in the trait. Listing 12.3 shows an example. If you want to mix in multiple traits, you add more with clauses. For example, given a trait HasLegs, you could mix both Philosophical and HasLegs into Frog as shown in Listing 12.4. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.1 Chapter 12 · Traits 260 class Animal class Frog extends Animal with Philosophical { override def toString = "green" } Listing 12.3· Mixing in a trait using with. class Animal trait HasLegs class Frog extends Animal with Philosophical with HasLegs { override def toString = "green" } Listing 12.4· Mixing in multiple traits. In the examples you’ve seen so far, class Frog has inherited an imple- mentation of philosophize from trait Philosophical. Alternatively, Frog could override philosophize. The syntax looks the same as overriding a method declared in a superclass. Here’s an example: class Animal class Frog extends Animal with Philosophical { override def toString = "green" override def philosophize() { println("It ain't easy being "+ toString +"!") } } Because this new definition of Frog still mixes in trait Philosophical, you can still use it from a variable of that type. But because Frog overrides Philosophical’s implementation of philosophize, you’ll get a new be- havior when you call it: scala> val phrog: Philosophical = new Frog phrog: Philosophical = green scala> phrog.philosophize() It ain't easy being green! Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.2 Chapter 12 · Traits 261 At this point you might philosophize that traits are like Java interfaces with concrete methods, but they can actually do much more. Traits can, for example, declare fields and maintain state. In fact, you can do anything in a trait definition that you can do in a class definition, and the syntax looks exactly the same, with only two exceptions. First, a trait cannot have any “class” parameters, i.e., parameters passed to the primary constructor of a class. In other words, although you could define a class like this: class Point(x: Int, y: Int) The following attempt to define a trait would not compile: trait NoPoint(x: Int, y: Int) // Does not compile You’ll find out in Section 20.5 how to work around this restriction. The other difference between classes and traits is that whereas in classes, super calls are statically bound, in traits, they are dynamically bound. If you write “super.toString” in a class, you know exactly which method implementation will be invoked. When you write the same thing in a trait, however, the method implementation to invoke for the super call is unde- fined when you define the trait. Rather, the implementation to invoke will be determined anew each time the trait is mixed into a concrete class. This curious behavior of super is key to allowing traits to work as stackable mod- ifications, which will be described in Section 12.5. The rules for resolving super calls will be given in Section 12.6. 12.2 Thin versus rich interfaces One major use of traits is to automatically add methods to a class in terms of methods the class already has. That is, traits can enrich a thin interface, making it into a rich interface. Thin versus rich interfaces represents a commonly faced trade-off in object-oriented design. The trade-off is between the implementers and the clients of an interface. A rich interface has many methods, which make it convenient for the caller. Clients can pick a method that exactly matches the functionality they need. A thin interface, on the other hand, has fewer methods, and thus is easier on the implementers. Clients calling into a thin interface, however, have to write more code. Given the smaller selection of Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.3 Chapter 12 · Traits 262 methods to call, they may have to choose a less than perfect match for their needs and write extra code to use it. Java’s interfaces are more often thin than rich. For example, interface CharSequence, which was introduced in Java 1.4, is a thin interface com- mon to all string-like classes that hold a sequence of characters. Here’s its definition when seen as a Scala trait: trait CharSequence { def charAt(index: Int): Char def length: Int def subSequence(start: Int, end: Int): CharSequence def toString(): String } Although most of the dozens of methods in class String would apply to any CharSequence, Java’s CharSequence interface declares only four meth- ods. Had CharSequence instead included the full String interface, it would have placed a large burden on implementers of CharSequence. Every pro- grammer that implemented CharSequence in Java would have had to define dozens more methods. Because Scala traits can contain concrete methods, they make rich interfaces far more convenient. Adding a concrete method to a trait tilts the thin-rich trade-off heavily towards rich interfaces. Unlike in Java, adding a concrete method to a Scala trait is a one-time effort. You only need to implement the method once, in the trait itself, instead of needing to reimplement it for every class that mixes in the trait. Thus, rich interfaces are less work to provide in Scala than in a language without traits. To enrich an interface using traits, simply define a trait with a small num- ber of abstract methods—the thin part of the trait’s interface—and a poten- tially large number of concrete methods, all implemented in terms of the abstract methods. Then you can mix the enrichment trait into a class, imple- ment the thin portion of the interface, and end up with a class that has all of the rich interface available. 12.3 Example: Rectangular objects Graphics libraries often have many different classes that represent something rectangular. Some examples are windows, bitmap images, and regions se- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.3 Chapter 12 · Traits 263 lected with a mouse. To make these rectangular objects convenient to use, it is nice if the library provides geometric queries such as width, height, left, right, topLeft, and so on. However, many such methods exist that would be nice to have, so it can be a large burden on library writers to pro- vide all of them for all rectangular objects in a Java library. If such a library were written in Scala, by contrast, the library writer could use traits to easily supply all of these convenience methods on all the classes they’d like. To see how, first imagine what the code would look like without traits. There would be some basic geometric classes like Point and Rectangle: class Point(val x: Int, val y: Int) class Rectangle(val topLeft: Point, val bottomRight: Point){ def left = topLeft.x def right = bottomRight.x def width = right - left // and many more geometric methods... } This Rectangle class takes two points in its primary constructor: the co- ordinates of the top-left and bottom-right corners. It then implements many convenience methods such as left, right, and width by performing simple calculations on these two points. Another class a graphics library might have is a 2-D graphical widget: abstract class Component { def topLeft: Point def bottomRight: Point def left = topLeft.x def right = bottomRight.x def width = right - left // and many more geometric methods... } Notice that the definitions of left, right, and width are exactly the same in the two classes. They will also be the same, aside from minor variations, in any other classes for rectangular objects. This repetition can be eliminated with an enrichment trait. The trait will have two abstract methods: one that returns the top-left coordinate of the ob- ject, and another that returns the bottom-right coordinate. It can then supply Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.3 Chapter 12 · Traits 264 concrete implementations of all the other geometric queries. Listing 12.5 shows what it will look like: trait Rectangular{ def topLeft: Point def bottomRight: Point def left = topLeft.x def right = bottomRight.x def width = right - left // and many more geometric methods... } Listing 12.5· Defining an enrichment trait. Class Component can mix in this trait to get all the geometric methods provided by Rectangular: abstract class Component extends Rectangular { // other methods... } Similarly, Rectangle itself can mix in the trait: class Rectangle(val topLeft: Point, val bottomRight: Point) extends Rectangular { // other methods... } Given these definitions, you can create a Rectangle and call geometric methods such as width and left on it: scala> val rect = new Rectangle(new Point(1, 1), new Point(10, 10)) rect: Rectangle = Rectangle@3536fd scala> rect.left res2: Int = 1 scala> rect.right res3: Int = 10 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.4 Chapter 12 · Traits 265 scala> rect.width res4: Int = 9 12.4 The Ordered trait Comparison is another domain where a rich interface is convenient. When- ever you compare two objects that are ordered, it is convenient if you use a single method call to ask about the precise comparison you want. If you want “is less than,” you would like to call <, and if you want “is less than or equal,” you would like to call <=. With a thin comparison interface, you might just have the < method, and you would sometimes have to write things like “(x < y) || (x == y)”. A rich interface would provide you with all of the usual comparison operators, thus allowing you to directly write things like “x <= y”. Before looking at Ordered, imagine what you might do without it. Sup- pose you took the Rational class from Chapter 6 and added comparison operations to it. You would end up with something like this:1 class Rational(n: Int, d: Int){ // ... def < (that: Rational) = this.numer * that.denom > that.numer * this.denom def > (that: Rational) = that < this def <= (that: Rational) = (this < that) || (this == that) def >= (that: Rational) = (this > that) || (this == that) } This class defines four comparison operators (<, >, <=, and >=), and it’s a classic demonstration of the costs of defining a rich interface. First, notice that three of the comparison operators are defined in terms of the first one. For example, > is defined as the reverse of <, and <= is defined as literally “less than or equal.” Additionally, notice that all three of these methods would be the same for any other class that is comparable. There is nothing special about rational numbers regarding <=. In a comparison context, <= is always used to mean “less than or equals.” Overall, there is quite a lot of 1The full code for the Rational class on which this example is based is shown in List- ing 6.5 on page 155. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.4 Chapter 12 · Traits 266 boilerplate code in this class which would be the same in any other class that implements comparison operations. This problem is so common that Scala provides a trait to help with it. The trait is called Ordered. To use it, you replace all of the individual comparison methods with a single compare method. The Ordered trait then defines <, >, <=, and >= for you in terms of this one method. Thus, trait Ordered allows you to enrich a class with comparison methods by implementing only one method, compare. Here is how it looks if you define comparison operations on Rational by using the Ordered trait: class Rational(n: Int, d: Int) extends Ordered[Rational] { // ... def compare(that: Rational) = (this.numer * that.denom) - (that.numer * this.denom) } There are just two things to do. First, this version of Rational mixes in the Ordered trait. Unlike the traits you have seen so far, Ordered requires you to specify a type parameter when you mix it in. Type parameters are not discussed in detail until Chapter 19, but for now all you need to know is that when you mix in Ordered, you must actually mix in Ordered[C], where C is the class whose elements you compare. In this case, Rational mixes in Ordered[Rational]. The second thing you need to do is define a compare method for com- paring two objects. This method should compare the receiver, this, with the object passed as an argument to the method. It should return an integer that is zero if the objects are the same, negative if receiver is less than the argument, and positive if the receiver is greater than the argument. In this case, the comparison method of Rational uses a formula based on convert- ing the fractions to a common denominator and then subtracting the resulting numerators. Given this mixin and the definition of compare, class Rational now has all four comparison methods: scala> val half = new Rational(1, 2) half: Rational = 1/2 scala> val third = new Rational(1, 3) third: Rational = 1/3 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.5 Chapter 12 · Traits 267 scala> half < third res5: Boolean = false scala> half > third res6: Boolean = true Any time you implement a class that is ordered by some comparison, you should consider mixing in the Ordered trait. If you do, you will provide the class’s users with a rich set of comparison methods. Beware that the Ordered trait does not define equals for you, because it is unable to do so. The problem is that implementing equals in terms of compare requires checking the type of the passed object, and because of type erasure, Ordered itself cannot do this test. Thus, you need to define equals yourself, even if you inherit Ordered. You’ll find out how to go about this in Chapter 30. 12.5 Traits as stackable modifications You have now seen one major use of traits: turning a thin interface into a rich one. Now we’ll turn to a second major use: providing stackable modifi- cations to classes. Traits let you modify the methods of a class, and they do so in a way that allows you to stack those modifications with each other. As an example, consider stacking modifications to a queue of integers. The queue will have two operations: put, which places integers in the queue, and get, which takes them back out. Queues are first-in, first-out, so get should return the integers in the same order they were put in the queue. Given a class that implements such a queue, you could define traits to perform modifications such as these: • Doubling: double all integers that are put in the queue • Incrementing: increment all integers that are put in the queue • Filtering: filter out negative integers from a queue These three traits represent modifications, because they modify the be- havior of an underlying queue class rather than defining a full queue class themselves. The three are also stackable. You can select any of the three you like, mix them into a class, and obtain a new class that has all of the modifications you chose. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.5 Chapter 12 · Traits 268 An abstract IntQueue class is shown in Listing 12.6. IntQueue has a put method that adds new integers to the queue and a get method that removes and returns them. A basic implementation of IntQueue that uses an ArrayBuffer is shown in Listing 12.7. abstract class IntQueue { def get(): Int def put(x: Int) } Listing 12.6· Abstract class IntQueue. import scala.collection.mutable.ArrayBuffer class BasicIntQueue extends IntQueue { private val buf = new ArrayBuffer[Int] def get() = buf.remove(0) def put(x: Int) { buf += x } } Listing 12.7· A BasicIntQueue implemented with an ArrayBuffer. Class BasicIntQueue has a private field holding an array buffer. The get method removes an entry from one end of the buffer, while the put method adds elements to the other end. Here’s how this implementation looks when you use it: scala> val queue = new BasicIntQueue queue: BasicIntQueue = BasicIntQueue@24655f scala> queue.put(10) scala> queue.put(20) scala> queue.get() res9: Int = 10 scala> queue.get() res10: Int = 20 So far so good. Now take a look at using traits to modify this behavior. Listing 12.8 shows a trait that doubles integers as they are put in the queue. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.5 Chapter 12 · Traits 269 The Doubling trait has two funny things going on. The first is that it declares a superclass, IntQueue. This declaration means that the trait can only be mixed into a class that also extends IntQueue. Thus, you can mix Doubling into BasicIntQueue, but not into Rational. trait Doubling extends IntQueue { abstract override def put(x: Int){ super.put(2 * x) } } Listing 12.8· The Doubling stackable modification trait. The second funny thing is that the trait has a super call on a method declared abstract. Such calls are illegal for normal classes, because they will certainly fail at run time. For a trait, however, such a call can actually succeed. Since super calls in a trait are dynamically bound, the super call in trait Doubling will work so long as the trait is mixed in after another trait or class that gives a concrete definition to the method. This arrangement is frequently needed with traits that implement stack- able modifications. To tell the compiler you are doing this on purpose, you must mark such methods as abstract override. This combination of mod- ifiers is only allowed for members of traits, not classes, and it means that the trait must be mixed into some class that has a concrete definition of the method in question. There is a lot going on with such a simple trait, isn’t there! Here’s how it looks to use the trait: scala> class MyQueue extends BasicIntQueue with Doubling defined class MyQueue scala> val queue = new MyQueue queue: MyQueue = MyQueue@91f017 scala> queue.put(10) scala> queue.get() res12: Int = 20 In the first line in this interpreter session, we define class MyQueue, which extends BasicIntQueue and mixes in Doubling. We then put a 10 in the queue, but because Doubling has been mixed in, the 10 is doubled. When we get an integer from the queue, it is a 20. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.5 Chapter 12 · Traits 270 Note that MyQueue defines no new code. It simply identifies a class and mixes in a trait. In this situation, you could supply “BasicIntQueue with Doubling” directly to new instead of defining a named class. It would look as shown in Listing 12.9: scala> val queue = new BasicIntQueue with Doubling queue: BasicIntQueue with Doubling = $anon$1@5fa12d scala> queue.put(10) scala> queue.get() res14: Int = 20 Listing 12.9· Mixing in a trait when instantiating with new. To see how to stack modifications, we need to define the other two mod- ification traits, Incrementing and Filtering. Implementations of these traits are shown in Listing 12.10: trait Incrementing extends IntQueue { abstract override def put(x: Int){ super.put(x + 1)} } trait Filtering extends IntQueue { abstract override def put(x: Int){ if (x >= 0) super.put(x) } } Listing 12.10: Stackable modification traits Incrementing and Filtering. Given these modifications, you can now pick and choose which ones you want for a particular queue. For example, here is a queue that both filters negative numbers and adds one to all numbers that it keeps: scala> val queue = (new BasicIntQueue with Incrementing with Filtering) queue: BasicIntQueue with Incrementing with Filtering... scala> queue.put(-1); queue.put(0); queue.put(1) scala> queue.get() res15: Int = 1 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.6 Chapter 12 · Traits 271 scala> queue.get() res16: Int = 2 The order of mixins is significant.2 The precise rules are given in the following section, but, roughly speaking, traits further to the right take effect first. When you call a method on a class with mixins, the method in the trait furthest to the right is called first. If that method calls super, it invokes the method in the next trait to its left, and so on. In the previous example, Filtering’s put is invoked first, so it removes integers that were negative to begin with. Incrementing’s put is invoked second, so it adds one to those integers that remain. If you reverse the order, first integers will be incremented, and then the integers that are still negative will be discarded: scala> val queue = (new BasicIntQueue with Filtering with Incrementing) queue: BasicIntQueue with Filtering with Incrementing... scala> queue.put(-1); queue.put(0); queue.put(1) scala> queue.get() res17: Int = 0 scala> queue.get() res18: Int = 1 scala> queue.get() res19: Int = 2 Overall, code written in this style gives you a great deal of flexibility. You can define sixteen different classes by mixing in these three traits in different combinations and orders. That’s a lot of flexibility for a small amount of code, so you should keep your eyes open for opportunities to arrange code as stackable modifications. 12.6 Why not multiple inheritance? Traits are a way to inherit from multiple class-like constructs, but they differ in important ways from the multiple inheritance present in many languages. One difference is especially important: the interpretation of super. With 2Once a trait is mixed into a class, you can alternatively call it a mixin. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.6 Chapter 12 · Traits 272 multiple inheritance, the method called by a super call can be determined right where the call appears. With traits, the method called is determined by a linearization of the classes and traits that are mixed into a class. This is the difference that enables the stacking of modifications described in the previous section. Before looking at linearization, take a moment to consider how to stack modifications in a language with traditional multiple inheritance. Imagine the following code, but this time interpreted as multiple inheritance instead of trait mixin: // Multiple inheritance thought experiment val q = new BasicIntQueue with Incrementing with Doubling q.put(42) // which put would be called? The first question is, which put method would get invoked by this call? Per- haps the rule would be that the last superclass wins, in which case Doubling would get called. Doubling would double its argument and call super.put, and that would be it. No incrementing would happen! Likewise, if the rule were that the first superclass wins, the resulting queue would increment in- tegers but not double them. Thus neither ordering would work. You might also entertain the possibility of allowing programmers to iden- tify exactly which superclass method they want when they say super. For example, imagine the following Scala-like code, in which super appears to be explicitly invoked on both Incrementing and Doubling: // Multiple inheritance thought experiment trait MyQueue extends BasicIntQueue with Incrementing with Doubling { def put(x: Int){ Incrementing.super.put(x) // (Not real Scala) Doubling.super.put(x) } } This approach would give us new problems. The verbosity of this attempt is the least of its problems. What would happen is that the base class’s put method would get called twice—once with an incremented value and once with a doubled value, but neither time with an incremented, doubled value. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.6 Chapter 12 · Traits 273 There is simply no good solution to this problem using multiple inher- itance. You would have to back up in your design and factor the code dif- ferently. By contrast, the traits solution in Scala is straightforward. You simply mix in Incrementing and Doubling, and Scala’s special treatment of super in traits makes it all work out. Something is clearly different here from traditional multiple inheritance, but what? As hinted previously, the answer is linearization. When you instantiate a class with new, Scala takes the class and all of its inherited classes and traits and puts them in a single, linear order. Then, whenever you call super inside one of those classes, the invoked method is the next one up the chain. If all of the methods but the last call super, the net result is stackable behavior. The precise order of the linearization is described in the language spec- ification. It is a little bit complicated, but the main thing you need to know is that, in any linearization, a class is always linearized before all of its su- perclasses and mixed in traits. Thus, when you write a method that calls super, that method is definitely modifying the behavior of the superclasses and mixed in traits, not the other way around. Note The remainder of this section describes the details of linearization. You can safely skip the rest of this section if you are not interested in understanding those details right now. The main properties of Scala’s linearization are illustrated by the follow- ing example: Say you have a class Cat, which inherits from a superclass Animal and two traits Furry and FourLegged. FourLegged extends in turn another trait HasLegs: class Animal trait Furry extends Animal trait HasLegs extends Animal trait FourLegged extends HasLegs class Cat extends Animal with Furry with FourLegged Class Cat’s inheritance hierarchy and linearization are shown in Fig- ure 12.1. Inheritance is indicated using traditional UML notation:3 arrows with white, triangular arrowheads indicate inheritance, with the arrowhead 3Rumbaugh, et. al., The Unified Modeling Language Reference Manual.[Rum04] Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.6 Chapter 12 · Traits 274 FourLegged Cat Furry HasLegsAnimal AnyRef Any Figure 12.1· Inheritance hierarchy and linearization of class Cat. pointing to the supertype. The arrows with darkened, non-triangular arrow- heads depict linearization. The darkened arrowheads point in the direction in which super calls will be resolved. The linearization of Cat is computed from back to front as follows. The last part of the linearization of Cat is the linearization of its superclass, Animal. This linearization is copied over without any changes. (The lin- earization of each of these types is shown in Table 12.1 on page 275.) Be- cause Animal doesn’t explicitly extend a superclass or mix in any supertraits, it by default extends AnyRef, which extends Any. Animal’s linearization, therefore, looks like: Animal AnyRef Any The second to last part is the linearization of the first mixin, trait Furry, but all classes that are already in the linearization of Animal are left out now, so that each class appears only once in Cat’s linearization. The result is: Furry Animal AnyRef Any This is preceded by the linearization of FourLegged, where again any classes that have already been copied in the linearizations of the superclass or the first mixin are left out: FourLegged FurryHasLegs Animal AnyRef Any Finally, the first class in the linearization of Cat is Cat itself: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.7 Chapter 12 · Traits 275 Table 12.1 · Linearization of types in Cat’s hierarchy Type Linearization Animal Animal, AnyRef, Any Furry Furry, Animal, AnyRef, Any FourLegged FourLegged, HasLegs, Animal, AnyRef, Any HasLegs HasLegs, Animal, AnyRef, Any Cat Cat, FourLegged, HasLegs, Furry, Animal, AnyRef, Any FourLeggedCat FurryHasLegs Animal AnyRef Any When any of these classes and traits invokes a method via super, the im- plementation invoked will be the first implementation to its right in the lin- earization. 12.7 To trait, or not to trait? Whenever you implement a reusable collection of behavior, you will have to decide whether you want to use a trait or an abstract class. There is no firm rule, but this section contains a few guidelines to consider. If the behavior will not be reused, then make it a concrete class. It is not reusable behavior after all. If it might be reused in multiple, unrelated classes, make it a trait. Only traits can be mixed into different parts of the class hierarchy. If you want to inherit from it in Java code, use an abstract class. Since traits with code do not have a close Java analog, it tends to be awkward to inherit from a trait in a Java class. Inheriting from a Scala class, meanwhile, is exactly like inheriting from a Java class. As one exception, a Scala trait with only abstract members translates directly to a Java interface, so you should feel free to define such traits even if you expect Java code to inherit from it. See Chapter 31 for more information on working with Java and Scala together. If you plan to distribute it in compiled form, and you expect outside groups to write classes inheriting from it, you might lean towards using an abstract class. The issue is that when a trait gains or loses a member, any classes that inherit from it must be recompiled, even if they have not changed. If outside clients will only call into the behavior, instead of inheriting from Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 12.8 Chapter 12 · Traits 276 it, then using a trait is fine. If efficiency is very important, lean towards using a class. Most Java runtimes make a virtual method invocation of a class member a faster oper- ation than an interface method invocation. Traits get compiled to interfaces and therefore may pay a slight performance overhead. However, you should make this choice only if you know that the trait in question constitutes a per- formance bottleneck and have evidence that using a class instead actually solves the problem. If you still do not know, after considering the above, then start by making it as a trait. You can always change it later, and in general using a trait keeps more options open. 12.8 Conclusion This chapter has shown you how traits work and how to use them in several common idioms. You saw that traits are similar to multiple inheritance, but because they interpret super using linearization, they both avoid some of the difficulties of traditional multiple inheritance, and allow you to stack behaviors. You also saw the Ordered trait and learned how to write your own enrichment traits. Now that you have seen all of these facets, it is worth stepping back and taking another look at traits as a whole. Traits do not merely support the idioms described in this chapter. They are a fundamental unit of code that is reusable through inheritance. Because of this nature, many experienced Scala programmers start with traits when they are at the early stages of im- plementation. Each trait can hold less than an entire concept, a mere frag- ment of a concept. As the design solidifies, the fragments can be combined into more complete concepts through trait mixin. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 13 Packages and Imports When working on a program, especially a large one, it is important to min- imize coupling—the extent to which the various parts of the program rely on the other parts. Low coupling reduces the risk that a small, seemingly innocuous change in one part of the program will have devastating conse- quences in another part. One way to minimize coupling is to write in a modular style. You divide the program into a number of smaller modules, each of which has an inside and an outside. When working on the inside of a module—its implementation—you need only coordinate with other pro- grammers working on that very same module. Only when you must change the outside of a module—its interface—is it necessary to coordinate with developers working on other modules. This chapter shows several constructs that help you program in a modular style. It shows how to place things in packages, make names visible through imports, and control the visibility of definitions through access modifiers. The constructs are similar in spirit to constructs in Java, but there are some differences—usually ways that are more consistent—so it’s worth reading this chapter even if you already know Java. 13.1 Putting code in packages Scala code resides in the Java platform’s global hierarchy of packages. The example code you’ve seen so far in this book has been in the unnamed package. You can place code into named packages in Scala in two ways. First, you can place the contents of an entire file into a package by putting a package clause at the top of the file, as shown in Listing 13.1. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.2 Chapter 13 · Packages and Imports 278 package bobsrockets.navigation class Navigator Listing 13.1· Placing the contents of an entire file into a package. The package clause of Listing 13.1 places class Navigator into the package named bobsrockets.navigation. Presumably, this is the navi- gation software developed by Bob’s Rockets, Inc. Note Because Scala code is part of the Java ecosystem, it is recommended to follow Java’s reverse-domain-name convention for Scala packages that you release to the public. Thus, a better name for Navigator’s package might be com.bobsrockets.navigation. In this chapter, however, we’ll leave off the “com.” to make the examples easier to understand. The other way you can place code into packages in Scala is more like C# namespaces. You follow a package clause by a section in curly braces that contains the definitions that go into the package. This syntax is called a packaging. The packaging shown in Listing 13.2 has the same effect as the code in Listing 13.1: package bobsrockets.navigation { class Navigator } Listing 13.2· Long form of a simple package declaration. For such simple examples, you might as well use the syntactic sugar shown in Listing 13.1. However, one use of the more general notation is to have different parts of a file in different packages. For example, you might include a class’s tests in the same file as the original code, but put the tests in a different package, as shown in Listing 13.3. 13.2 Concise access to related code When code is divided into a package hierarchy, it doesn’t just help people browse through the code. It also tells the compiler that code in the same Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.2 Chapter 13 · Packages and Imports 279 package bobsrockets { package navigation { // In package bobsrockets.navigation class Navigator package tests { // In package bobsrockets.navigation.tests class NavigatorSuite } } } Listing 13.3· Multiple packages in the same file. package bobsrockets { package navigation { class Navigator{ // No need to say bobsrockets.navigation.StarMap val map = new StarMap } class StarMap } class Ship { // No need to say bobsrockets.navigation.Navigator val nav = new navigation.Navigator } package fleets { class Fleet { // No need to say bobsrockets.Ship def addShip() { new Ship } } } } Listing 13.4· Concise access to classes and packages. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.2 Chapter 13 · Packages and Imports 280 package bobsrockets { class Ship } package bobsrockets.fleets { class Fleet{ // Doesn’t compile! Ship is not in scope. def addShip() { new Ship } } } Listing 13.5· Symbols in enclosing packages not automatically available. // In file launch.scala package launch { class Booster3 } // In file bobsrockets.scala package bobsrockets { package navigation { package launch { class Booster1 } class MissionControl{ val booster1 = new launch.Booster1 val booster2 = new bobsrockets.launch.Booster2 val booster3 = new _root_.launch.Booster3 } } package launch { class Booster2 } } Listing 13.6· Accessing hidden package names. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.2 Chapter 13 · Packages and Imports 281 package is related in some way to each other. Scala takes advantage of this relatedness by allowing short, unqualified names when accessing code that is in the same package. Listing 13.4 gives three simple examples. First, as you would expect, a class can be accessed from within its own package without needing a prefix. That’s why new StarMap compiles. Class StarMap is in the same package, bobsrockets.navigation, as the new expression that accesses it, so the package name doesn’t need to be prefixed. Second, a package itself can be accessed from its containing package without needing a prefix. In Listing 13.4, look at how class Navigator is instantiated. The new expression appears in package bobsrockets, which is the containing package of bobsrockets.navigation. Thus, it can access package bobsrockets.navigation as simply navigation. Third, when using the curly-braces packaging syntax, all names accessi- ble in scopes outside the packaging are also available inside it. An example in Listing 13.4 is the way addShip() creates a new Ship. The method is defined within two packagings: an outer one for bobsrockets, and an in- ner one for bobsrockets.fleets. Since Ship is accessible in the outer packaging, it can be referenced from within addShip(). Note that this kind of access is only available if you explicitly nest the packagings. If you stick to one package per file, then—like in Java—the only names available will be the ones defined in the current package. In List- ing 13.5, the packaging of bobsrockets.fleets has been moved to the top level. Since it is no longer enclosed in a packaging for bobsrockets, names from bobsrockets are not immediately in scope. As a result, new Ship gives a compile error. If nesting packages with braces shifts your code uncom- fortably to the right, you can also use multiple package clauses without the braces.1 For instance, the code below also defines class Fleet in two nested packages bobrockets and fleets, just like you saw it in Listing 13.4: package bobsrockets package fleets class Fleet { // Doesn’t compile! Ship is not in scope. def addShip() { new Ship } } 1This style of multiple package clauses without braces is called chained package clauses. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.3 Chapter 13 · Packages and Imports 282 One final trick is important to know. Sometimes, you end up coding in a heavily crowded scope where package names are hiding each other. In List- ing 13.6, the scope of class MissionControl includes three separate pack- ages named launch! There’s one launch in bobsrockets.navigation, one in bobsrockets, and one at the top level. How would you reference each of Booster1, Booster2, and Booster3? Accessing the first one is easiest. A reference to launch by itself will get you to package bobsrockets.navigation.launch, because that is the launch package defined in the closest enclosing scope. Thus, you can refer to the first booster class as simply launch.Booster1. Referring to the sec- ond one also is not tricky. You can write bobrockets.launch.Booster2 and be clear about which one you are referencing. That leaves the question of the third booster class, however. How can you access Booster3, considering that a nested launch package shadows the top-level one? To help in this situation, Scala provides a package named _root_ that is outside any package a user can write. Put another way, every top-level package you can write is treated as a member of package _root_. For exam- ple, both launch and bobsrockets of Listing 13.6 are members of package _root_. As a result, _root_.launch gives you the top-level launch pack- age, and _root_.launch.Booster3 designates the outermost booster class. 13.3 Imports In Scala, packages and their members can be imported using import clauses. Imported items can then be accessed by a simple name like File, as opposed to requiring a qualified name like java.io.File. For example, consider the code shown in Listing 13.7. An import clause makes members of a package or object available by their names alone without needing to prefix them by the package or object name. Here are some simple examples: // easy access to Fruit import bobsdelights.Fruit // easy access to all members of bobsdelights import bobsdelights._ // easy access to all members of Fruits import bobsdelights.Fruits._ Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.3 Chapter 13 · Packages and Imports 283 package bobsdelights abstract class Fruit( val name: String, val color: String ) object Fruits{ object Apple extends Fruit("apple", "red") object Orange extends Fruit("orange", "orange") object Pear extends Fruit("pear", "yellowish") val menu = List(Apple, Orange, Pear) } Listing 13.7· Bob’s delightful fruits, ready for import. The first of these corresponds to Java’s single type import, the second to Java’s on-demand import. The only difference is that Scala’s on-demand imports are written with a trailing underscore (_) instead of an asterisk (*) (after all, * is a valid identifier in Scala!). The third import clause above corresponds to Java’s import of static class fields. These three imports give you a taste of what imports can do, but Scala imports are actually much more general. For one, imports in Scala can ap- pear anywhere, not just at the beginning of a compilation unit. Also, they can refer to arbitrary values. For instance, the import shown in Listing 13.8 is possible: def showFruit(fruit: Fruit){ import fruit._ println(name +"s are "+ color) } Listing 13.8· Importing the members of a regular (not singleton) object. Method showFruit imports all members of its parameter fruit, which is of type Fruit. The subsequent println statement can refer to name and color directly. These two references are equivalent to fruit.name and fruit.color. This syntax is particularly useful when you use objects as modules, which will be described in Chapter 29. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.3 Chapter 13 · Packages and Imports 284 Scala’s flexible imports Scala’s import clauses are quite a bit more flexible than Java’s. There are three principal differences. In Scala, imports: • may appear anywhere • may refer to objects (singleton or regular) in addition to packages • let you rename and hide some of the imported members Another way Scala’s imports are flexible is that they can import packages themselves, not just their non-package members. This is only natural if you think of nested packages being contained in their surrounding package. For example, in Listing 13.9, the package java.util.regex is imported. This makes regex usable as a simple name. To access the Pattern singleton ob- ject from the java.util.regex package, you can just say, regex.Pattern, as shown in Listing 13.9: import java.util.regex class AStarB{ // Accesses java.util.regex.Pattern val pat = regex.Pattern.compile("a*b") } Listing 13.9· Importing a package name. Imports in Scala can also rename or hide members. This is done with an import selector clause enclosed in braces, which follows the object from which members are imported. Here are some examples: import Fruits.{Apple, Orange} This imports just members Apple and Orange from object Fruits. import Fruits.{Apple => McIntosh, Orange} This imports the two members Apple and Orange from object Fruits. However, the Apple object is renamed to McIntosh. So this object can be Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.3 Chapter 13 · Packages and Imports 285 accessed with either Fruits.Apple or McIntosh. A renaming clause is always of the form “ => ”. import java.sql.{Date => SDate} This imports the SQL date class as SDate, so that you can simultaneously import the normal Java date class as simply Date. import java.{sql => S} This imports the java.sql package as S, so that you can write things like S.Date. import Fruits.{_} This imports all members from object Fruits. It means the same thing as import Fruits._. import Fruits.{Apple => McIntosh, _} This imports all members from object Fruits but renames Apple to McIntosh. import Fruits.{Pear => _, _} This imports all members of Fruits except Pear. A clause of the form “ => _” excludes from the names that are imported. In a sense, renaming something to ‘_’ means hiding it alto- gether. This is useful to avoid ambiguities. Say you have two packages, Fruits and Notebooks, which both define a class Apple. If you want to get just the notebook named Apple, and not the fruit, you could still use two imports on demand like this: import Notebooks._ import Fruits.{Apple => _, _} This would import all Notebooks and all Fruits except for Apple. These examples demonstrate the great flexibility Scala offers when it comes to importing members selectively and possibly under different names. In summary, an import selector can consist of the following: • A simple name x. This includes x in the set of imported names. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.4 Chapter 13 · Packages and Imports 286 • A renaming clause x => y. This makes the member named x visible under the name y. • A hiding clause x => _. This excludes x from the set of imported names. •A catch-all ‘_’. This imports all members except those members men- tioned in a preceding clause. If a catch-all is given, it must come last in the list of import selectors. The simpler import clauses shown at the beginning of this section can be seen as special abbreviations of import clauses with a selector clause. For example, “import p._” is equivalent to “import p.{_}” and “import p.n” is equivalent to “import p.{n}”. 13.4 Implicit imports Scala adds some imports implicitly to every program. In essence, it is as if the following three import clauses had been added to the top of every source file with extension “.scala”: import java.lang._ // everything in the java.lang package import scala._ // everything in the scala package import Predef._ // everything in the Predef object The java.lang package contains standard Java classes. It is always im- plicitly imported on the JVM implementation of Scala. The .NET implemen- tation would import package system instead, which is the .NET analogue of java.lang. Because java.lang is imported implicitly, you can write Thread instead of java.lang.Thread, for instance. As you have no doubt realized by now, the scala package contains the standard Scala library, with many common classes and objects. Because scala is imported implicitly, you can write List instead of scala.List, for instance. The Predef object contains many definitions of types, methods, and im- plicit conversions that are commonly used on Scala programs. For exam- ple, because Predef is imported implicitly, you can write assert instead of Predef.assert. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.5 Chapter 13 · Packages and Imports 287 The three import clauses above are treated a bit specially in that later imports overshadow earlier ones. For instance, the StringBuilder class is defined both in package scala and, from Java version 1.5 on, also in package java.lang. Because the scala import overshadows the java.lang import, the simple name StringBuilder will refer to scala.StringBuilder, not java.lang.StringBuilder. 13.5 Access modifiers Members of packages, classes, or objects can be labeled with the access modifiers private and protected. These modifiers restrict accesses to the members to certain regions of code. Scala’s treatment of access modifiers roughly follows Java’s but there are some important differences which are explained in this section. Private members Private members are treated similarly to Java. A member labeled private is visible only inside the class or object that contains the member definition. In Scala, this rule applies also for inner classes. This treatment is more con- sistent, but differs from Java. Consider the example shown in Listing 13.10: class Outer{ class Inner{ private def f() { println("f")} class InnerMost{ f() // OK } } (new Inner).f() // error: f is not accessible } Listing 13.10· How private access differs in Scala and Java. In Scala, the access (new Inner).f() is illegal because f is declared private in Inner and the access is not from within class Inner. By con- trast, the first access to f in class InnerMost is OK, because that access Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.5 Chapter 13 · Packages and Imports 288 is contained in the body of class Inner. Java would permit both accesses because it lets an outer class access private members of its inner classes. Protected members Access to protected members is also a bit more restrictive than in Java. In Scala, a protected member is only accessible from subclasses of the class in which the member is defined. In Java such accesses are also possible from other classes in the same package. In Scala, there is another way to achieve this effect, as described below, so protected is free to be left as is. The example shown in Listing 13.11 illustrates protected accesses: packagep{ class Super{ protected def f() { println("f")} } class Sub extends Super { f() } class Other { (new Super).f() // error: f is not accessible } } Listing 13.11· How protected access differs in Scala and Java. In Listing 13.11, the access to f in class Sub is OK because f is declared protected in Super and Sub is a subclass of Super. By contrast the access to f in Other is not permitted, because Other does not inherit from Super. In Java, the latter access would be still permitted because Other is in the same package as Sub. Public members Every member not labeled private or protected is public. There is no explicit modifier for public members. Such members can be accessed from anywhere. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.5 Chapter 13 · Packages and Imports 289 package bobsrockets package navigation { private[bobsrockets] class Navigator { protected[navigation] def useStarChart() {} class LegOfJourney { private[Navigator] val distance = 100 } private[this] var speed = 200 } } package launch { import navigation._ object Vehicle { private[launch] val guide = new Navigator } } Listing 13.12· Flexible scope of protection with access qualifiers. Scope of protection Access modifiers in Scala can be augmented with qualifiers. A modifier of the form private[X] or protected[X] means that access is private or protected “up to” X, where X designates some enclosing package, class or singleton object. Qualified access modifiers give you very fine-grained control over vis- ibility. In particular they enable you to express Java’s accessibility notions such as package private, package protected, or private up to outermost class, which are not directly expressible with simple modifiers in Scala. But they also let you express accessibility rules that cannot be expressed in Java. List- ing 13.12 presents an example with many access qualifiers being used. In this listing, class Navigator is labeled private[bobsrockets]. This means that this class is visible in all classes and objects that are contained in pack- age bobsrockets. In particular, the access to Navigator in object Vehicle is permitted, because Vehicle is contained in package launch, which is contained in bobsrockets. On the other hand, all code outside the package bobsrockets cannot access class Navigator. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.5 Chapter 13 · Packages and Imports 290 This technique is quite useful in large projects that span several packages. It allows you to define things that are visible in several sub-packages of your project but that remain hidden from clients external to your project. The same technique is not possible in Java. There, once a definition escapes its immediate package boundary, it is visible to the world at large. Of course, the qualifier of a private may also be the directly enclosing package. An example is the access modifier of guide in object Vehicle in Listing 13.12. Such an access modifier is equivalent to Java’s package- private access. Table 13.1 · Effects of private qualifiers on LegOfJourney.distance no access modifier public access private[bobsrockets] access within outer package private[navigation] same as package visibility in Java private[Navigator] same as private in Java private[LegOfJourney] same as private in Scala private[this] access only from same object All qualifiers can also be applied to protected, with the same meaning as private. That is, a modifier protected[X] in a class C allows access to the labeled definition in all subclasses of C and also within the enclosing package, class, or object X. For instance, the useStarChart method in List- ing 13.12 is accessible in all subclasses of Navigator and also in all code contained in the enclosing package navigation. It thus corresponds exactly to the meaning of protected in Java. The qualifiers of private can also refer to an enclosing class or object. For instance the distance variable in class LegOfJourney in Listing 13.12 is labeled private[Navigator], so it is visible from everywhere in class Navigator. This gives the same access capabilities as for private members of inner classes in Java. A private[C] where C is the outermost enclosing class is the same as just private in Java. Finally, Scala also has an access modifier that is even more restrictive than private. A definition labeled private[this] is accessible only from within the same object that contains the definition. Such a definition is called object-private. For instance, the definition of speed in class Navigator in Listing 13.12 is object-private. This means that any access must not only be within class Navigator, but it must also be made from the very same in- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.5 Chapter 13 · Packages and Imports 291 stance of Navigator. Thus the accesses “speed” and “this.speed” would be legal from within Navigator. The following access, though, would not be allowed, even if it appeared inside class Navigator: val other = new Navigator other.speed // this line would not compile Marking a member private[this] is a guarantee that it will not be seen from other objects of the same class. This can be useful for documenta- tion. It also sometimes lets you write more general variance annotations (see Section 19.7 for details). To summarize, Table 13.1 on page 290 lists the effects of private qual- ifiers. Each line shows a qualified private modifier and what it would mean if such a modifier were attached to the distance variable declared in class LegOfJourney in Listing 13.12. Visibility and companion objects In Java, static members and instance members belong to the same class, so access modifiers apply uniformly to them. You have already seen that in Scala there are no static members; instead you can have a companion object that contains members that exist only once. For instance, in Listing 13.13 object Rocket is a companion of class Rocket. Scala’s access rules privilege companion objects and classes when it comes to private or protected accesses. A class shares all its access rights with its companion object and vice versa. In particular, an object can ac- cess all private members of its companion class, just as a class can access all private members of its companion object. For instance, the Rocket class above can access method fuel, which is declared private in object Rocket. Analogously, the Rocket object can access the private method canGoHomeAgain in class Rocket. One exception where the similarity between Scala and Java breaks down concerns protected static members. A protected static member of a Java class C can be accessed in all subclasses of C. By contrast, a protected member in a companion object makes no sense, as singleton objects don’t have any subclasses. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.6 Chapter 13 · Packages and Imports 292 class Rocket{ import Rocket.fuel private def canGoHomeAgain = fuel > 20 } object Rocket { private def fuel = 10 def chooseStrategy(rocket: Rocket){ if (rocket.canGoHomeAgain) goHome() else pickAStar() } def goHome() {} def pickAStar() {} } Listing 13.13: Accessing private members of companion classes and objects. 13.6 Package objects So far, the only code you have seen added to packages are classes, traits, and standalone objects. These are by far the most common definitions that are placed at the top level of a package, but Scala doesn’t limit you to just those. Any kind of definition that you can put inside a class, you can also put at the top level of a package. If you have some helper method you’d like to be in scope for an entire package, go ahead and put it right at the top level of the package. To do so, put the definitions in a package object. Each package is allowed to have one package object. Any definitions placed in a package object are considered members of the package itself. An example is shown in Listing 13.14. File package.scala holds a package object for package bobsdelights. Syntactically, a package ob- ject looks much like one of the curly-braces packagings shown earlier in the chapter. The only difference is that it includes the object keyword. It’s a package object, not a package. The contents of the curly braces can in- clude any definitions you like. In this case, the package object includes the showFruit utility method from Listing 13.8. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.6 Chapter 13 · Packages and Imports 293 Given that definition, any other code in any package can import the method just like it would import a class. For example, Listing 13.14 also shows the standalone object PrintMenu, which is located in a different pack- age. PrintMenu can import the utility method showFruit in the same way it would import the class Fruit. // In file bobsdelights/package.scala package object bobsdelights { def showFruit(fruit: Fruit){ import fruit._ println(name +"s are "+ color) } } // In file PrintMenu.scala package printmenu import bobsdelights.Fruits import bobsdelights.showFruit object PrintMenu{ def main(args: Array[String]){ for (fruit <- Fruits.menu) { showFruit(fruit) } } } Listing 13.14· A package object. Looking ahead, there are other uses of package objects for kinds of definitions you haven’t seen yet. Package objects are frequently used to hold package-wide type aliases (Chapter 20) and implicit conversions (Chap- ter 21). The top-level scala package has a package object, and its definitions are available to all Scala code. Package objects are compiled to class files named package.class that are the located in the directory of the package that they augment. It’s useful to keep the same convention for source files. So you would typically put the source file of the package object bobsdelights of Listing 13.14 into a file named package.scala that resides in the bobsdelights directory. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 13.7 Chapter 13 · Packages and Imports 294 13.7 Conclusion In this chapter, you saw the basic constructs for dividing a program into packages. This gives you a simple and useful kind of modularity, so that you can work with very large bodies of code without different parts of the code trampling on each other. This system is the same in spirit as Java’s packages, but there are some differences where Scala chooses to be more consistent or more general. Looking ahead, Chapter 29 describes a more flexible module system than division into packages. In addition to letting you separate code into several namespaces, that approach allows modules to be parameterized and to inherit from each other. In the next chapter, we’ll turn our attention to assertions and unit testing. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 14 Assertions and Unit Testing Two important ways to check that the behavior of the software you write is as you expect are assertions and unit tests. In this chapter, we’ll show you several options you have in Scala to write and run them. 14.1 Assertions Assertions in Scala are written as calls of a predefined method assert.1 The expression assert(condition) throws an AssertionError if condition does not hold. There’s also a two-argument version of assert. The expres- sion assert(condition, explanation) tests condition, and, if it does not hold, throws an AssertionError that contains the given explanation. The type of explanation is Any, so you can pass any object as the explana- tion. The assert method will call toString on it to get a string explanation to place inside the AssertionError. For example, in the method named “above” of class Element, shown in Listing 10.13 on page 247, you might place an assert after the calls to widen to make sure that the widened elements have equal widths. This is shown in Listing 14.1. Another way you might choose to do this is to check the widths at the end of the widen method, right before you return the value. You can accomplish this by storing the result in a val, performing an assertion on the result, then mentioning the val last so the result is returned if the assertion succeeds. You 1The assert method is defined in the Predef singleton object, whose members are automatically imported into every Scala source file. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.1 Chapter 14 · Assertions and Unit Testing 296 def above(that: Element): Element = { val this1 = this widen that.width val that1 = that widen this.width assert(this1.width == that1.width) elem(this1.contents ++ that1.contents) } Listing 14.1· Using an assertion. can do this more concisely, however, with a convenience method in Predef named ensuring, as shown in Listing 14.2. The ensuring method can be used with any result type because of an implicit conversion. Although it looks in this code as if we’re invoking ensuring on widen’s result, which is type Element, we’re actually invok- ing ensuring on a type to which Element is implicitly converted. The ensuring method takes one argument, a predicate function that takes a result type and returns Boolean. ensuring will pass the result to the predicate. If the predicate returns true, ensuring will return the result. Otherwise, ensuring will throw an AssertionError. In this example, the predicate is “w <= _.width”. The underscore is a placeholder for the one argument passed to the predicate, the Element result of the widen method. If the width passed as w to widen is less than or equal to the width of the result Element, the predicate will result in true, and ensuring will result in the Element on which it was invoked. Because this is the last expression of the widen method, widen itself will then result in the Element. private def widen(w: Int): Element = if (w <= width) this else { val left = elem('', (w - width) / 2, height) var right = elem('', w - width - left.width, height) left beside this beside right } ensuring (w <= _.width) Listing 14.2· Using ensuring to assert a function’s result. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.2 Chapter 14 · Assertions and Unit Testing 297 Assertions (and ensuring checks) can be enabled and disabled using the JVM’s -ea and -da command-line flags. When enabled, each assertion serves as a little test that uses the actual data encountered as the software runs. In the remainder of this chapter, we’ll focus on the writing of external unit tests, which provide their own test data and run independently from the application. 14.2 Unit testing in Scala You have many options for unit testing in Scala, from established Java tools, such as JUnit and TestNG, to new tools written in Scala, such as ScalaTest, specs, and ScalaCheck. In the remainder of this chapter, we’ll give you a quick tour of these tools. We’ll start with ScalaTest. ScalaTest provides several ways to write tests, the simplest of which is to create classes that extend org.scalatest.Suite and define test methods in those classes. A Suite represents a suite of tests. Test methods start with "test". Listing 14.3 shows an example: import org.scalatest.Suite import Element.elem class ElementSuite extends Suite { def testUniformElement() { val ele = elem('x', 2, 3) assert(ele.width == 2) } } Listing 14.3· Writing a test method with Suite. Although ScalaTest includes a Runner application, you can also run a Suite directly from the Scala interpreter by invoking execute on it. Trait Suite’s execute method uses reflection to discover its test methods and invokes them. Here’s an example: scala> (new ElementSuite).execute() Test Starting - ElementSuite.testUniformElement Test Succeeded - ElementSuite.testUniformElement Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.3 Chapter 14 · Assertions and Unit Testing 298 ScalaTest facilitates different styles of testing, because execute can be overridden in Suite subtypes. For example, ScalaTest offers a trait called FunSuite, which overrides execute so that you can define tests as function values rather than methods. Listing 14.4 shows an example: import org.scalatest.FunSuite import Element.elem class ElementSuite extends FunSuite { test("elem result should have passed width"){ val ele = elem('x', 2, 3) assert(ele.width == 2) } } Listing 14.4· Writing a test function with FunSuite. The “Fun” in FunSuite stands for function. “test” is a method de- fined in FunSuite, which will be invoked by the primary constructor of ElementSuite. You specify the name of the test as a string between the parentheses, and the test code itself between curly braces. The test code is a function passed as a by-name parameter to test, which registers it for later execution. One benefit of FunSuite is you need not name all your tests start- ing with “test”. In addition, you can more easily give long names to your tests, because you need not encode them in camel case, as you must do with test methods.2 14.3 Informative failure reports The tests in the previous two examples attempt to create an element of width 2 and assert that the width of the resulting element is indeed 2. Were this assertion to fail, you would see a message that indicated an assertion failed. You’d be given a line number, but wouldn’t know the two values that were unequal. You could find out by placing a string message in the assertion that includes both values, but a more concise approach is to use the triple-equals operator, which ScalaTest provides for this purpose: 2You can download ScalaTest from http://www.scalatest.org/. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.3 Chapter 14 · Assertions and Unit Testing 299 assert(ele.width === 2) Were this assertion to fail, you would see a message such as “3 did not equal 2” in the failure report. This would tell you that ele.width wrongly returned 3. The triple-equals operator does not differentiate between the actual and expected result. It just indicates that the left operand did not equal the right operand. If you wish to emphasize this distinction, you could alternatively use ScalaTest’s expect method, like this: expect(2){ ele.width } With this expression you indicate that you expect the code between the curly braces to result in 2. Were the code between the braces to result in 3, you’d see the message, “Expected 2, but got 3” in the test failure report. If you want to check that a method throws an expected exception, you can use ScalaTest’s intercept method, like this: intercept[IllegalArgumentException]{ elem('x',-2, 3) } If the code between the curly braces completes abruptly with an instance of the passed exception class, intercept will return the caught exception, in case you want to inspect it further. Most often, you’ll probably only care that the expected exception was thrown, and ignore the result of intercept, as is done in this example. On the other hand, if the code does not throw an exception, or throws a different exception, the intercept method will throw a TestFailedException, and you’ll get a helpful error message in the failure report, such as: Expected IllegalArgumentException to be thrown, but NegativeArraySizeException was thrown. The goal of ScalaTest’s === operator and its expect and intercept methods is to help you write assertion-based tests that are clear and con- cise. In the next section, we’ll show you how to use this syntax in JUnit and TestNG tests written in Scala. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.4 Chapter 14 · Assertions and Unit Testing 300 14.4 Using JUnit and TestNG The most popular unit testing framework on the Java platform is JUnit, an open source tool written by Kent Beck and Erich Gamma. You can write JUnit tests in Scala quite easily. Here’s an example using JUnit 3.8.1: import junit.framework.TestCase import junit.framework.Assert.assertEquals import junit.framework.Assert.fail import Element.elem class ElementTestCase extends TestCase { def testUniformElement() { val ele = elem('x', 2, 3) assertEquals(2, ele.width) assertEquals(3, ele.height) try { elem('x',-2, 3) fail() } catch { case e: IllegalArgumentException => // expected } } } Once you compile this class, JUnit will run it like any other TestCase. JU- nit doesn’t care that it was written in Scala. If you wish to use ScalaTest’s assertion syntax in your JUnit 3 test, however, you can instead subclass JUnit3Suite, as shown Listing 14.5. Trait JUnit3Suite extends TestCase, so once you compile this class, JUnit will run it just fine, even though it uses ScalaTest’s more concise as- sertion syntax. Moreover, because JUnit3Suite mixes in ScalaTest’s trait Suite, you can alternatively run this test class with ScalaTest’s runner. The goal is to provide a gentle migration path to enable JUnit users to start writ- ing JUnit tests in Scala that take advantage of the conciseness afforded by Scala. ScalaTest also has a JUnitWrapperSuite, which enables you to run existing JUnit tests written in Java with ScalaTest’s runner. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.4 Chapter 14 · Assertions and Unit Testing 301 import org.scalatest.junit.JUnit3Suite import Element.elem class ElementSuite extends JUnit3Suite { def testUniformElement() { val ele = elem('x', 2, 3) assert(ele.width === 2) expect(3) { ele.height } intercept[IllegalArgumentException]{ elem('x',-2, 3) } } } Listing 14.5· Writing a JUnit test with JUnit3Suite. ScalaTest offers similar integration classes for JUnit 4 and TestNG, both of which make heavy use of annotations. We’ll show an example using TestNG, an open source framework written by Cédric Beust and Alexan- dru Popescu. As with JUnit, you can simply write TestNG tests in Scala, compile them, and run them with TestNG’s runner. Here’s an example: import org.testng.annotations.Test import org.testng.Assert.assertEquals import Element.elem class ElementTests { @Test def verifyUniformElement() { val ele = elem('x', 2, 3) assertEquals(ele.width, 2) assertEquals(ele.height, 3) } @Test( expectedExceptions = Array(classOf[IllegalArgumentException]) ) def elemShouldThrowIAE() { elem('x',-2, 3)} } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.5 Chapter 14 · Assertions and Unit Testing 302 If you prefer to use ScalaTest’s assertion syntax in your TestNG tests, how- ever, you can extend trait TestNGSuite, as shown in Listing 14.6: import org.scalatest.testng.TestNGSuite import org.testng.annotations.Test import Element.elem class ElementSuite extends TestNGSuite { @Test def verifyUniformElement() { val ele = elem('x', 2, 3) assert(ele.width === 2) expect(3) { ele.height } intercept[IllegalArgumentException]{ elem('x',-2, 3) } } } Listing 14.6· Writing a TestNG test with TestNGSuite. As with JUnit3Suite, you can run a TestNGSuite with either TestNG or ScalaTest, and ScalaTest also provides a TestNGWrapperSuite that en- ables you to run existing TestNG tests written in Java with ScalaTest. To see an example of JUnit 4 tests written in Scala, see Section 31.2. 14.5 Tests as specifications In the behavior-driven development (BDD) testing style, the emphasis is on writing human-readable specifications of the expected behavior of code, and accompanying tests that verify the code has the specified behavior. ScalaTest includes several traits—Spec, WordSpec, FlatSpec, and FeatureSpec— which facilitate this style of testing. An example of a FlatSpec is shown in Listing 14.7. In a FlatSpec, you write tests as specifier clauses. You start by writing a name for the subject under test as a string ("A UniformElement" in List- ing 14.7), then should (or must or can), then a string that specifies a bit of behavior required of the subject, then in. In the curly braces following in, you write code that tests the specified behavior. In subsequent clauses you Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.5 Chapter 14 · Assertions and Unit Testing 303 import org.scalatest.FlatSpec import org.scalatest.matchers.ShouldMatchers import Element.elem class ElementSpec extends FlatSpec with ShouldMatchers { "A UniformElement" should "have a width equal to the passed value" in { val ele = elem('x', 2, 3) ele.width should be (2) } it should "have a height equal to the passed value" in { val ele = elem('x', 2, 3) ele.height should be (3) } it should "throw an IAE if passed a negative width" in { evaluating { elem('x',-2, 3) } should produce [IllegalArgumentException] } } Listing 14.7· Specifying and testing behavior with a ScalaTest FlatSpec. can write it to refer to the most recently given subject. When a FlatSpec is executed, it will run each specifier clause as a ScalaTest test. FlatSpec (and ScalaTest’s other specification traits) generate output that reads more like a specification when run. For example, here’s what the output will look like if you run ElementSpec from Listing 14.7 in the interpreter: scala> (new ElementSpec).execute() A UniformElement - should have a width equal to the passed value - should have a height equal to the passed value - should throw an IAE if passed a negative width Listing 14.7 also illustrates ScalaTest’s matchers DSL. By mixing in trait ShouldMatchers, you can write assertions that read more like natu- ral language and generate more descriptive failure messages. ScalaTest pro- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.5 Chapter 14 · Assertions and Unit Testing 304 vides many matchers in its DSL, and also enables you to create your own matchers. The matchers shown in Listing 14.7 include the “should be” and “evaluating { ...} should produce” syntax. You can alternatively mix in MustMatchers if you prefer must to should. For example, mixing in MustMatchers would allow you to write expressions such as: result must be >= 0 array must have length 3 map must contain key 'c' If the last assertion failed, you’d see an error message similar to: Map('a' -> 1, 'b' -> 2) did not contain key 'c' The specs testing framework, an open source tool written in Scala by Eric Torreborre, also supports the BDD style of testing but with a different syntax. For example, you could use specs to write the test shown in Listing 14.8: import org.specs._ import Element.elem object ElementSpecification extends Specification { "A UniformElement" should { "have a width equal to the passed value" in { val ele = elem('x', 2, 3) ele.width must be_==(2) } "have a height equal to the passed value" in { val ele = elem('x', 2, 3) ele.height must be_==(3) } "throw an IAE if passed a negative width" in { elem('x',-2, 3) must throwA[IllegalArgumentException] } } } Listing 14.8· Specifying and testing behavior with the specs framework. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.6 Chapter 14 · Assertions and Unit Testing 305 Like ScalaTest, specs provides a matchers DSL. You can see some ex- amples of specs matchers in action in Listing 14.8 in the lines that contain “must be_==” and “must throwA”. You can use specs standalone, but it is also integrated with ScalaTest and JUnit, so you can run specs tests with those tools as well.3 14.6 Property-based testing Another useful testing tool for Scala is ScalaCheck, an open source frame- work written by Rickard Nilsson. ScalaCheck enables you to specify prop- erties that the code under test must obey. For each property, ScalaCheck will generate test data and run tests that check whether the property holds. List- ing 14.9 show an example of using ScalaCheck from a ScalaTest WordSpec that mixes in trait Checkers: import org.scalatest.WordSpec import org.scalatest.prop.Checkers import org.scalacheck.Prop._ import Element.elem class ElementSpec extends WordSpec with Checkers { "elem result" must { "have passed width" in { check((w: Int) => w > 0 ==> (elem('x', w, 3).width == w)) } "have passed height" in { check((h: Int) => h > 0 ==> (elem('x', 2, h).height == h)) } } } Listing 14.9· Writing property-based tests with ScalaCheck. WordSpec is a ScalaTest trait that provides syntax similar to a specs Specification. The Checkers trait provides several check methods that allow you to mix ScalaCheck property-based tests with traditional assertion- 3You can download specs from http://code.google.com/p/specs/. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.7 Chapter 14 · Assertions and Unit Testing 306 or matcher-based tests. In this example, we check two properties that the elem factory should obey. ScalaCheck properties are expressed as function values that take as parameters the required test data, which will be generated by ScalaCheck. In the first property shown in Listing 14.9, the test data is an integer named w that represents a width. Inside the body of the function, you see this code: w > 0 ==> (elem('x', w, 3).width == w) The ==> symbol is a ScalaCheck implication operator. It implies that when- ever the left hand expression is true, the expression on the right must hold true. Thus in this case, the expression on the right of ==> must hold true whenever w is greater than 0. The right-hand expression in this case will yield true if the width passed to the elem factory is the same as the width of the Element returned by the factory. With this small amount of code, ScalaCheck will generate possibly hun- dreds of values for w and test each one, looking for a value for which the property doesn’t hold. If the property holds true for every value ScalaCheck tries, the test will pass. Otherwise, the test will complete abruptly with an AssertionError that contains information including the value that caused the failure. 14.7 Organizing and running tests Each framework mentioned in this chapter provides some mechanism for organizing and running tests. In this section, we’ll give a quick overview of ScalaTest’s approach. To get the full story on any of these frameworks, however, you’ll need to consult their documentation. In ScalaTest, you organize large test suites by nesting Suites inside Suites. When a Suite is executed, it will execute its nested Suites as well as its tests. The nested Suites will in turn execute their nested Suites, and so on. A large test suite, therefore, is represented as a tree of Suite objects. When you execute the root Suite in the tree, all Suites in the tree will be executed. You can nest suites manually or automatically. To nest manually, you ei- ther override the nestedSuites method on your Suites, or pass the Suites you want to nest to the constructor of class SuperSuite, which ScalaTest provides for this purpose. To nest automatically, you provide package names Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.7 Chapter 14 · Assertions and Unit Testing 307 Figure 14.1· ScalaTest’s graphical reporter. to ScalaTest’s Runner, which will discover Suites automatically, nest them under a root Suite, and execute the root Suite. You can invoke ScalaTest’s Runner application from the command line or an ant task. You must specify which suites you want to run, either by naming the suites explicitly or indicating name prefixes with which you want Runner to perform automatic discovery. You can optionally specify a run- path, a list of directories and JAR files from which to load class files for the tests and the code they exercise.4 You can also specify one or more reporters, which will determine how test results will be presented. For example, the ScalaTest distribution includes the suites that test Scala- Test itself. You can run one of these suites, SuiteSuite,5 with the following command: $ scala -cp scalatest-1.2.jar org.scalatest.tools.Runner -p "scalatest-1.2-tests.jar" -s org.scalatest.SuiteSuite With -cp you place ScalaTest’s JAR file on the class path. The next token, org.scalatest.tools.Runner, is the fully qualified name of the Runner 4Tests can be anywhere on the runpath or classpath, but typically you would keep your tests separate from your production code, in a separate directory hierarchy that mirrors your source tree’s directory hierarchy. 5SuiteSuite is so-named because it is a suite of tests that test trait Suite itself. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 14.8 Chapter 14 · Assertions and Unit Testing 308 application. Scala will run this application and pass the remaining tokens as command line arguments. The -p specifies the runpath, which in this case is a JAR file that contains the suite classes: scalatest-1.2-tests.jar. The -s indicates SuiteSuite is the suite to execute. Because you don’t explicitly specify a reporter, you will by default get the graphical reporter. The result is shown in Figure 14.1. 14.8 Conclusion In this chapter you saw examples of mixing assertions directly in production code as well as writing them externally in unit tests. You saw that as a Scala programmer, you can take advantage of popular testing tools from the Java community, such as JUnit and TestNG, as well as newer tools designed ex- plicitly for Scala, such as ScalaTest, ScalaCheck, and specs. Both in-code assertions and unit testing can help you achieve your software quality goals. We felt that these techniques are important enough to justify the short de- tour from the Scala tutorial that this chapter represented. In the next chapter, however, we’ll return to the language tutorial and cover a very useful aspect of Scala: pattern matching. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 15 Case Classes and Pattern Matching This chapter introduces case classes and pattern matching, twin constructs that support you when writing regular, non-encapsulated data structures. These two constructs are particularly helpful for tree-like recursive data. If you have programmed in a functional language before, then you will probably recognize pattern matching. Case classes will be new to you, though. Case classes are Scala’s way to allow pattern matching on objects without requiring a large amount of boilerplate. In the common case, all you need to do is add a single case keyword to each class that you want to be pattern matchable. This chapter starts with a simple example of case classes and pattern matching. It then goes through all of the kinds of patterns that are supported, talks about the role of sealed classes, discusses the Option type, and shows some non-obvious places in the language where pattern matching is used. Finally, a larger, more realistic example of pattern matching is shown. 15.1 A simple example Before delving into all the rules and nuances of pattern matching, it is worth looking at a simple example to get the general idea. Let’s say you need to write a library that manipulates arithmetic expressions, perhaps as part of a domain-specific language you are designing. A first step to tackle this problem is the definition of the input data. To keep things simple, we’ll concentrate on arithmetic expressions consisting of variables, numbers, and unary and binary operations. This is expressed by the hierarchy of Scala classes shown in Listing 15.1. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.1 Chapter 15 · Case Classes and Pattern Matching 310 abstract class Expr case class Var(name: String) extends Expr case class Number(num: Double) extends Expr case class UnOp(operator: String, arg: Expr) extends Expr case class BinOp(operator: String, left: Expr, right: Expr) extends Expr Listing 15.1· Defining case classes. The hierarchy includes an abstract base class Expr with four subclasses, one for each kind of expression being considered.1 The bodies of all five classes are empty. As mentioned previously, in Scala you can leave out the braces around an empty class body if you wish, so class C is the same as class C {}. Case classes The other noteworthy thing about the declarations of Listing 15.1 is that each subclass has a case modifier. Classes with such a modifier are called case classes. Using the modifier makes the Scala compiler add some syntactic conveniences to your class. First, it adds a factory method with the name of the class. This means you can write say, Var("x") to construct a Var object instead of the slightly longer new Var("x"): scala> val v = Var("x") v: Var = Var(x) The factory methods are particularly nice when you nest them. Because there are no noisy new keywords sprinkled throughout the code, you can take in the expression’s structure at a glance: scala> val op = BinOp("+", Number(1), v) op: BinOp = BinOp(+,Number(1.0),Var(x)) The second syntactic convenience is that all arguments in the parameter list of a case class implicitly get a val prefix, so they are maintained as fields: 1Instead of an abstract class, we could have equally well chosen to model the root of that class hierarchy as a trait. Modeling it as an abstract class may be slightly more efficient. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.1 Chapter 15 · Case Classes and Pattern Matching 311 scala> v.name res0: String = x scala> op.left res1: Expr = Number(1.0) Third, the compiler adds “natural” implementations of methods toString, hashCode, and equals to your class. They will print, hash, and compare a whole tree consisting of the class and (recursively) all its arguments. Since == in Scala always delegates to equals, this means that elements of case classes are always compared structurally: scala> println(op) BinOp(+,Number(1.0),Var(x)) scala> op.right == Var("x") res3: Boolean = true Finally, the compiler adds a copy method to your class for making modified copies. This method is useful for making a new instance of the class that is the same as another one except that one or two attributes are different. The method works by using named and default parameters (Section 8.8). You specify the changes you’d like to make by using named parameters. For any parameter you don’t specify, the value from the old object is used. As an example, here is how you can make an operation just like op except that the operator has changed: scala> op.copy(operator = "-") res4: BinOp = BinOp(-,Number(1.0),Var(x)) All these conventions add a lot of convenience, at a small price. The price is that you have to write the case modifier and that your classes and objects become a bit larger. They are larger because additional methods are generated and an implicit field is added for each constructor parameter. However, the biggest advantage of case classes is that they support pattern matching. Pattern matching Say you want to simplify arithmetic expressions of the kinds just presented. There is a multitude of possible simplification rules. The following three rules just serve as an illustration: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.1 Chapter 15 · Case Classes and Pattern Matching 312 UnOp("-", UnOp("-", e)) => e // Double negation BinOp("+", e, Number(0)) => e // Adding zero BinOp("*", e, Number(1)) => e // Multiplying by one Using pattern matching, these rules can be taken almost as they are to form the core of a simplification function in Scala, as shown in Listing 15.2. The function, simplifyTop, can be used like this: scala> simplifyTop(UnOp("-", UnOp("-", Var("x")))) res4: Expr = Var(x) def simplifyTop(expr: Expr): Expr = expr match { case UnOp("-", UnOp("-", e)) => e // Double negation case BinOp("+", e, Number(0)) => e // Adding zero case BinOp("*", e, Number(1)) => e // Multiplying by one case _ => expr } Listing 15.2· The simplifyTop function, which does a pattern match. The right-hand side of simplifyTop consists of a match expression. match corresponds to switch in Java, but it’s written after the selector ex- pression. I.e., it’s: selector match { alternatives } instead of: switch (selector){ alternatives } A pattern match includes a sequence of alternatives, each starting with the keyword case. Each alternative includes a pattern and one or more expres- sions, which will be evaluated if the pattern matches. An arrow symbol => separates the pattern from the expressions. A match expression is evaluated by trying each of the patterns in the order they are written. The first pattern that matches is selected, and the part following the arrow is selected and executed. A constant pattern like "+" or 1 matches values that are equal to the constant with respect to ==.A variable pattern like e matches every value. The variable then refers to that value in the right hand side of the case clause. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.1 Chapter 15 · Case Classes and Pattern Matching 313 In this example, note that the first three examples evaluate to e, a variable that is bound within the associated pattern. The wildcard pattern (_) also matches every value, but it does not introduce a variable name to refer to that value. In Listing 15.2, notice how the match ends with a default case that does nothing to the expression. Instead, it just results in expr, the expression matched upon. A constructor pattern looks like UnOp("-", e). This pattern matches all values of type UnOp whose first argument matches "-" and whose sec- ond argument matches e. Note that the arguments to the constructor are themselves patterns. This allows you to write deep patterns using a concise notation. Here’s an example: UnOp("-", UnOp("-", e)) Imagine trying to implement this same functionality using the visitor design pattern!2 Almost as awkward, imagine implementing it as a long sequence of if statements, type tests, and type casts. match compared to switch Match expressions can be seen as a generalization of Java-style switches. A Java-style switch can be naturally expressed as a match expression where each pattern is a constant and the last pattern may be a wildcard (which rep- resents the default case of the switch). There are three differences to keep in mind, however. First, match is an expression in Scala, i.e., it always re- sults in a value. Second, Scala’s alternative expressions never “fall through” into the next case. Third, if none of the patterns match, an exception named MatchError is thrown. This means you always have to make sure that all cases are covered, even if it means adding a default case where there’s noth- ing to do. Listing 15.3 shows an example. The second case is necessary in Listing 15.3, because otherwise the match expression would throw a MatchError for every expr argument that is not a BinOp. In this example, no code is specified for that second case, so if that case runs it does nothing. The result of either case is the unit value ‘()’, which is also, therefore, the result of the entire match expression. 2Gamma, et. al., Design Patterns [Gam95] Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 314 expr match{ case BinOp(op, left, right) => println(expr +" is a binary operation") case _ => } Listing 15.3· A pattern match with an empty “default” case. 15.2 Kinds of patterns The previous example showed several kinds of patterns in quick succession. Now take a minute to look at each. The syntax of patterns is easy, so do not worry about that too much. All patterns look exactly like the corresponding expression. For instance, given the hierarchy of Listing 15.1, the pattern Var(x) matches any variable expression, binding x to the name of the variable. Used as an expression, Var(x)—exactly the same syntax—recreates an equivalent object, assuming x is already bound to the variable’s name. Since the syntax of patterns is so transparent, the main thing to pay attention to is just what kinds of patterns are possible. Wildcard patterns The wildcard pattern (_) matches any object whatsoever. You have already seen it used as a default, catch-all alternative, like this: expr match { case BinOp(op, left, right) => println(expr +" is a binary operation") case _ => } Wildcards can also be used to ignore parts of an object that you do not care about. For example, the previous example does not actually care what the elements of a binary operation are. It just checks whether it is a binary operation at all. Thus the code can just as well use the wildcard pattern for the elements of the BinOp, as shown in Listing 15.4: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 315 expr match{ case BinOp(_, _, _) => println(expr +" is a binary operation") case _ => println("It's something else") } Listing 15.4· A pattern match with wildcard patterns. Constant patterns A constant pattern matches only itself. Any literal may be used as a constant. For example, 5, true, and "hello" are all constant patterns. Also, any val or singleton object can be used as a constant. For example, Nil, a singleton object, is a pattern that matches only the empty list. Listing 15.5 shows some examples of constant patterns: def describe(x: Any) = x match { case 5 => "five" case true => "truth" case "hello" => "hi!" case Nil => "the empty list" case _ => "something else" } Listing 15.5· A pattern match with constant patterns. Here is how the pattern match shown in Listing 15.5 looks in action: scala> describe(5) res6: java.lang.String = five scala> describe(true) res7: java.lang.String = truth scala> describe("hello") res8: java.lang.String = hi! scala> describe(Nil) res9: java.lang.String = the empty list scala> describe(List(1,2,3)) res10: java.lang.String = something else Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 316 Variable patterns A variable pattern matches any object, just like a wildcard. Unlike a wild- card, Scala binds the variable to whatever the object is. You can then use this variable to act on the object further. For example, Listing 15.6 shows a pattern match that has a special case for zero, and a default case for all other values. The default case uses a variable pattern so that it has a name for the value, no matter what it is. expr match{ case0 => "zero" case somethingElse => "not zero: "+ somethingElse } Listing 15.6· A pattern match with a variable pattern. Variable or constant? Constant patterns can have symbolic names. You saw this already when we used Nil as a pattern. Here is a related example, where a pattern match involves the constants E (2.71828. . . ) and Pi (3.14159. . . ): scala> import math.{E, Pi} import math.{E, Pi} scala> E match { case Pi => "strange math? Pi = "+ Pi case _ => "OK" } res11: java.lang.String = OK As expected, E does not match Pi, so the “strange math” case is not used. How does the Scala compiler know that Pi is a constant imported from scala.math, and not a variable that stands for the selector value itself? Scala uses a simple lexical rule for disambiguation: a simple name starting with a lowercase letter is taken to be a pattern variable; all other references are taken to be constants. To see the difference, create a lowercase alias for pi and try with that: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 317 scala> val pi = math.Pi pi: Double = 3.141592653589793 scala> E match { case pi => "strange math? Pi = "+ pi } res12: java.lang.String = strange math? Pi = 2.718281828459045 Here the compiler will not even let you add a default case at all. Since pi is a variable pattern, it will match all inputs, and so no cases following it can be reached: scala> E match { case pi => "strange math? Pi = "+ pi case _ => "OK" } :9: error: unreachable code case _ => "OK" ˆ If you need to, you can still use a lowercase name for a pattern constant, using one of two tricks. First, if the constant is a field of some object, you can prefix it with a qualifier. For instance, pi is a variable pattern, but this.pi or obj.pi are constants even though they start with lowercase letters. If that does not work (because pi is a local variable, say), you can alternatively enclose the variable name in back ticks. For instance, `pi` would again be interpreted as a constant, not as a variable: scala> E match { case `pi` => "strange math? Pi = "+ pi case _ => "OK" } res14: java.lang.String = OK As you can see, the back-tick syntax for identifiers is used for two different purposes in Scala to help you code your way out of unusual circumstances. Here you see that it can be used to treat a lowercase identifier as a constant in a pattern match. Earlier on, in Section 6.10, you saw that it can also be used to treat a keyword as an ordinary identifier, e.g., writing Thread.`yield`() treats yield as an identifier rather than a keyword. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 318 Constructor patterns Constructors are where pattern matching becomes really powerful. A con- structor pattern looks like “BinOp("+", e, Number(0))”. It consists of a name (BinOp) and then a number of patterns within parentheses: "+", e, and Number(0). Assuming the name designates a case class, such a pattern means to first check that the object is a member of the named case class, and then to check that the constructor parameters of the object match the extra patterns supplied. These extra patterns mean that Scala patterns support deep matches. Such patterns not only check the top-level object supplied, but also check the contents of the object against further patterns. Since the extra patterns can themselves be constructor patterns, you can use them to check arbitrarily deep into an object. For example, the pattern shown in Listing 15.7 checks that the top-level object is a BinOp, that its third constructor parameter is a Number, and that the value field of that number is 0. This pattern is one line long yet checks three levels deep. expr match{ case BinOp("+", e, Number(0)) => println("a deep match") case _ => } Listing 15.7· A pattern match with a constructor pattern. Sequence patterns You can match against sequence types like List or Array just like you match against case classes. Use the same syntax, but now you can specify any number of elements within the pattern. For example, Listing 15.8 shows a pattern that checks for a three-element list starting with zero: expr match{ case List(0, _, _) => println("found it") case _ => } Listing 15.8· A sequence pattern with a fixed length. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 319 If you want to match against a sequence without specifying how long it can be, you can specify _* as the last element of the pattern. This funny- looking pattern matches any number of elements within a sequence, includ- ing zero elements. Listing 15.9 shows an example that matches any list that starts with zero, regardless of how long the list is. expr match{ case List(0,_*) => println("found it") case _ => } Listing 15.9· A sequence pattern with an arbitrary length. Tuple patterns You can match against tuples, too. A pattern like (a, b, c) matches an arbitrary 3-tuple. An example is shown in Listing 15.10: def tupleDemo(expr: Any) = expr match{ case (a, b, c) => println("matched "+ a + b + c) case _ => } Listing 15.10· A pattern match with a tuple pattern. If you load the tupleDemo method shown in Listing 15.10 into the inter- preter, and pass to it a tuple with three elements, you’ll see: scala> tupleDemo(("a ", 3, "-tuple")) matched a 3-tuple Typed patterns You can use a typed pattern as a convenient replacement for type tests and type casts. Listing 15.11 shows an example: Here are a few examples of using the generalSize method in the Scala interpreter: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 320 def generalSize(x: Any) = x match { case s: String => s.length case m: Map[_, _] => m.size case _ => -1 } Listing 15.11· A pattern match with typed patterns. scala> generalSize("abc") res16: Int = 3 scala> generalSize(Map(1 -> 'a', 2 -> 'b')) res17: Int = 2 scala> generalSize(math.Pi) res18: Int = -1 The generalSize method returns the size or length of objects of various types. Its argument is of type Any, so it could be any value. If the argument is a String, the method returns the string’s length. The pattern “s: String” is a typed pattern; it matches every (non-null) instance of String. The pattern variable s then refers to that string. Note that, even though s and x refer to the same value, the type of x is Any, but the type of s is String. So you can write s.length in the alternative expression that corresponds to the pattern, but you could not write x.length, because the type Any does not have a length member. An equivalent but more long-winded way that achieves the effect of a match against a typed pattern employs a type test followed by a type cast. Scala uses a different syntax than Java for these. To test whether an expres- sion expr has type String, say, you write: expr.isInstanceOf[String] To cast the same expression to type String, you use: expr.asInstanceOf[String] Using a type test and cast, you could rewrite the first case of the previous match expression as shown in Listing 15.12. The operators isInstanceOf and asInstanceOf are treated as prede- fined methods of class Any which take a type parameter in square brackets. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 321 if (x.isInstanceOf[String]) { val s = x.asInstanceOf[String] s.length } else ... Listing 15.12· Using isInstanceOf and asInstanceOf (poor style). In fact, x.asInstanceOf[String] is a special case of a method invocation with an explicit type parameter String. As you will have noted by now, writing type tests and casts is rather verbose in Scala. That’s intentional, because it is not encouraged practice. You are usually better off using a pattern match with a typed pattern. That’s particularly true if you need to do both a type test and a type cast, because both operations are then rolled into a single pattern match. The second case of the previous match expression contains the type pat- tern “m: Map[_, _]”. This pattern matches any value that is a Map of some arbitrary key and value types and lets m refer to that value. Therefore, m.size is well typed and returns the size of the map. The underscores in the type pattern are like wildcards in other patterns. You could have also used (low- ercase) type variables instead. Type erasure Can you also test for a map with specific element types? This would be handy, say for testing whether a given value is a map from type Int to type Int. Let’s try: scala> def isIntIntMap(x: Any) = x match { case m: Map[Int, Int] => true case _ => false } warning: there were unchecked warnings; re-run with -unchecked for details isIntIntMap: (x: Any)Boolean The interpreter emitted an “unchecked warning.” You can find out details by starting the interpreter again with the -unchecked command-line option: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 322 scala> :quit $ scala -unchecked Welcome to Scala version 2.8.1 (Java HotSpot(TM) Client VM, Java 1.5.0_13). Type in expressions to have them evaluated. Type :help for more information. scala> def isIntIntMap(x: Any) = x match { case m: Map[Int, Int] => true case _ => false } :5: warning: non variable type-argument Int in type pattern is unchecked since it is eliminated by erasure case m: Map[Int, Int] => true ˆ Scala uses the erasure model of generics, just like Java does. This means that no information about type arguments is maintained at runtime. Conse- quently, there is no way to determine at runtime whether a given Map object has been created with two Int arguments, rather than with arguments of dif- ferent types. All the system can do is determine that a value is a Map of some arbitrary type parameters. You can verify this behavior by applying isIntIntMap to arguments of different instances of class Map: scala> isIntIntMap(Map(1 -> 1)) res19: Boolean = true scala> isIntIntMap(Map("abc" -> "abc")) res20: Boolean = true The first application returns true, which looks correct, but the second ap- plication also returns true, which might be a surprise. To alert you to the possibly non-intuitive runtime behavior, the compiler emits unchecked warn- ings like the one shown above. The only exception to the erasure rule is arrays, because they are handled specially in Java as well as in Scala. The element type of an array is stored with the array value, so you can pattern match on it. Here’s an example: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.2 Chapter 15 · Case Classes and Pattern Matching 323 scala> def isStringArray(x: Any) = x match { case a: Array[String] => "yes" case _ => "no" } isStringArray: (x: Any)java.lang.String scala> val as = Array("abc") as: Array[java.lang.String] = Array(abc) scala> isStringArray(as) res21: java.lang.String = yes scala> val ai = Array(1, 2, 3) ai: Array[Int] = Array(1, 2, 3) scala> isStringArray(ai) res22: java.lang.String = no Variable binding In addition to the standalone variable patterns, you can also add a variable to any other pattern. You simply write the variable name, an at sign (@), and then the pattern. This gives you a variable-binding pattern. The meaning of such a pattern is to perform the pattern match as normal, and if the pattern succeeds, set the variable to the matched object just as with a simple variable pattern. As an example, Listing 15.13 shows a pattern match that looks for the absolute value operation being applied twice in a row. Such an expression can be simplified to only take the absolute value one time. expr match{ case UnOp("abs", e @ UnOp("abs", _)) => e case _ => } Listing 15.13· A pattern with a variable binding (via the @ sign). In Listing 15.13, there is a variable-binding pattern with e as the variable and UnOp("abs", _) as the pattern. If the entire pattern match succeeds, then the portion that matched the UnOp("abs", _) part is made available as variable e. As the code is written, e then gets returned as is. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.3 Chapter 15 · Case Classes and Pattern Matching 324 15.3 Pattern guards Sometimes, syntactic pattern matching is not precise enough. For instance, say you are given the task of formulating a simplification rule that replaces sum expressions with two identical operands such as e + e by multiplications of two, e.g., e * 2. In the language of Expr trees, an expression like: BinOp("+", Var("x"), Var("x")) would be transformed by this rule to: BinOp("*", Var("x"), Number(2)) You might try to define this rule as follows: scala> def simplifyAdd(e: Expr) = e match { case BinOp("+", x, x) => BinOp("*", x, Number(2)) case _ => e } :11: error: x is already defined as value x case BinOp("+", x, x) => BinOp("*", x, Number(2)) ˆ This fails, because Scala restricts patterns to be linear: a pattern variable may only appear once in a pattern. However, you can re-formulate the match with a pattern guard, as shown in Listing 15.14: scala> def simplifyAdd(e: Expr) = e match { case BinOp("+", x, y) if x == y => BinOp("*", x, Number(2)) case _ => e } simplifyAdd: (e: Expr)Expr Listing 15.14· A match expression with a pattern guard. A pattern guard comes after a pattern and starts with an if. The guard can be an arbitrary boolean expression, which typically refers to variables in the pattern. If a pattern guard is present, the match succeeds only if the guard evaluates to true. Hence, the first case above would only match binary operations with two equal operands. Some other examples of guarded patterns are: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.4 Chapter 15 · Case Classes and Pattern Matching 325 // match only positive integers case n: Int if 0 < n => ... // match only strings starting with the letter ‘a’ case s: String if s(0) == 'a' => ... 15.4 Pattern overlaps Patterns are tried in the order in which they are written. The version of simplify shown in Listing 15.15 presents an example where the order of the cases matters: def simplifyAll(expr: Expr): Expr = expr match { case UnOp("-", UnOp("-", e)) => simplifyAll(e) // ‘-’ is its own inverse case BinOp("+", e, Number(0)) => simplifyAll(e) // ‘0’ is a neutral element for ‘+’ case BinOp("*", e, Number(1)) => simplifyAll(e) // ‘1’ is a neutral element for ‘*’ case UnOp(op, e) => UnOp(op, simplifyAll(e)) case BinOp(op, l, r) => BinOp(op, simplifyAll(l), simplifyAll(r)) case _ => expr } Listing 15.15· Match expression in which case order matters. The version of simplify shown in Listing 15.15 will apply simplification rules everywhere in an expression, not just at the top, as simplifyTop did. It can be derived from simplifyTop by adding two more cases for general unary and binary expressions (cases four and five in Listing 15.15). The fourth case has the pattern UnOp(op, e); i.e., it matches every unary operation. The operator and operand of the unary operation can be arbitrary. They are bound to the pattern variables op and e, respectively. The alterna- tive in this case applies simplifyAll recursively to the operand e and then rebuilds the same unary operation with the (possibly) simplified operand. The fifth case for BinOp is analogous: it is a “catch-all” case for arbitrary Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.5 Chapter 15 · Case Classes and Pattern Matching 326 binary operations, which recursively applies the simplification method to its two operands. In this example, it is important that the catch-all cases come after the more specific simplification rules. If you wrote them in the other order, then the catch-all case would be run in favor of the more specific rules. In many cases, the compiler will even complain if you try. For example, here’s a match expression that won’t compile because the first case will match anything that would be matched by the second case: scala> def simplifyBad(expr: Expr): Expr = expr match { case UnOp(op, e) => UnOp(op, simplifyBad(e)) case UnOp("-", UnOp("-", e)) => e } :18: error: unreachable code case UnOp("-", UnOp("-", e)) => e ˆ 15.5 Sealed classes Whenever you write a pattern match, you need to make sure you have cov- ered all of the possible cases. Sometimes you can do this by adding a default case at the end of the match, but that only applies if there is a sensible default behavior. What do you do if there is no default? How can you ever feel safe that you covered all the cases? In fact, you can enlist the help of the Scala compiler in detecting missing combinations of patterns in a match expression. To be able to do this, the compiler needs to be able to tell which are the possible cases. In general, this is impossible in Scala, because new case classes can be defined at any time and in arbitrary compilation units. For instance, nothing would prevent you from adding a fifth case class to the Expr class hierarchy in a different compilation unit from the one where the other four cases are defined. The alternative is to make the superclass of your case classes sealed. A sealed class cannot have any new subclasses added except the ones in the same file. This is very useful for pattern matching, because it means you only need to worry about the subclasses you already know about. What’s more, you get better compiler support as well. If you match against case classes that inherit from a sealed class, the compiler will flag missing combinations of patterns with a warning message. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.5 Chapter 15 · Case Classes and Pattern Matching 327 Therefore, if you write a hierarchy of classes intended to be pattern matched, you should consider sealing them. Simply put the sealed keyword in front of the class at the top of the hierarchy. Programmers using your class hierarchy will then feel confident in pattern matching against it. The sealed keyword, therefore, is often a license to pattern match. Listing 15.16 shows an example in which Expr is turned into a sealed class. sealed abstract class Expr case class Var(name: String) extends Expr case class Number(num: Double) extends Expr case class UnOp(operator: String, arg: Expr) extends Expr case class BinOp(operator: String, left: Expr, right: Expr) extends Expr Listing 15.16· A sealed hierarchy of case classes. Now define a pattern match where some of the possible cases are left out: def describe(e: Expr): String = e match { case Number(_) => "a number" case Var(_) => "a variable" } You will get a compiler warning like the following: warning: match is not exhaustive! missing combination UnOp missing combination BinOp Such a warning tells you that there’s a risk your code might produce a MatchError exception because some possible patterns (UnOp, BinOp) are not handled. The warning points to a potential source of runtime faults, so it is usually a welcome help in getting your program right. However, at times you might encounter a situation where the compiler is too picky in emitting the warning. For instance, you might know from the context that you will only ever apply the describe method above to expressions that are either Numbers or Vars. So you know that in fact no MatchError will be produced. To make the warning go away, you could add a third catch-all case to the method, like this: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.6 Chapter 15 · Case Classes and Pattern Matching 328 def describe(e: Expr): String = e match { case Number(_) => "a number" case Var(_) => "a variable" case _ => throw new RuntimeException // Should not happen } That works, but it is not ideal. You will probably not be very happy that you were forced to add code that will never be executed (or so you think), just to make the compiler shut up. A more lightweight alternative is to add an @unchecked annotation to the selector expression of the match. This is done as follows: def describe(e: Expr): String = (e: @unchecked) match { case Number(_) => "a number" case Var(_) => "a variable" } Annotations are described in Chapter 27. In general, you can add an annota- tion to an expression in the same way you add a type: follow the expression with a colon and the name of the annotation (preceded by an at sign). For example, in this case you add an @unchecked annotation to the variable e, with “e: @unchecked”. The @unchecked annotation has a special meaning for pattern matching. If a match’s selector expression carries this annotation, exhaustivity checking for the patterns that follow will be suppressed. 15.6 The Option type Scala has a standard type named Option for optional values. Such a value can be of two forms. It can be of the form Some(x) where x is the actual value. Or it can be the None object, which represents a missing value. Optional values are produced by some of the standard operations on Scala’s collections. For instance, the get method of Scala’s Map produces Some(value) if a value corresponding to a given key has been found, or None if the given key is not defined in the Map. Here’s an example: scala> val capitals = Map("France" -> "Paris", "Japan" -> "Tokyo") capitals: scala.collection.immutable.Map[java.lang.String, java.lang.String] = Map(France -> Paris, Japan -> Tokyo) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.6 Chapter 15 · Case Classes and Pattern Matching 329 scala> capitals get "France" res23: Option[java.lang.String] = Some(Paris) scala> capitals get "North Pole" res24: Option[java.lang.String] = None The most common way to take optional values apart is through a pattern match. For instance: scala> def show(x: Option[String]) = x match { case Some(s) => s case None => "?" } show: (x: Option[String])String scala> show(capitals get "Japan") res25: String = Tokyo scala> show(capitals get "France") res26: String = Paris scala> show(capitals get "North Pole") res27: String = ? The Option type is used frequently in Scala programs. Compare this to the dominant idiom in Java of using null to indicate no value. For example, the get method of java.util.HashMap returns either a value stored in the HashMap, or null if no value was found. This approach works for Java, but is error prone, because it is difficult in practice to keep track of which variables in a program are allowed to be null. If a variable is allowed to be null, then you must remember to check it for null every time you use it. When you forget to check, you open the possibility that a NullPointerException may result at runtime. Because such exceptions may not happen very often, it can be difficult to discover the bug during testing. For Scala, the approach would not work at all, because it is possible to store value types in hash maps, and null is not a legal element for a value type. For instance, a HashMap[Int, Int] cannot return null to signify “no element.” By contrast, Scala encourages the use of Option to indicate an optional value. This approach to optional values has several advantages over Java’s. First, it is far more obvious to readers of code that a variable whose type is Option[String] is an optional String than a variable of type String, which may sometimes be null. But most importantly, that programming Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.7 Chapter 15 · Case Classes and Pattern Matching 330 error described earlier of using a variable that may be null without first checking it for null becomes in Scala a type error. If a variable is of type Option[String] and you try to use it as a String, your Scala program will not compile. 15.7 Patterns everywhere Patterns are allowed in many parts of Scala, not just in standalone match expressions. Take a look at some other places you can use patterns. Patterns in variable definitions Any time you define a val or a var, you can use a pattern instead of a simple identifier. For example, you can use this to take apart a tuple and assign each of its parts to its own variable, as shown in Listing 15.17: scala> val myTuple = (123, "abc") myTuple: (Int, java.lang.String) = (123,abc) scala> val (number, string) = myTuple number: Int = 123 string: java.lang.String = abc Listing 15.17· Defining multiple variables with one assignment. This construct is quite useful when working with case classes. If you know the precise case class you are working with, then you can deconstruct it with a pattern. Here’s an example: scala> val exp = new BinOp("*", Number(5), Number(1)) exp: BinOp = BinOp(*,Number(5.0),Number(1.0)) scala> val BinOp(op, left, right) = exp op: String = * left: Expr = Number(5.0) right: Expr = Number(1.0) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.7 Chapter 15 · Case Classes and Pattern Matching 331 Case sequences as partial functions A sequence of cases (i.e., alternatives) in curly braces can be used anywhere a function literal can be used. Essentially, a case sequence is a function literal, only more general. Instead of having a single entry point and list of parameters, a case sequence has multiple entry points, each with their own list of parameters. Each case is an entry point to the function, and the parameters are specified with the pattern. The body of each entry point is the right-hand side of the case. Here is a simple example: val withDefault: Option[Int] => Int = { case Some(x) => x case None => 0 } The body of this function has two cases. The first case matches a Some, and returns the number inside the Some. The second case matches a None, and returns a default value of zero. Here is this function in use: scala> withDefault(Some(10)) res28: Int = 10 scala> withDefault(None) res29: Int = 0 This facility is quite useful for the actors library, described in Chapter 32. Here is some typical actors code. It passes a pattern match directly to the react method: react { case (name: String, actor: Actor) => { actor ! getip(name) act() } case msg => { println("Unhandled message: "+ msg) act() } } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.7 Chapter 15 · Case Classes and Pattern Matching 332 One other generalization is worth noting: a sequence of cases gives you a partial function. If you apply such a function on a value it does not support, it will generate a run-time exception. For example, here is a partial function that returns the second element of a list of integers: val second: List[Int] => Int = { case x :: y :: _ => y } When you compile this, the compiler will correctly complain that the match is not exhaustive: :17: warning: match is not exhaustive! missing combination Nil This function will succeed if you pass it a three-element list, but not if you pass it an empty list: scala> second(List(5, 6, 7)) res24: Int = 6 scala> second(List()) scala.MatchError: List() at $anonfun$1.apply(:17) at $anonfun$1.apply(:17) If you want to check whether a partial function is defined, you must first tell the compiler that you know you are working with partial func- tions. The type List[Int] => Int includes all functions from lists of in- tegers to integers, whether or not the functions are partial. The type that only includes partial functions from lists of integers to integers is written PartialFunction[List[Int],Int]. Here is the second function again, this time written with a partial function type: val second: PartialFunction[List[Int],Int] = { case x :: y :: _ => y } Partial functions have a method isDefinedAt, which can be used to test whether the function is defined at a particular value. In this case, the function is defined for any list that has at least two elements: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.7 Chapter 15 · Case Classes and Pattern Matching 333 scala> second.isDefinedAt(List(5,6,7)) res30: Boolean = true scala> second.isDefinedAt(List()) res31: Boolean = false The typical example of a partial function is a pattern matching function lit- eral like the one in the previous example. In fact, such an expression gets translated by the Scala compiler to a partial function by translating the pat- terns twice—once for the implementation of the real function, and once to test whether the function is defined or not. For instance, the function literal { case x :: y :: _ => y } above gets translated to the following partial function value: new PartialFunction[List[Int], Int] { def apply(xs: List[Int]) = xs match { case x :: y :: _ => y } def isDefinedAt(xs: List[Int]) = xs match { case x :: y :: _ => true case _ => false } } This translation takes effect whenever the declared type of a function literal is PartialFunction. If the declared type is just Function1, or is missing, the function literal is instead translated to a complete function. In general, you should try to work with complete functions whenever possible, because using partial functions allows for runtime errors that the compiler cannot help you with. Sometimes partial functions are really help- ful, though. You might be sure that an unhandled value will never be sup- plied. Alternatively, you might be using a framework that expects partial functions and so will always check isDefinedAt before calling the func- tion. An example of the latter is the react example given above, where the argument is a partially defined function, defined precisely for those messages that the caller wants to handle. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.7 Chapter 15 · Case Classes and Pattern Matching 334 Patterns in for expressions You can also use a pattern in a for expression, as shown in Listing 15.18. This for expression retrieves all key/value pairs from the capitals map. Each pair is matched against the pattern (country, city), which defines the two variables country and city. scala> for ((country, city) <- capitals) println("The capital of "+ country +" is "+ city) The capital of France is Paris The capital of Japan is Tokyo Listing 15.18· A for expression with a tuple pattern. The pair pattern shown in Listing 15.18 was special because the match against it can never fail. Indeed, capitals yields a sequence of pairs, so you can be sure that every generated pair can be matched against a pair pattern. But it is equally possible that a pattern might not match a generated value. Listing 15.19 shows an example where that is the case: scala> val results = List(Some("apple"), None, Some("orange")) results: List[Option[java.lang.String]] = List(Some(apple), None, Some(orange)) scala> for (Some(fruit) <- results) println(fruit) apple orange Listing 15.19· Picking elements of a list that match a pattern. As you can see from this example, generated values that do not match the pattern are discarded. For instance, the second element None in the results list does not match the pattern Some(fruit); therefore it does not show up in the output. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.8 Chapter 15 · Case Classes and Pattern Matching 335 15.8 A larger example After having learned the different forms of patterns, you might be interested in seeing them applied in a larger example. The proposed task is to write an expression formatter class that displays an arithmetic expression in a two- dimensional layout. Divisions such as “x / (x + 1)” should be printed verti- cally, by placing the numerator on top of the denominator, like this: x ----- x + 1 As another example, here’s the expression ((a / (b * c) + 1 / n) / 3) in two dimensional layout: a 1 ----- + - b * c n --------- 3 From these examples it looks like the class (we’ll call it ExprFormatter) will have to do a fair bit of layout juggling, so it makes sense to use the layout library developed in Chapter 10. We’ll also use the Expr family of case classes you saw previously in this chapter, and place both Chapter 10’s layout library and this chapter’s expression formatter into named packages. The full code for the example will be shown in Listings 15.20 and 15.21. A useful first step is to concentrate on horizontal layout. A structured expression like: BinOp("+", BinOp("*", BinOp("+", Var("x"), Var("y")), Var("z")), Number(1)) should print (x + y) * z + 1. Note that parentheses are mandatory around x + y, but would be optional around (x + y) * z. To keep the layout as legible as possible, your goal should be to omit parentheses wherever they are redundant, while ensuring that all necessary parentheses are present. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.8 Chapter 15 · Case Classes and Pattern Matching 336 To know where to put parentheses, the code needs to know about the relative precedence of each operator, so it’s a good idea to tackle this first. You could express the relative precedence directly as a map literal of the following form: Map( "|" -> 0, "||" -> 0, "&" -> 1, "&&" -> 1, ... ) However, this would involve some amount of pre-computation of prece- dences on your part. A more convenient approach is to just define groups of operators of increasing precedence and then calculate the precedence of each operator from that. Listing 15.20 shows the code. The precedence variable is a map from operators to their precedences, which are integers starting with 0. It is calculated using a for expres- sion with two generators. The first generator produces every index i of the opGroups array. The second generator produces every operator op in opGroups(i). For each such operator the for expression yields an associ- ation from the operator op to its index i. Hence, the relative position of an operator in the array is taken to be its precedence. Associations are written with an infix arrow, e.g., op -> i. So far you have seen associations only as part of map constructions, but they are also values in their own right. In fact, the association op -> i is nothing else but the pair (op, i). Now that you have fixed the precedence of all binary operators except /, it makes sense to generalize this concept to also cover unary operators. The precedence of a unary operator is higher than the precedence of every binary operator. Thus we can set unaryPrecedence (shown in Listing 15.20) to the length of the opGroups array, which is one more than the precedence of the * and % operators. The precedence of a fraction is treated differently from the other opera- tors because fractions use vertical layout. However, it will prove convenient to assign to the division operator the special precedence value -1, so we’ll initialize fractionPrecedence to -1 (shown in Listing 15.20). After these preparations, you are ready to write the main format method. This method takes two arguments: an expression e, of type Expr, and the precedence enclPrec of the operator directly enclosing the expression e (if there’s no enclosing operator, enclPrec should be zero). The method yields a layout element that represents a two-dimensional array of characters. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.8 Chapter 15 · Case Classes and Pattern Matching 337 package org.stairwaybook.expr import org.stairwaybook.layout.Element.elem sealed abstract class Expr case class Var(name: String) extends Expr case class Number(num: Double) extends Expr case class UnOp(operator: String, arg: Expr) extends Expr case class BinOp(operator: String, left: Expr, right: Expr) extends Expr class ExprFormatter { // Contains operators in groups of increasing precedence private val opGroups = Array( Set("|", "||"), Set("&", "&&"), Set("ˆ"), Set("==", "!="), Set("<", "<=", ">", ">="), Set("+", "-"), Set("*", "%") ) // A mapping from operators to their precedence private val precedence = { val assocs = for { i <- 0 until opGroups.length op <- opGroups(i) } yield op -> i assocs.toMap } private val unaryPrecedence = opGroups.length private val fractionPrecedence = -1 // continued in Listing 15.21... Listing 15.20· The top half of the expression formatter. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.8 Chapter 15 · Case Classes and Pattern Matching 338 // ...continued from Listing 15.20 private def format(e: Expr, enclPrec: Int): Element = e match { case Var(name) => elem(name) case Number(num) => def stripDot(s: String) = if (s endsWith ".0") s.substring(0, s.length - 2) else s elem(stripDot(num.toString)) case UnOp(op, arg) => elem(op) beside format(arg, unaryPrecedence) case BinOp("/", left, right) => val top = format(left, fractionPrecedence) val bot = format(right, fractionPrecedence) val line = elem('-', top.width max bot.width, 1) val frac = top above line above bot if (enclPrec != fractionPrecedence) frac else elem("") beside frac beside elem("") case BinOp(op, left, right) => val opPrec = precedence(op) val l = format(left, opPrec) val r = format(right, opPrec + 1) val oper = l beside elem(""+ op +"") beside r if (enclPrec <= opPrec) oper else elem("(") beside oper beside elem(")") } def format(e: Expr): Element = format(e, 0) } Listing 15.21· The bottom half of the expression formatter. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.8 Chapter 15 · Case Classes and Pattern Matching 339 Listing 15.21 shows the remainder of class ExprFormatter, which in- cludes three methods. The first method, stripDot, is a helper method.The next method, the private format method, does most of the work to format expressions. The last method, also named format, is the lone public method in the library, which takes an expression to format. The private format method does its work by performing a pattern match on the kind of expression. The match expression has five cases. We’ll dis- cuss each case individually. The first case is: case Var(name) => elem(name) If the expression is a variable, the result is an element formed from the vari- able’s name. The second case is: case Number(num) => def stripDot(s: String) = if (s endsWith ".0") s.substring(0, s.length - 2) else s elem(stripDot(num.toString)) If the expression is a number, the result is an element formed from the num- ber’s value. The stripDot function cleans up the display of a floating-point number by stripping any ".0" suffix from a string. The third case is: case UnOp(op, arg) => elem(op) beside format(arg, unaryPrecedence) If the expression is a unary operation UnOp(op, arg) the result is formed from the operation op and the result of formatting the argument arg with the highest-possible environment precedence.3 This means that if arg is a binary operation (but not a fraction) it will always be displayed in parentheses. The fourth case is: 3The value of unaryPrecedence is the highest possible precedence, because it was ini- tialized to one more than the precedence of the * and % operators. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.8 Chapter 15 · Case Classes and Pattern Matching 340 case BinOp("/", left, right) => val top = format(left, fractionPrecedence) val bot = format(right, fractionPrecedence) val line = elem('-', top.width max bot.width, 1) val frac = top above line above bot if (enclPrec != fractionPrecedence) frac else elem("") beside frac beside elem("") If the expression is a fraction, an intermediate result frac is formed by plac- ing the formatted operands left and right on top of each other, separated by an horizontal line element. The width of the horizontal line is the max- imum of the widths of the formatted operands. This intermediate result is also the final result unless the fraction appears itself as an argument of an- other fraction. In the latter case, a space is added on each side of frac. To see the reason why, consider the expression “(a / b) / c”. Without the widening correction, formatting this expression would give: a - b - c The problem with this layout is evident—it’s not clear where the top-level fractional bar is. The expression above could mean either “(a / b) / c” or “a / (b / c)”. To disambiguate, a space should be added on each side to the layout of the nested fraction “a / b”. Then the layout becomes unambiguous: a - b --- c The fifth and last case is: case BinOp(op, left, right) => val opPrec = precedence(op) val l = format(left, opPrec) val r = format(right, opPrec + 1) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.8 Chapter 15 · Case Classes and Pattern Matching 341 val oper = l beside elem(""+ op +"") beside r if (enclPrec <= opPrec) oper else elem("(") beside oper beside elem(")") This case applies for all other binary operations. Since it comes after the case starting with: case BinOp("/", left, right) => ... you know that the operator op in the pattern BinOp(op, left, right) can- not be a division. To format such a binary operation, one needs to format first its operands left and right. The precedence parameter for formatting the left operand is the precedence opPrec of the operator op, while for the right operand it is one more than that. This scheme ensures that parentheses also reflect the correct associativity. For instance, the operation: BinOp("-", Var("a"), BinOp("-", Var("b"), Var("c"))) would be correctly parenthesized as “a - (b - c)”. The intermediate result oper is then formed by placing the formatted left and right operands side- by-side, separated by the operator. If the precedence of the current operator is smaller than the precedence of the enclosing operator, r is placed between parentheses, otherwise it is returned as is. import org.stairwaybook.expr._ object Express extends Application { val f = new ExprFormatter val e1 = BinOp("*", BinOp("/", Number(1), Number(2)), BinOp("+", Var("x"), Number(1))) val e2 = BinOp("+", BinOp("/", Var("x"), Number(2)), BinOp("/", Number(1.5), Var("x"))) val e3 = BinOp("/", e1, e2) def show(e: Expr) = println(f.format(e)+ "\n\n") for (e <- Array(e1, e2, e3)) show(e) } Listing 15.22· An application that prints formatted expressions. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.8 Chapter 15 · Case Classes and Pattern Matching 342 This finishes the design of the private format function. The only re- maining method is the public format method, which allows client program- mers to format a top-level expression without passing a precedence argu- ment. Listing 15.22 shows a demo program that exercises ExprFormatter. Note that, even though this program does not define a main method, it is still a runnable application because it inherits from the Application trait. As mentioned in Section 4.5, trait Application simply defines an empty main method that gets inherited by the Express object. The actual work in the Express object gets done as part of the object’s initialization, before the main method is run. That’s why you can apply this trick only if your program does not take any command-line arguments. Once there are arguments, you need to write the main method explicitly. You can run the Express program with the command: scala Express This will give the following output: 1 - * (x + 1) 2 x 1.5 - + --- 2 x 1 - * (x + 1) 2 ----------- x 1.5 - + --- 2 x Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 15.9 Chapter 15 · Case Classes and Pattern Matching 343 15.9 Conclusion In this chapter, you learned about Scala’s case classes and pattern matching in detail. Using them, you can take advantage of several concise idioms not normally available in object-oriented languages. Scala’s pattern matching goes further than this chapter describes, however. If you want to use pattern matching on one of your classes, but you do not want to open access to your classes the way case classes do, then you can use the extractors described in Chapter 26. In the next chapter, however, we’ll turn our attention to lists. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 16 Working with Lists Lists are probably the most commonly used data structure in Scala programs. This chapter explains lists in detail. It presents many common operations that can be performed on lists. It also teaches some important design principles for programs working on lists. 16.1 List literals You saw lists already in the preceding chapters, so you know that a list con- taining the elements 'a', 'b', and 'c' is written List('a', 'b', 'c'). Here are some other examples: val fruit = List("apples", "oranges", "pears") val nums = List(1, 2, 3, 4) val diag3 = List( List(1, 0, 0), List(0, 1, 0), List(0, 0, 1) ) val empty = List() Lists are quite similar to arrays, but there are two important differences. First, lists are immutable. That is, elements of a list cannot be changed by assignment. Second, lists have a recursive structure (i.e., a linked list),1 whereas arrays are flat. 1For a graphical depiction of the structure of a List, see Figure 22.2 on page 508. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.2 Chapter 16 · Working with Lists 345 16.2 The List type Like arrays, lists are homogeneous: the elements of a list all have the same type. The type of a list that has elements of type T is written List[T]. For instance, here are the same four lists with explicit types added: val fruit: List[String] = List("apples", "oranges", "pears") val nums: List[Int] = List(1, 2, 3, 4) val diag3: List[List[Int]] = List( List(1, 0, 0), List(0, 1, 0), List(0, 0, 1) ) val empty: List[Nothing] = List() The list type in Scala is covariant. This means that for each pair of types S and T, if S is a subtype of T, then List[S] is a subtype of List[T]. For instance, List[String] is a subtype of List[Object]. This is natural because every list of strings can also be seen as a list of objects.2 Note that the empty list has type List[Nothing]. You saw in Sec- tion 11.3 that Nothing is the bottom type in Scala’s class hierarchy. It is a subtype of every other Scala type. Because lists are covariant, it follows that List[Nothing] is a subtype of List[T], for any type T. So the empty list object, which has type List[Nothing], can also be seen as an object of every other list type of the form List[T]. That’s why it is permissible to write code like: // List() is also of type List[String]! val xs: List[String] = List() 16.3 Constructing lists All lists are built from two fundamental building blocks, Nil and :: (pro- nounced “cons”). Nil represents the empty list. The infix operator, ::, expresses list extension at the front. That is, x :: xs represents a list whose 2Chapter 19 gives more details on covariance and other kinds of variance. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.4 Chapter 16 · Working with Lists 346 first element is x, followed by (the elements of) list xs. Hence, the previous list values could also have been defined as follows: val fruit = "apples" :: ("oranges" :: ("pears" :: Nil)) val nums = 1 :: (2 :: (3 :: (4 :: Nil))) val diag3 = (1 :: (0 :: (0 :: Nil))) :: (0 :: (1 :: (0 :: Nil))) :: (0 :: (0 :: (1 :: Nil))) :: Nil val empty = Nil In fact the previous definitions of fruit, nums, diag3, and empty in terms of List(...) are just wrappers that expand to these definitions. For instance, List(1, 2, 3) creates the list 1 :: (2 :: (3 :: Nil)). Because it ends in a colon, the :: operation associates to the right: A :: B :: C is interpreted as A :: (B :: C). Therefore, you can drop the parentheses in the previous definitions. For instance: val nums = 1 :: 2 :: 3 :: 4 :: Nil is equivalent to the previous definition of nums. 16.4 Basic operations on lists All operations on lists can be expressed in terms of the following three: head returns the first element of a list tail returns a list consisting of all elements except the first isEmpty returns true if the list is empty These operations are defined as methods of class List. Some examples are shown in Table 16.1. The head and tail methods are defined only for non-empty lists. When selected from an empty list, they throw an exception. For instance: scala> Nil.head java.util.NoSuchElementException: head of empty list As an example of how lists can be processed, consider sorting the elements of a list of numbers into ascending order. One simple way to do so is insertion sort, which works as follows: To sort a non-empty list x :: xs, sort the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.5 Chapter 16 · Working with Lists 347 Table 16.1 · Basic list operations What it is What it does empty.isEmpty returns true fruit.isEmpty returns false fruit.head returns "apples" fruit.tail.head returns "oranges" diag3.head returns List(1, 0, 0) remainder xs and insert the first element x at the right position in the result. Sorting an empty list yields the empty list. Expressed as Scala code, the insertion sort algorithm looks like: def isort(xs: List[Int]): List[Int] = if (xs.isEmpty) Nil else insert(xs.head, isort(xs.tail)) def insert(x: Int, xs: List[Int]): List[Int] = if (xs.isEmpty || x <= xs.head) x :: xs else xs.head :: insert(x, xs.tail) 16.5 List patterns Lists can also be taken apart using pattern matching. List patterns correspond one-by-one to list expressions. You can either match on all elements of a list using a pattern of the form List(...), or you take lists apart bit by bit using patterns composed from the :: operator and the Nil constant. Here’s an example of the first kind of pattern: scala> val List(a, b, c) = fruit a: String = apples b: String = oranges c: String = pears The pattern List(a, b, c) matches lists of length 3, and binds the three elements to the pattern variables a, b, and c. If you don’t know the number of list elements beforehand, it’s better to match with :: instead. For instance, the pattern a :: b :: rest matches lists of length 2 or greater: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.5 Chapter 16 · Working with Lists 348 About pattern matching on Lists If you review the possible forms of patterns explained in Chapter 15, you might find that neither List(...) nor :: looks like it fits one of the kinds of patterns defined there. In fact, List(...) is an instance of a library-defined extractor pattern. Such patterns will be treated in Chapter 26. The “cons” pattern x :: xs is a special case of an infix operation pattern. You know already that, when seen as an expression, an infix operation is equivalent to a method call. For patterns, the rules are different: When seen as a pattern, an infix operation such as p op q is equivalent to op(p, q). That is, the infix operator op is treated as a constructor pattern. In particular, a cons pattern such as x :: xs is treated as ::(x, xs). This hints that there should be a class named :: that corresponds to the pattern constructor. Indeed there is such as class. It is named scala.:: and is exactly the class that builds non- empty lists. So :: exists twice in Scala, once as a name of a class in package scala, and again as a method in class List. The effect of the method :: is to produce an instance of the class scala.::. You’ll find out more details about how the List class is implemented in Chapter 22. scala> val a :: b :: rest = fruit a: String = apples b: String = oranges rest: List[String] = List(pears) Taking lists apart with patterns is an alternative to taking them apart with the basic methods head, tail, and isEmpty. For instance, here’s insertion sort again, this time written with pattern matching: def isort(xs: List[Int]): List[Int] = xs match { case List() => List() case x :: xs1 => insert(x, isort(xs1)) } def insert(x: Int, xs: List[Int]): List[Int] = xs match { case List() => List(x) case y :: ys => if (x <= y) x :: xs else y :: insert(x, ys) } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 349 Often, pattern matching over lists is clearer than decomposing them with methods, so pattern matching should be a part of your list processing toolbox. This is all you need to know about lists in Scala to be able to use them correctly. However, there are also a large number of methods that capture common patterns of operations over lists. These methods make list process- ing programs more concise and often clearer. The next two sections present the most important methods defined in the List class. 16.6 First-order methods on class List This section explains most first-order methods defined in the List class. A method is first-order if it does not take any functions as arguments. The section also introduces by means of two examples some recommended tech- niques to structure programs that operate on lists. Concatenating two lists An operation similar to :: is list concatenation, written ‘:::’. Unlike ::, ::: takes two lists as operands. The result of xs ::: ys is a new list that contains all the elements of xs, followed by all the elements of ys. Here are some examples: scala> List(1, 2) ::: List(3, 4, 5) res0: List[Int] = List(1, 2, 3, 4, 5) scala> List() ::: List(1, 2, 3) res1: List[Int] = List(1, 2, 3) scala> List(1, 2, 3) ::: List(4) res2: List[Int] = List(1, 2, 3, 4) Like cons, list concatenation associates to the right. An expression like this: xs ::: ys ::: zs is interpreted like this: xs ::: (ys ::: zs) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 350 The Divide and Conquer principle Concatenation (:::) is implemented as a method in class List. It would also be possible to implement concatenation “by hand,” using pattern matching on lists. It’s instructive to try to do that yourself, because it shows a common way to implement algorithms using lists. First, we’ll settle on a signature for the concatenation method, which we’ll call append. In order not to mix things up too much, assume that append is defined outside the List class. So it will take the two lists to be concatenated as parameters. These two lists must agree on their element type, but that element type can be arbitrary. This can be expressed by giving append a type parameter3 that represents the element type of the two input lists: def append[T](xs: List[T], ys: List[T]): List[T] To design the implementation of append, it pays to remember the “divide and conquer” design principle for programs over recursive data structures such as lists. Many algorithms over lists first split an input list into simpler cases using a pattern match. That’s the divide part of the principle. They then construct a result for each case. If the result is a non-empty list, some of its parts may be constructed by recursive invocations of the same algorithm. That’s the conquer part of the principle. To apply this principle to the implementation of the append method, the first question to ask is on which list to match. This is less trivial in the case of append than for many other methods because there are two choices. How- ever, the subsequent “conquer” phase tells you that you need to construct a list consisting of all elements of both input lists. Since lists are constructed from the back towards the front, ys can remain intact whereas xs will need to be taken apart and prepended to ys. Thus, it makes sense to concentrate on xs as a source for a pattern match. The most common pattern match over lists simply distinguishes an empty from a non-empty list. So this gives the following outline of an append method: def append[T](xs: List[T], ys: List[T]): List[T] = xs match { case List() => // ?? case x :: xs1 => // ?? } 3Type parameters will be explained in more detail in Chapter 19. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 351 All that remains is to fill in the two places marked with “??”. The first such place is the alternative where the input list xs is empty. In this case concatenation yields the second list: case List() => ys The second place left open is the alternative where the input list xs consists of some head x followed by a tail xs1. In this case the result is also a non- empty list. To construct a non-empty list you need to know what the head and the tail of that list should be. You know that the first element of the result list is x. As for the remaining elements, these can be computed by appending the rest of the first list, xs1, to the second list ys. This completes the design and gives: def append[T](xs: List[T], ys: List[T]): List[T] = xs match { case List() => ys case x :: xs1 => x :: append(xs1, ys) } The computation of the second alternative illustrated the “conquer” part of the divide and conquer principle: Think first what the shape of the desired output should be, then compute the individual parts of that shape, using re- cursive invocations of the algorithm where appropriate. Finally, construct the output from these parts. Taking the length of a list: length The length method computes the length of a list. scala> List(1, 2, 3).length res3: Int = 3 On lists, unlike arrays, length is a relatively expensive operation. It needs to traverse the whole list to find its end and therefore takes time proportional to the number of elements in the list. That’s why it’s not a good idea to replace a test such as xs.isEmpty by xs.length == 0. The result of the two tests are equivalent, but the second one is slower, in particular if the list xs is long. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 352 Accessing the end of a list: init and last You know already the basic operations head and tail, which respectively take the first element of a list, and the rest of the list except the first element. They each have a dual operation: last returns the last element of a (non- empty) list, whereas init returns a list consisting of all elements except the last one: scala> val abcde = List('a', 'b', 'c', 'd', 'e') abcde: List[Char] = List(a, b, c, d, e) scala> abcde.last res4: Char = e scala> abcde.init res5: List[Char] = List(a, b, c, d) Like head and tail, these methods throw an exception when applied to an empty list: scala> List().init java.lang.UnsupportedOperationException: Nil.init at scala.List.init(List.scala:544) at ... scala> List().last java.util.NoSuchElementException: Nil.last at scala.List.last(List.scala:563) at ... Unlike head and tail, which both run in constant time, init and last need to traverse the whole list to compute their result. They therefore take time proportional to the length of the list. It’s a good idea to organize your data so that most accesses are at the head of a list, rather than the last element. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 353 Reversing lists: reverse If at some point in the computation an algorithm demands frequent accesses to the end of a list, it’s sometimes better to reverse the list first and work with the result instead. Here’s how to do the reversal: scala> abcde.reverse res6: List[Char] = List(e, d, c, b, a) Note that, like all other list operations, reverse creates a new list rather than changing the one it operates on. Since lists are immutable, such a change would not be possible, anyway. To verify this, check that the original value of abcde is unchanged after the reverse operation: scala> abcde res7: List[Char] = List(a, b, c, d, e) The reverse, init, and last operations satisfy some laws that can be used for reasoning about computations and for simplifying programs. 1. reverse is its own inverse: xs.reverse.reverse equals xs 2. reverse turns init to tail and last to head, except that the ele- ments are reversed: xs.reverse.init equals xs.tail.reverse xs.reverse.tail equals xs.init.reverse xs.reverse.head equals xs.last xs.reverse.last equals xs.head Reverse could be implemented using concatenation (:::), like in the follow- ing method, rev: def rev[T](xs: List[T]): List[T] = xs match { case List() => xs case x :: xs1 => rev(xs1) ::: List(x) } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 354 However, this method is less efficient than one would hope for. To study the complexity of rev, assume that the list xs has length n. Notice that there are n recursive calls to rev. Each call except the last involves a list concatenation. List concatenation xs ::: ys takes time proportional to the length of its first argument xs. Hence, the total complexity of rev is: n+ (n−1) +...+1 = (1+n)∗n/2 In other words, rev’s complexity is quadratic in the length of its input ar- gument. This is disappointing when compared to the standard reversal of a mutable, linked list, which has linear complexity. However, the current im- plementation of rev is not the best implementation possible. You will see in Section 4 how to speed it up. Prefixes and suffixes: drop, take, and splitAt The drop and take operations generalize tail and init in that they return arbitrary prefixes or suffixes of a list. The expression “xs take n” returns the first n elements of the list xs. If n is greater than xs.length, the whole list xs is returned. The operation “xs drop n” returns all elements of the list xs except the first n ones. If n is greater than xs.length, the empty list is returned. The splitAt operation splits the list at a given index, returning a pair of two lists.4 It is defined by the equality: xs splitAt n equals (xs take n, xs drop n) However, splitAt avoids traversing the list xs twice. Here are some exam- ples of these three methods: scala> abcde take 2 res8: List[Char] = List(a, b) scala> abcde drop 2 res9: List[Char] = List(c, d, e) scala> abcde splitAt 2 res10: (List[Char], List[Char]) = (List(a, b),List(c, d, e)) 4As mentioned in Section 10.12, the term pair is an informal name for Tuple2. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 355 Element selection: apply and indices Random element selection is supported through the apply method; however it is a less common operation for lists than it is for arrays. scala> abcde apply 2 // rare in Scala res11: Char = c As for all other types, apply is implicitly inserted when an object appears in the function position in a method call, so the line above can be shortened to: scala> abcde(2) // rare in Scala res12: Char = c One reason why random element selection is less popular for lists than for arrays is that xs(n) takes time proportional to the index n. In fact, apply is simply defined by a combination of drop and head: xs apply n equals (xs drop n).head This definition also makes clear that list indices range from 0 up to the length of the list minus one, the same as for arrays. The indices method returns a list consisting of all valid indices of a given list: scala> abcde.indices res13: scala.collection.immutable.Range = Range(0, 1, 2, 3, 4) Flattening a list of lists: flatten The flatten method takes a list of lists and flattens it out to a single list: scala> List(List(1, 2), List(3), List(), List(4, 5)).flatten res14: List[Int] = List(1, 2, 3, 4, 5) scala> fruit.map(_.toCharArray).flatten res15: List[Char] = List(a, p, p, l, e, s, o, r, a, n, g, e, s, p, e, a, r, s) It can only be applied to lists whose elements are all lists. Trying to flatten any other list will give a compilation error: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 356 scala> List(1, 2, 3).flatten :5: error: could not find implicit value for parameter asTraversable: (Int) => Traversable[B] List(1, 2, 3).flatten ˆ Zipping lists: zip and unzip The zip operation takes two lists and forms a list of pairs: scala> abcde.indices zip abcde res17: scala.collection.immutable.IndexedSeq[(Int, Char)] = IndexedSeq((0,a), (1,b), (2,c), (3,d), (4,e)) If the two lists are of different length, any unmatched elements are dropped: scala> val zipped = abcde zip List(1, 2, 3) zipped: List[(Char, Int)] = List((a,1), (b,2), (c,3)) A useful special case is to zip a list with its index. This is done most effi- ciently with the zipWithIndex method, which pairs every element of a list with the position where it appears in the list. scala> abcde.zipWithIndex res18: List[(Char, Int)] = List((a,0), (b,1), (c,2), (d,3), (e,4)) Any list of tuples can also be changed back to a tuple of lists by using the unzip method: scala> zipped.unzip res19: (List[Char], List[Int]) = (List(a, b, c),List(1, 2, 3)) The zip and unzip methods provide one way to operate on multiple lists together. See Section 16.9, later in the chapter, for a way that is sometimes more concise. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 357 Displaying lists: toString and mkString The toString operation returns the canonical string representation of a list: scala> abcde.toString res20: String = List(a, b, c, d, e) If you want a different representation you can use the mkString method. The operation xs mkString (pre, sep, post) involves four operands: the list xs to be displayed, a prefix string pre to be displayed in front of all elements, a separator string sep to be displayed between successive elements, and a postfix string post to be displayed at the end. The result of the operation is the string: pre + xs(0) + sep + ... + sep + xs(xs.length - 1) + post The mkString method has two overloaded variants that let you drop some or all of its arguments. The first variant only takes a separator string: xs mkString sep equals xs mkString ("", sep, "") The second variant lets you omit all arguments: xs.mkString equals xs mkString "" Here are some examples: scala> abcde mkString ("[", ",", "]") res21: String = [a,b,c,d,e] scala> abcde mkString "" res22: String = abcde scala> abcde.mkString res23: String = abcde scala> abcde mkString ("List(", ", ", ")") res24: String = List(a, b, c, d, e) There are also variants of the mkString methods called addString which append the constructed string to a StringBuilder object,5 rather than re- turning them as a result: 5This is class scala.StringBuilder, not java.lang.StringBuilder. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 358 scala> val buf = new StringBuilder buf: StringBuilder = scala> abcde addString (buf, "(", ";", ")") res25: StringBuilder = (a;b;c;d;e) The mkString and addString methods are inherited from List’s super trait Traversable, so they are applicable to all other collections, as well. Converting lists: iterator, toArray, copyToArray To convert data between the flat world of arrays and the recursive world of lists, you can use method toArray in class List and toList in class Array: scala> val arr = abcde.toArray arr: Array[Char] = Array(a, b, c, d, e) scala> arr.toList res26: List[Char] = List(a, b, c, d, e) There’s also a method copyToArray, which copies list elements to succes- sive array positions within some destination array. The operation: xs copyToArray (arr, start) copies all elements of the list xs to the array arr, beginning with position start. You must ensure that the destination array arr is large enough to hold the list in full. Here’s an example: scala> val arr2 = new Array[Int](10) arr2: Array[Int] = Array(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) scala> List(1, 2, 3) copyToArray (arr2, 3) scala> arr2 res28: Array[Int] = Array(0, 0, 0, 1, 2, 3, 0, 0, 0, 0) Finally, if you need to access list elements via an iterator, you can use the iterator method: scala> val it = abcde.iterator it: Iterator[Char] = non-empty iterator Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 359 scala> it.next res29: Char = a scala> it.next res30: Char = b Example: Merge sort The insertion sort presented earlier is concise to write, but it is not very efficient. Its average complexity is proportional to the square of the length of the input list. A more efficient algorithm is merge sort. The fast track This example provides another illustration of the divide and conquer principle and currying, as well as a useful discussion of algorithmic complexity. If you prefer to move a bit faster on your first pass through this book, however, you can safely skip to Section 16.7. Merge sort works as follows: First, if the list has zero or one elements, it is already sorted, so the list can be returned unchanged. Longer lists are split into two sub-lists, each containing about half the elements of the original list. Each sub-list is sorted by a recursive call to the sort function, and the resulting two sorted lists are then combined in a merge operation. For a general implementation of merge sort, you want to leave open the type of list elements to be sorted, and also want to leave open the function to be used for the comparison of elements. You obtain a function of maxi- mal generality by passing these two items as parameters. This leads to the implementation shown in Listing 16.1. The complexity of msort is order (n log(n)), where n is the length of the input list. To see why, note that splitting a list in two and merging two sorted lists each take time proportional to the length of the argument list(s). Each recursive call of msort halves the number of elements in its input, so there are about log(n) consecutive recursive calls until the base case of lists of length 1 is reached. However, for longer lists each call spawns off two further calls. Adding everything up we obtain that at each of the log(n) call levels, every element of the original lists takes part in one split operation and in one merge operation. Hence, every call level has a total cost proportional to n. Since there are log(n) call levels, we obtain an overall cost proportional to n log(n). That cost does not depend on the initial distribution of elements Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.6 Chapter 16 · Working with Lists 360 def msort[T](less: (T, T) => Boolean) (xs: List[T]): List[T] = { def merge(xs: List[T], ys: List[T]): List[T] = (xs, ys) match { case (Nil, _) => ys case (_, Nil) => xs case (x :: xs1, y :: ys1) => if (less(x, y)) x :: merge(xs1, ys) else y :: merge(xs, ys1) } val n = xs.length / 2 if (n == 0) xs else { val (ys, zs) = xs splitAt n merge(msort(less)(ys), msort(less)(zs)) } } Listing 16.1· A merge sort function for Lists. in the list, so the worst case cost is the same as the average case cost. This property makes merge sort an attractive algorithm for sorting lists. Here is an example of how msort is used: scala> msort((x: Int, y: Int) => x < y)(List(5, 7, 1, 3)) res31: List[Int] = List(1, 3, 5, 7) The msort function is a classical example of the currying concept dis- cussed in Section 9.3. Currying makes it easy to specialize the function for particular comparison functions. Here’s an example: scala> val intSort = msort((x: Int, y: Int) => x < y) _ intSort: (List[Int]) => List[Int] = The intSort variable refers to a function that takes a list of integers and sorts them in numerical order. As described in Section 8.6, an underscore stands for a missing argument list. In this case, the missing argument is the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.7 Chapter 16 · Working with Lists 361 list that should be sorted. As another example, here’s how you could define a function that sorts a list of integers in reverse numerical order: scala> val reverseIntSort = msort((x: Int, y: Int) => x > y) _ reverseIntSort: (List[Int]) => List[Int] = Because you provided the comparison function already via currying, you now need only provide the list to sort when you invoke the intSort or reverseIntSort functions. Here are some examples: scala> val mixedInts = List(4, 1, 9, 0, 5, 8, 3, 6, 2, 7) mixedInts: List[Int] = List(4, 1, 9, 0, 5, 8, 3, 6, 2, 7) scala> intSort(mixedInts) res0: List[Int] = List(0, 1, 2, 3, 4, 5, 6, 7, 8, 9) scala> reverseIntSort(mixedInts) res1: List[Int] = List(9, 8, 7, 6, 5, 4, 3, 2, 1, 0) 16.7 Higher-order methods on class List Many operations over lists have a similar structure. Several patterns appear time and time again. Some examples are: transforming every element of a list in some way, verifying whether a property holds for all elements of a list, extracting from a list elements satisfying a certain criterion, or combining the elements of a list using some operator. In Java, such patterns would usually be expressed by idiomatic combinations of for or while loops. In Scala, they can be expressed more concisely and directly using higher-order operators,6 which are implemented as methods in class List. These higher- order operators are discussed in this section. Mapping over lists: map, flatMap and foreach The operation xs map f takes as operands a list xs of type List[T] and a function f of type T => U. It returns the list resulting from applying the function f to each list element in xs. For instance: 6By higher-order operators, we mean higher-order functions used in operator notation. As mentioned in Section 9.1, higher-order functions are functions that take other functions as parameters. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.7 Chapter 16 · Working with Lists 362 scala> List(1, 2, 3) map (_ + 1) res32: List[Int] = List(2, 3, 4) scala> val words = List("the", "quick", "brown", "fox") words: List[java.lang.String] = List(the, quick, brown, fox) scala> words map (_.length) res33: List[Int] = List(3, 5, 5, 3) scala> words map (_.toList.reverse.mkString) res34: List[String] = List(eht, kciuq, nworb, xof) The flatMap operator is similar to map, but it takes a function returning a list of elements as its right operand. It applies the function to each list element and returns the concatenation of all function results. The difference between map and flatMap is illustrated in the following example: scala> words map (_.toList) res35: List[List[Char]] = List(List(t, h, e), List(q, u, i, c, k), List(b, r, o, w, n), List(f, o, x)) scala> words flatMap (_.toList) res36: List[Char] = List(t, h, e, q, u, i, c, k, b, r, o, w, n, f, o, x) You see that where map returns a list of lists, flatMap returns a single list in which all element lists are concatenated. The differences and interplay between map and flatMap are also demon- strated by the following expression, which constructs a list of all pairs (i, j) such that 1 ≤ j < i < 5: scala> List.range(1, 5) flatMap ( i => List.range(1, i) map (j => (i, j)) ) res37: List[(Int, Int)] = List((2,1), (3,1), (3,2), (4,1), (4,2), (4,3)) List.range is a utility method that creates a list of all integers in some range. It is used twice in this example: once to generate a list of integers from 1 (including) until 5 (excluding), and in a second time to generate a list of integers from 1 until i, for each value of i taken from the first list. The map in this expression generates a list of tuples (i, j) where j < i. The outer Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.7 Chapter 16 · Working with Lists 363 flatMap in this example generates this list for each i between 1 and 5, and then concatenates all the results. Note that the same list can alternatively be constructed with a for ex- pression: for (i <- List.range(1, 5); j <- List.range(1, i)) yield (i, j) You’ll learn more about the interplay of for expressions and list operations in Chapter 23. The third map-like operation is foreach. Unlike map and flatMap, how- ever, foreach takes a procedure (a function with result type Unit) as right operand. It simply applies the procedure to each list element. The result of the operation itself is again Unit; no list of results is assembled. As an example, here is a concise way of summing up all numbers in a list: scala> var sum = 0 sum: Int = 0 scala> List(1, 2, 3, 4, 5) foreach (sum += _) scala> sum res39: Int = 15 Filtering lists: filter, partition, find, takeWhile, dropWhile, and span The operation “xs filter p” takes as operands a list xs of type List[T] and a predicate function p of type T => Boolean. It yields the list of all elements x in xs for which p(x) is true. For instance: scala> List(1, 2, 3, 4, 5) filter (_ % 2 == 0) res40: List[Int] = List(2, 4) scala> words filter (_.length == 3) res41: List[java.lang.String] = List(the, fox) The partition method is like filter, but it returns a pair of lists. One list contains all elements for which the predicate is true, while the other list contains all elements for which the predicate is false. It is defined by the equality: xs partition p equals (xs filter p, xs filter (!p(_))) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.7 Chapter 16 · Working with Lists 364 Here’s an example: scala> List(1, 2, 3, 4, 5) partition (_ % 2 == 0) res42: (List[Int], List[Int]) = (List(2, 4),List(1, 3, 5)) The find method is also similar to filter but it returns the first element satisfying a given predicate, rather than all such elements. The operation xs find p takes a list xs and a predicate p as operands. It returns an optional value. If there is an element x in xs for which p(x) is true, Some(x) is returned. Otherwise, p is false for all elements, and None is returned. Here are some examples: scala> List(1, 2, 3, 4, 5) find (_ % 2 == 0) res43: Option[Int] = Some(2) scala> List(1, 2, 3, 4, 5) find (_ <= 0) res44: Option[Int] = None The takeWhile and dropWhile operators also take a predicate as their right operand. The operation xs takeWhile p takes the longest prefix of list xs such that every element in the prefix satisfies p. Analogously, the operation xs dropWhile p removes the longest prefix from list xs such that every element in the prefix satisfies p. Here are some examples: scala> List(1, 2, 3,-4, 5) takeWhile (_ > 0) res45: List[Int] = List(1, 2, 3) scala> words dropWhile (_ startsWith "t") res46: List[java.lang.String] = List(quick, brown, fox) The span method combines takeWhile and dropWhile in one operation, just like splitAt combines take and drop. It returns a pair of two lists, defined by the equality: xs span p equals (xs takeWhile p, xs dropWhile p) Like splitAt, span avoids traversing the list xs twice: scala> List(1, 2, 3,-4, 5) span (_ > 0) res47: (List[Int], List[Int]) = (List(1, 2, 3),List(-4, 5)) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.7 Chapter 16 · Working with Lists 365 Predicates over lists: forall and exists The operation xs forall p takes as arguments a list xs and a predicate p. Its result is true if all elements in the list satisfy p. Conversely, the operation xs exists p returns true if there is an element in xs that satisfies the predi- cate p. For instance, to find out whether a matrix represented as a list of lists has a row with only zeroes as elements: scala> def hasZeroRow(m: List[List[Int]]) = m exists (row => row forall (_ == 0)) hasZeroRow: (m: List[List[Int]])Boolean scala> hasZeroRow(diag3) res48: Boolean = false Folding lists: /: and :\ Another common kind of operation combines the elements of a list with some operator. For instance: sum(List(a, b, c)) equals 0 + a + b + c This is a special instance of a fold operation: scala> def sum(xs: List[Int]): Int = (0 /: xs) (_ + _) sum: (xs: List[Int])Int Similarly: product(List(a, b, c)) equals 1 * a * b * c is a special instance of this fold operation: scala> def product(xs: List[Int]): Int = (1 /: xs) (_ * _) product: (xs: List[Int])Int A fold left operation “(z /: xs) (op)” involves three objects: a start value z, a list xs, and a binary operation op. The result of the fold is op applied between successive elements of the list prefixed by z. For instance: (z /: List(a, b, c)) (op) equals op(op(op(z, a), b), c) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.7 Chapter 16 · Working with Lists 366 Or, graphically: op op op c b az Here’s another example that illustrates how /: is used. To concatenate all words in a list of strings with spaces between them and in front, you can write this: scala> ("" /: words) (_ +""+ _) res49: java.lang.String = the quick brown fox This gives an extra space at the beginning. To remove the space, you can use this slight variation: scala> (words.head /: words.tail) (_ +""+ _) res50: java.lang.String = the quick brown fox The /: operator produces left-leaning operation trees (its syntax with the slash rising forward is intended to be a reflection of that). The operator has :\ as an analog that produces right-leaning trees. For instance: (List(a, b, c) :\ z) (op) equals op(a, op(b, op(c, z))) Or, graphically: op op opa b c z The :\ operator is pronounced fold right. It involves the same three operands as fold left, but the first two appear in reversed order: The first operand is the list to fold, the second is the start value. For associative operations, fold left and fold right are equivalent, but there might be a difference in efficiency. Consider for instance an operation corresponding to the flatten method, which concatenates all elements in a list of lists. This could be implemented with either fold left or fold right: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.7 Chapter 16 · Working with Lists 367 def flattenLeft[T](xss: List[List[T]]) = (List[T]() /: xss) (_ ::: _) def flattenRight[T](xss: List[List[T]]) = (xss :\ List[T]()) (_ ::: _) Because list concatenation, xs ::: ys, takes time proportional to its first argument xs, the implementation in terms of fold right in flattenRight is more efficient than the fold left implementation in flattenLeft. The problem is that flattenLeft(xss) copies the first element list xss.head n−1 times, where n is the length of the list xss. Note that both versions of flatten require a type annotation on the empty list that is the start value of the fold. This is due to a limitation in Scala’s type inferencer, which fails to infer the correct type of the list auto- matically. If you try to leave out the annotation, you get the following: scala> def flattenRight[T](xss: List[List[T]]) = (xss :\ List()) (_ ::: _) :5: error: type mismatch; found : scala.List[T] required: List[Nothing] (xss :\ List()) (_ ::: _) ˆ To find out why the type inferencer goes wrong, you’ll need to know about the types of the fold methods and how they are implemented. More on this in Chapter 22. Lastly, although the /: and :\ operators have the advantage that the direction of the slash resembles the graphical depiction of their respective left or right-leaning trees, and the associativity of the colon character places the start value in the same position in the expression as it is in the tree, some may find the resulting code less than intuitive. If you prefer, you can alternatively use the methods named foldLeft and foldRight, which are also defined on class List. Example: List reversal using fold Earlier in the chapter you saw an implementation of method reverse, named rev, whose running time was quadratic in the length of the list to be reversed. Here is now a different implementation of reverse that has linear cost. The idea is to use a fold left operation based on the following scheme: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.7 Chapter 16 · Working with Lists 368 def reverseLeft[T](xs: List[T]) = (startvalue /: xs)(operation) It only remains to fill in the startvalue and operation parts. In fact, you can try to deduce these parts from some simple examples. To deduce the correct value of startvalue, you can start with the smallest possible list, List(), and calculate as follows: List() equals (by the properties of reverseLeft) reverseLeft(List()) equals (by the template for reverseLeft) (startvalue /: List())(operation) equals (by the definition of /:) startvalue Hence, startvalue must be List(). To deduce the second operand, you can pick the next smallest list as an example case. You know already that startvalue is List(), so you can calculate as follows: List(x) equals (by the properties of reverseLeft) reverseLeft(List(x)) equals (by the template for reverseLeft, with startvalue = List()) (List() /: List(x)) (operation) equals (by the definition of /:) operation(List(), x) Hence, operation(List(), x) equals List(x), which can also be written as x :: List(). This suggests taking as operation the :: operator with its operands exchanged. (This operation is sometimes called “snoc,” in refer- ence to ::, which is called cons.) We arrive then at the following implemen- tation for reverseLeft: def reverseLeft[T](xs: List[T]) = (List[T]() /: xs) {(ys, y) => y :: ys} (Again, the type annotation in List[T]() is necessary to make the type inferencer work.) If you analyze the complexity of reverseLeft, you’ll Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.8 Chapter 16 · Working with Lists 369 find that it applies a constant-time operation (“snoc”) n times, where n is the length of the argument list. Hence, the complexity of reverseLeft is linear, as hoped for. Sorting lists: sortWith The operation xs sortWith before, where “xs” is a list and “before” is a function that can be used to compare two elements, sorts the elements of list xs. The expression x before y should return true if x should come before y in the intended ordering for the sort. For instance: scala> List(1,-3, 4, 2, 6) sortWith (_ < _) res51: List[Int] = List(-3, 1, 2, 4, 6) scala> words sortWith (_.length > _.length) res52: List[java.lang.String] = List(quick, brown, the, fox) Note that sortWith performs a merge sort similar to the msort algorithm shown in the last section, but sortWith is a method of class List whereas msort was defined outside lists. 16.8 Methods of the List object So far, all operations you have seen in this chapter are implemented as meth- ods of class List, so you invoke them on individual list objects. There are also a number of methods in the globally accessible object scala.List, which is the companion object of class List. Some of these operations are factory methods that create lists. Others are operations that work on lists of some specific shape. Both kinds of methods will be presented in this section. Creating lists from their elements: List.apply You’ve already seen on several occasions list literals such as List(1, 2, 3). There’s nothing special about their syntax. A literal like List(1, 2, 3) is simply the application of the object List to the elements 1, 2, 3. That is, it is equivalent to List.apply(1, 2, 3): scala> List.apply(1, 2, 3) res53: List[Int] = List(1, 2, 3) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.8 Chapter 16 · Working with Lists 370 Creating a range of numbers: List.range The range method, which you saw briefly earlier in the chapter in the dis- cussion of map and flatmap, creates a list consisting of a range of numbers. Its simplest form is List.range(from, until), which creates a list of all numbers starting at from and going up to until minus one. So the end value, until, does not form part of the range. There’s also a version of range that takes a step value as third parame- ter. This operation will yield list elements that are step values apart, starting at from. The step can be positive or negative: scala> List.range(1, 5) res54: List[Int] = List(1, 2, 3, 4) scala> List.range(1, 9, 2) res55: List[Int] = List(1, 3, 5, 7) scala> List.range(9, 1,-3) res56: List[Int] = List(9, 6, 3) Creating uniform lists: List.fill The fill method creates a list consisting of zero or more copies of the same element. It takes two parameters: the length of the list to be created, and the element to be repeated. Each parameter is given in a separate list: scala> List.fill(5)('a') res57: List[Char] = List(a, a, a, a, a) scala> List.fill(3)("hello") res58: List[java.lang.String] = List(hello, hello, hello) If fill is given more than two arguments, then it will make multi- dimensional lists. That is, it will make lists of lists, lists of lists of lists, etc. The additional arguments go in the first argument list. scala> List.fill(2, 3)('b') res59: List[List[Char]] = List(List(b, b, b), List(b, b, b)) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.9 Chapter 16 · Working with Lists 371 Tabulating a function: List.tabulate The tabulate method creates a list whose elements are computed according to a supplied function. Its arguments are just like those of List.fill: the first argument list gives the dimensions of the list to create, and the second describes the elements of the list. The only difference is that instead of the elements being fixed, they are computed from a function: scala> val squares = List.tabulate(5)(n => n * n) squares: List[Int] = List(0, 1, 4, 9, 16) scala> val multiplication = List.tabulate(5,5)(_ * _) multiplication: List[List[Int]] = List(List(0, 0, 0, 0, 0), List(0, 1, 2, 3, 4), List(0, 2, 4, 6, 8), List(0, 3, 6, 9, 12), List(0, 4, 8, 12, 16)) Concatenating multiple lists: List.concat The concat method concatenates a number of element lists. The lists to be concatenated are supplied as direct arguments to concat: scala> List.concat(List('a', 'b'), List('c')) res60: List[Char] = List(a, b, c) scala> List.concat(List(), List('b'), List('c')) res61: List[Char] = List(b, c) scala> List.concat() res62: List[Nothing] = List() 16.9 Processing multiple lists together The zipped method on tuples generalizes several common operations to work on multiple lists instead of just one. One such operation is map. The map method for two zipped lists maps pairs of elements rather than individ- ual elements. One pair is for the first element of each list, another pair is for the second element of each list, and so on—as many pairs as the lists are long. Here is an example of its use: scala> (List(10, 20), List(3, 4, 5)).zipped.map(_ * _) res63: List[Int] = List(30, 80) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.10 Chapter 16 · Working with Lists 372 Notice that the third element of the second list is discarded. The zipped method zips up only as many elements as appear in all the lists together. Any extra elements on the end are discarded. There are also zipped analogs to exists and forall. They are just like the single-list versions of those methods except they operate on elements from multiple lists instead of just one: scala> (List("abc", "de"), List(3, 2)).zipped. | forall(_.length == _) res64: Boolean = true scala> (List("abc", "de"), List(3, 2)).zipped. | exists(_.length != _) res65: Boolean = false The fast track In the next (and final) section of this chapter, we provide insight into Scala’s type inference algorithm. You can safely skip the entire section if you’re not interested in such details right now, and instead go straight to the conclusion on page 376. 16.10 Understanding Scala’s type inference algorithm One difference between the previous uses of sortWith and msort concerns the admissible syntactic forms of the comparison function. Compare: scala> msort((x: Char, y: Char) => x > y)(abcde) res66: List[Char] = List(e, d, c, b, a) with: scala> abcde sortWith (_ > _) res67: List[Char] = List(e, d, c, b, a) The two expressions are equivalent, but the first uses a longer form of com- parison function with named parameters and explicit types whereas the sec- ond uses the concise form, (_ > _), where named parameters are replaced by underscores. Of course, you could also use the first, longer form of compar- ison with sortWith. However, the short form cannot be used with msort: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.10 Chapter 16 · Working with Lists 373 scala> msort(_ > _)(abcde) :12: error: missing parameter type for expanded function ((x$1, x$2) => x$1.$greater(x$2)) msort(_ > _)(abcde) ˆ To understand why, you need to know some details of Scala’s type inference algorithm. Type inference in Scala is flow based. In a method application m(args), the inferencer first checks whether the method m has a known type. If it has, that type is used to infer the expected type of the arguments. For instance, in abcde.sortWith(_ > _), the type of abcde is List[Char], hence sortWith is known to be a method that takes an argument of type (Char, Char) => Boolean and produces a result of type List[Char]. Since the parameter types of the function arguments are thus known, they need not be written explicitly. With what it knows about sortWith, the inferencer can deduce that (_ > _) should expand to ((x: Char, y: Char) => x > y) where x and y are some arbitrary fresh names. Now consider the second case, msort(_ > _)(abcde). The type of msort is a curried, polymorphic method type that takes an argument of type (T, T) => Boolean to a function from List[T] to List[T] where T is some as-yet unknown type. The msort method needs to be instantiated with a type parameter before it can be applied to its arguments. Because the precise in- stance type of msort in the application is not yet known, it cannot be used to infer the type of its first argument. The type inferencer changes its strategy in this case; it first type checks method arguments to determine the proper instance type of the method. However, when tasked to type check the short- hand function literal, (_ > _), it fails because it has no information about the types of the implicit function parameters that are indicated by underscores. One way to resolve the problem is to pass an explicit type parameter to msort, as in: scala> msort[Char](_ > _)(abcde) res68: List[Char] = List(e, d, c, b, a) Because the correct instance type of msort is now known, it can be used to infer the type of the arguments. Another possible solution is to rewrite the msort method so that its pa- rameters are swapped: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.10 Chapter 16 · Working with Lists 374 def msortSwapped[T](xs: List[T])(less: (T, T) => Boolean): List[T] = { // same implementation as msort, // but with arguments swapped } Now type inference would succeed: scala> msortSwapped(abcde)(_ > _) res69: List[Char] = List(e, d, c, b, a) What has happened is that the inferencer used the known type of the first parameter abcde to determine the type parameter of msortSwapped. Once the precise type of msortSwapped was known, it could be used in turn to infer the type of the second parameter, (_ > _). Generally, when tasked to infer the type parameters of a polymorphic method, the type inferencer consults the types of all value arguments in the first parameter list but no arguments beyond that. Since msortSwapped is a curried method with two parameter lists, the second argument (i.e., the function value) did not need to be consulted to determine the type parameter of the method. This inference scheme suggests the following library design principle: When designing a polymorphic method that takes some non-function argu- ments and a function argument, place the function argument last in a curried parameter list by its own. That way, the method’s correct instance type can be inferred from the non-function arguments, and that type can in turn be used to type check the function argument. The net effect is that users of the method will be able to give less type information and write function literals in more compact ways. Now to the more complicated case of a fold operation. Why is there the need for an explicit type parameter in an expression like the body of the flattenRight method shown on page 367? (xss :\ List[T]()) (_ ::: _) The type of the fold-right operation is polymorphic in two type variables. Given an expression: (xs :\ z) (op) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.10 Chapter 16 · Working with Lists 375 The type of xs must be a list of some arbitrary type A, say xs: List[A]. The start value z can be of some other type B. The operation op must then take two arguments of type A and B and must return a result of type B, i.e., op: (A, B) => B. Because the type of z is not related to the type of the list xs, type inference has no context information for z. Now consider the expression in the erroneous version of flattenRight, also shown on page 367: (xss :\ List()) (_ ::: _) // this won’t compile The start value z in this fold is an empty list, List(), so without additional type information its type is inferred to be a List[Nothing]. Hence, the inferencer will infer that the B type of the fold is List[Nothing]. Therefore, the operation (_ ::: _) of the fold is expected to be of the following type: (List[T], List[Nothing]) => List[Nothing] This is indeed a possible type for the operation in that fold but it is not a very useful one! It says that the operation always takes an empty list as second argument and always produces an empty list as result. In other words, the type inference settled too early on a type for List(), it should have waited until it had seen the type of the operation op. So the (otherwise very useful) rule to only consider the first argument section in a curried method application for determining the method’s type is at the root of the problem here. On the other hand, even if that rule were relaxed, the inferencer still could not come up with a type for op because its parameter types are not given. Hence, there is a Catch-22 situation that can only be resolved by an explicit type annotation from the programmer. This example highlights some limitations of the local, flow-based type inference scheme of Scala. It is not present in the more global Hindley- Milner style of type inference used in functional languages such as ML or Haskell. However, Scala’s local type inference deals much more gracefully with object-oriented subtyping than the Hindley-Milner style does. Fortu- nately, the limitations show up only in some corner cases, and are usually easily fixed by adding an explicit type annotation. Adding type annotations is also a useful debugging technique when you get confused by type error messages related to polymorphic methods. If you are unsure what caused a particular type error, just add some type arguments or other type annotations, which you think are correct. Then you should be able to quickly see where the real problem is. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 16.11 Chapter 16 · Working with Lists 376 16.11 Conclusion Now you have seen many ways to work with lists. You have seen the basic operations like head and tail, the first-order operations like reverse, the higher-order operations like map, and the utility methods in the List object. Along the way, you learned a bit about how Scala’s type inference works. Lists are a real work horse in Scala, so you will benefit from knowing how to use them. For that reason, this chapter has delved deeply into how to use lists. Lists are just one kind of collection that Scala supports, however. The next chapter is broad, rather than deep, and shows you how to use a variety of Scala’s collection types. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 17 Collections Scala has a rich collection library. This chapter gives a tour of the most commonly used collection types and operations, showing just the parts you will use most frequently. Chapter 24 will give a more comprehensive tour of what’s available, and Chapter 25 will show how Scala’s composition con- structs are used to provide such a rich API. 17.1 Sequences Sequences types let you work with groups of data lined up in order. Because the elements are ordered, you can ask for the first element, second element, 103rd element, and so on. In this section, we’ll give you a quick tour of the most important sequences. Lists Perhaps the most important sequence type to know about is class List, the immutable linked-list described in detail in the previous chapter. Lists sup- port fast addition and removal of items to the beginning of the list, but they do not provide fast access to arbitrary indexes because the implementation must iterate through the list linearly. This combination of features might sound odd, but they hit a sweet spot that works well for many algorithms. The fast addition and removal of initial elements means that pattern matching works well, as described in Chap- ter 15. The immutability of lists helps you develop correct, efficient al- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.1 Chapter 17 · Collections 378 gorithms because you never need to make copies of a list. Here’s a short example showing how to initialize a list and access its head and tail: scala> val colors = List("red", "blue", "green") colors: List[java.lang.String] = List(red, blue, green) scala> colors.head res0: java.lang.String = red scala> colors.tail res1: List[java.lang.String] = List(blue, green) For an introduction to lists see Step 8 in Chapter 3, and for the details on using lists, see Chapter 16. Lists will also be discussed in Chapter 22, which provides insight into how lists are implemented in Scala. Arrays Arrays allow you to hold a sequence of elements and efficiently access an element at an arbitrary position, both to get or update the element, with a zero-based index. Here’s how you create an array whose size you know, but for which you don’t yet know the element values: scala> val fiveInts = new Array[Int](5) fiveInts: Array[Int] = Array(0, 0, 0, 0, 0) Here’s how you initialize an array when you do know the element values: scala> val fiveToOne = Array(5, 4, 3, 2, 1) fiveToOne: Array[Int] = Array(5, 4, 3, 2, 1) As mentioned previously, arrays are accessed in Scala by placing an index in parentheses, not square brackets as in Java. Here’s an example of both accessing and updating an array element: scala> fiveInts(0) = fiveToOne(4) scala> fiveInts res3: Array[Int] = Array(1, 0, 0, 0, 0) Scala arrays are represented in the same way as Java arrays. So, you can seamlessly use existing Java methods that return arrays.1 1The difference in variance of Scala and Java’s arrays—i.e., whether Array[String] is a subtype of Array[AnyRef]—will be discussed in Section 19.3. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.1 Chapter 17 · Collections 379 You have seen arrays in action many times in previous chapters. The basics are in Step 7 in Chapter 3. Several examples of iterating through the elements of an array with a for expression are shown in Section 7.3. Arrays also figure prominently in the two-dimensional layout library of Chapter 10. List buffers Class List provides fast access to the head of the list, but not the end. Thus, when you need to build a list by appending to the end, you should consider building the list backwards by prepending elements to the front, then when you’re done, calling reverse to get the elements in the order you need. Another alternative, which avoids the reverse operation, is to use a ListBuffer.A ListBuffer is a mutable object (contained in package scala.collection.mutable), which can help you build lists more effi- ciently when you need to append. ListBuffer provides constant time ap- pend and prepend operations. You append elements with the += operator, and prepend them with the +=: operator. When you’re done building, you can obtain a List by invoking toList on the ListBuffer. Here’s an example: scala> import scala.collection.mutable.ListBuffer import scala.collection.mutable.ListBuffer scala> val buf = new ListBuffer[Int] buf: scala.collection.mutable.ListBuffer[Int] = ListBuffer() scala> buf += 1 res4: buf.type = ListBuffer(1) scala> buf += 2 res5: buf.type = ListBuffer(1, 2) scala> buf res6: scala.collection.mutable.ListBuffer[Int] = ListBuffer(1, 2) scala> 3 +=: buf res7: buf.type = ListBuffer(3, 1, 2) scala> buf.toList res8: List[Int] = List(3, 1, 2) Another reason to use ListBuffer instead of List is to prevent the po- tential for stack overflow. If you can build a list in the desired order by Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.1 Chapter 17 · Collections 380 prepending, but the recursive algorithm that would be required is not tail recursive, you can use a for expression or while loop and a ListBuffer instead. You’ll see ListBuffer being used in this way in Section 22.2. Array buffers An ArrayBuffer is like an array, except that you can additionally add and remove elements from the beginning and end of the sequence. All Array operations are available, though they are a little slower due to a layer of wrapping in the implementation. The new addition and removal operations are constant time on average, but occasionally require linear time due to the implementation needing to allocate a new array to hold the buffer’s contents. To use an ArrayBuffer, you must first import it from the mutable col- lections package: scala> import scala.collection.mutable.ArrayBuffer import scala.collection.mutable.ArrayBuffer When you create an ArrayBuffer, you must specify a type parameter, but need not specify a length. The ArrayBuffer will adjust the allocated space automatically as needed: scala> val buf = new ArrayBuffer[Int]() buf: scala.collection.mutable.ArrayBuffer[Int] = ArrayBuffer() You can append to an ArrayBuffer using the += method: scala> buf += 12 res9: buf.type = ArrayBuffer(12) scala> buf += 15 res10: buf.type = ArrayBuffer(12, 15) scala> buf res11: scala.collection.mutable.ArrayBuffer[Int] = ArrayBuffer(12, 15) All the normal array methods are available. For example, you can ask an ArrayBuffer its length, or you can retrieve an element by its index: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.2 Chapter 17 · Collections 381 scala> buf.length res12: Int = 2 scala> buf(0) res13: Int = 12 Strings (via StringOps) One other sequence to be aware of is StringOps, which implements many sequence methods. Because Predef has an implicit conversion from String to StringOps, you can treat any string like a sequence. Here’s an example: scala> def hasUpperCase(s: String) = s.exists(_.isUpper) hasUpperCase: (s: String)Boolean scala> hasUpperCase("Robert Frost") res14: Boolean = true scala> hasUpperCase("e e cummings") res15: Boolean = false In this example, the exists method is invoked on the string named s in the hasUpperCase method body. Because no method named “exists” is declared in class String itself, the Scala compiler will implicitly convert s to StringOps, which has the method. The exists method treats the string as a sequence of characters, and will return true if any of the characters are upper case.2 17.2 Sets and maps You have already seen the basics of sets and maps in previous chapters, start- ing with Step 10 in Chapter 3. In this section, we’ll give more insight into their use and show you a few more examples. As mentioned previously, the Scala collections library offers both muta- ble and immutable versions of sets and maps. The hierarchy for sets is shown in Figure 3.2 on page 92, and the hierarchy for maps is shown in Figure 3.3 on page 94. As these diagrams show, the simple names Set and Map are used by three traits each, residing in different packages. 2The code given on page 61 of Chapter 1 presents a similar example. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.2 Chapter 17 · Collections 382 By default when you write “Set” or “Map” you get an immutable object. If you want the mutable variant, you need to do an explicit import. Scala gives you easier access to the immutable variants, as a gentle encouragement to prefer them over their mutable counterparts. The easy access is provided via the Predef object, which is implicitly imported into every Scala source file. Listing 17.1 shows the relevant definitions: object Predef{ type Map[A, +B] = collection.immutable.Map[A, B] type Set[A] = collection.immutable.Set[A] val Map = collection.immutable.Map val Set = collection.immutable.Set // ... } Listing 17.1· Default map and set definitions in Predef. The “type” keyword is used in Predef to define Set and Map as aliases for the longer fully qualified names of the immutable set and map traits.3 The vals named Set and Map are initialized to refer to the singleton objects for the immutable Set and Map. So Map is the same as Predef.Map, which is defined to be the same as scala.collection.immutable.Map. This holds both for the Map type and Map object. If you want to use both mutable and immutable sets or maps in the same source file, one approach is to import the name of the package that contains the mutable variants: scala> import scala.collection.mutable import scala.collection.mutable You can continue to refer to the immutable set as Set, as before, but can now refer to the mutable set as mutable.Set. Here’s an example: scala> val mutaSet = mutable.Set(1, 2, 3) mutaSet: scala.collection.mutable.Set[Int] = Set(3, 1, 2) 3The type keyword will be explained in more detail in Section 20.6. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.2 Chapter 17 · Collections 383 Using sets The key characteristic of sets is that they will ensure that at most one of each object, as determined by ==, will be contained in the set at any one time. As an example, we’ll use a set to count the number of different words in a string. The split method on String can separate a string into words, if you specify spaces and punctuation as word separators. The regular expression “[ !,.]+” will suffice: it indicates the string should be split at each place that one or more space and/or punctuation characters exist: scala> val text = "See Spot run. Run, Spot. Run!" text: java.lang.String = See Spot run. Run, Spot. Run! scala> val wordsArray = text.split("[ !,.]+") wordsArray: Array[java.lang.String] = Array(See, Spot, run, Run, Spot, Run) To count the distinct words, you can convert them to the same case and then add them to a set. Because sets exclude duplicates, each distinct word will appear exactly one time in the set. First, you can create an empty set using the empty method provided on the Set companion objects: scala> val words = mutable.Set.empty[String] words: scala.collection.mutable.Set[String] = Set() Then, just iterate through the words with a for expression, convert each word to lower case, and add it to the mutable set with the += operator: scala> for (word <- wordsArray) words += word.toLowerCase scala> words res17: scala.collection.mutable.Set[String] = Set(spot, run, see) Thus, the text contained exactly three distinct words: spot, run, and see. The most commonly used methods on both mutable and immutable sets are shown in Table 17.1. Using maps Maps let you associate a value with each element of the collection. Using a map looks similar to using an array, except that instead of indexing with Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.2 Chapter 17 · Collections 384 integers counting from 0, you can use any kind of key. If you import the scala.collection.mutable package, you can create an empty mutable map like this: scala> val map = mutable.Map.empty[String, Int] map: scala.collection.mutable.Map[String,Int] = Map() Table 17.1 · Common operations for sets What it is What it does val nums = Set(1, 2, 3) Creates an immutable set (nums.toString returns Set(1, 2, 3)) nums + 5 Adds an element (returns Set(1, 2, 3, 5)) nums - 3 Removes an element (returns Set(1, 2)) nums ++ List(5, 6) Adds multiple elements (returns Set(1, 2, 3, 5, 6)) nums -- List(1, 2) Removes multiple elements (returns Set(3)) nums & Set(1, 3, 5, 7) Takes the intersection of two sets (returns Set(1, 3)) nums.size Returns the size of the set (returns 3) nums.contains(3) Checks for inclusion (returns true) import scala.collection.mutable Makes the mutable collections easy to access val words = mutable.Set.empty[String] Creates an empty, mutable set (words.toString returns Set()) words += "the" Adds an element (words.toString returns Set(the)) words -= "the" Removes an element, if it exists (words.toString returns Set()) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.2 Chapter 17 · Collections 385 Table 17.1 · continued words ++= List("do", "re", "mi") Adds multiple elements (words.toString returns Set(do, re, mi)) words --= List("do", "re") Removes multiple elements (words.toString returns Set(mi)) words.clear Removes all elements (words.toString returns Set()) Note that when you create a map, you must specify two types. The first type is for the keys of the map, the second for the values. In this case, the keys are strings and the values are integers. Setting entries in a map looks similar to setting entries in an array: scala> map("hello") = 1 scala> map("there") = 2 scala> map res20: scala.collection.mutable.Map[String,Int] = Map(hello -> 1, there -> 2) Likewise, reading a map is similar to reading an array: scala> map("hello") res21: Int = 1 Putting it all together, here is a method that counts the number of times each word occurs in a string: scala> def countWords(text: String) = { val counts = mutable.Map.empty[String, Int] for (rawWord <- text.split("[ ,!.]+")) { val word = rawWord.toLowerCase val oldCount = if (counts.contains(word)) counts(word) else 0 counts += (word -> (oldCount + 1)) } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.2 Chapter 17 · Collections 386 counts } countWords: (text: String)scala.collection.mutable.Map[String,Int] scala> countWords("See Spot run! Run, Spot. Run!") res22: scala.collection.mutable.Map[String,Int] = Map(see -> 1, run -> 3, spot -> 2) Given these counts, you can see that this text talks a lot about running, but not so much about seeing. The way this code works is that a mutable map, named counts, maps each word to the number of times it occurs in the text. For each word in the text, the word’s old count is looked up, that count is incremented by one, and the new count is saved back into counts. Note the use of contains to check whether a word has been seen yet or not. If counts.contains(word) is not true, then the word has not yet been seen and zero is used for the count. Many of the most commonly used methods on both mutable and im- mutable maps are shown in Table 17.2. Table 17.2 · Common operations for maps What it is What it does val nums = Map("i" -> 1, "ii" -> 2) Creates an immutable map (nums.toString returns Map(i -> 1, ii -> 2)) nums + ("vi" -> 6) Adds an entry (returns Map(i -> 1, ii -> 2, vi -> 6)) nums - "ii" Removes an entry (returns Map(i -> 1)) nums ++ List("iii" -> 3, "v" -> 5) Adds multiple entries (returns Map(i -> 1, ii -> 2, iii -> 3, v -> 5)) nums -- List("i", "ii") Removes multiple entries (returns Map()) nums.size Returns the size of the map (returns 2) nums.contains("ii") Checks for inclusion (returns true) nums("ii") Retrieves the value at a specified key (returns 2) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.2 Chapter 17 · Collections 387 Table 17.2 · continued nums.keys Returns the keys (returns an Iteratable over the strings "i" and "ii") nums.keySet Returns the keys as a set (returns Set(i, ii)) nums.values Returns the values (returns an Iterable over the integers 1 and 2) nums.isEmpty Indicates whether the map is empty (returns false) import scala.collection.mutable Makes the mutable collections easy to access val words = mutable.Map.empty[String, Int] Creates an empty, mutable map words += ("one" -> 1) Adds a map entry from "one" to 1 (words.toString returns Map(one -> 1)) words -= "one" Removes a map entry, if it exists (words.toString returns Map()) words ++= List("one" -> 1, "two" -> 2, "three" -> 3) Adds multiple map entries (words.toString returns Map(one -> 1, two -> 2, three -> 3)) words --= List("one", "two") Removes multiple objects (words.toString returns Map(three -> 3)) Default sets and maps For most uses, the implementations of mutable and immutable sets and maps provided by the Set(), scala.collection.mutable.Map(), etc., factories will likely be sufficient. The implementations provided by these factories use a fast lookup algorithm, usually involving a hash table, so they can quickly decide whether or not an object is in the collection. The scala.collection.mutable.Set() factory method, for example, returns a scala.collection.mutable.HashSet, which uses a hash table Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.2 Chapter 17 · Collections 388 Table 17.3 · Default immutable set implementations Number of elements Implementation 0 scala.collection.immutable.EmptySet 1 scala.collection.immutable.Set1 2 scala.collection.immutable.Set2 3 scala.collection.immutable.Set3 4 scala.collection.immutable.Set4 5 or more scala.collection.immutable.HashSet internally. Similarly, the scala.collection.mutable.Map() factory re- turns a scala.collection.mutable.HashMap. The story for immutable sets and maps is a bit more involved. The class returned by the scala.collection.immutable.Set() factory method, for example, depends on how many elements you pass to it, as shown in Ta- ble 17.3. For sets with fewer than five elements, a special class devoted exclusively to sets of each particular size is used, to maximize performance. Once you request a set that has five or more elements in it, however, the factory method will return an implementation that uses hash tries. Similarly, the scala.collection.immutable.Map() factory method will return a different class depending on how many key-value pairs you pass to it, as shown in Table 17.4. As with sets, for immutable maps with fewer than five elements, a special class devoted exclusively to maps of each particular size is used, to maximize performance. Once a map has five or more key-value pairs in it, however, an immutable HashMap is used. Table 17.4 · Default immutable map implementations Number of elements Implementation 0 scala.collection.immutable.EmptyMap 1 scala.collection.immutable.Map1 2 scala.collection.immutable.Map2 3 scala.collection.immutable.Map3 4 scala.collection.immutable.Map4 5 or more scala.collection.immutable.HashMap The default immutable implementation classes shown in Tables 17.3 and 17.4 work together to give you maximum performance. For example, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.2 Chapter 17 · Collections 389 if you add an element to an EmptySet, it will return a Set1. If you add an element to that Set1, it will return a Set2. If you then remove an element from the Set2, you’ll get another Set1. Sorted sets and maps On occasion you may need a set or map whose iterator returns elements in a particular order. For this purpose, the Scala collections library provides traits SortedSet and SortedMap. These traits are implemented by classes TreeSet and TreeMap, which use a red-black tree to keep elements (in the case of TreeSet) or keys (in the case of TreeMap) in order. The order is determined by the Ordered trait, which the element type of the set, or key type of the map, must either mix in or be implicitly convertible to. These classes only come in immutable variants. Here are some TreeSet examples: scala> import scala.collection.immutable.TreeSet import scala.collection.immutable.TreeSet scala> val ts = TreeSet(9, 3, 1, 8, 0, 2, 7, 4, 6, 5) ts: scala.collection.immutable.TreeSet[Int] = TreeSet(0, 1, 2, 3, 4, 5, 6, 7, 8, 9) scala> val cs = TreeSet('f', 'u', 'n') cs: scala.collection.immutable.TreeSet[Char] = TreeSet(f, n, u) And here are a few TreeMap examples: scala> import scala.collection.immutable.TreeMap import scala.collection.immutable.TreeMap scala> var tm = TreeMap(3 -> 'x', 1 -> 'x', 4 -> 'x') tm: scala.collection.immutable.TreeMap[Int,Char] = Map(1 -> x, 3 -> x, 4 -> x) scala> tm += (2 -> 'x') scala> tm res30: scala.collection.immutable.TreeMap[Int,Char] = Map(1 -> x, 2 -> x, 3 -> x, 4 -> x) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.3 Chapter 17 · Collections 390 17.3 Selecting mutable versus immutable collections For some problems, mutable collections work better, and for others, im- mutable collections work better. When in doubt, it is better to start with an immutable collection and change it later if you need to, because immutable collections can be easier to reason about than mutable ones. It can also sometimes be worthwhile to go the opposite way. If you find some code that uses mutable collections becoming complicated and hard to reason about, consider whether it would help to change some of the collec- tions to immutable alternatives. In particular, if you find yourself worrying about making copies of mutable collections in just the right places, or think- ing a lot about who “owns” or “contains” a mutable collection, consider switching some of the collections to their immutable counterparts. Besides being potentially easier to reason about, immutable collections can usually be stored more compactly than mutable ones if the number of el- ements stored in the collection is small. For instance an empty mutable map in its default representation of HashMap takes up about 80 bytes and about 16 more are added for each entry that’s added to it. An empty immutable Map is a single object that’s shared between all references, so referring to it es- sentially costs just a single pointer field. What’s more, the Scala collections library currently stores immutable maps and sets with up to four entries in a single object, which typically takes up between 16 and 40 bytes, depending on the number of entries stored in the collection.4 So for small maps and sets, the immutable versions are much more compact than the mutable ones. Given that many collections are small, switching them to be immutable can give important space savings and performance advantages. To make it easier to switch from immutable to mutable collections, and vice versa, Scala provides some syntactic sugar. Even though immutable sets and maps do not support a true += method, Scala gives a useful alternate interpretation to +=. Whenever you write a += b, and a does not support a method named +=, Scala will try interpreting it as a = a + b. For example, immutable sets do not support a += operator: scala> val people = Set("Nancy", "Jane") people: scala.collection.immutable.Set[java.lang.String] = Set(Nancy, Jane) 4The “single object” is an instance of Set1 through Set4, or Map1 through Map4, as shown in Tables 17.3 and 17.4. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.3 Chapter 17 · Collections 391 scala> people += "Bob" :11: error: reassignment to val people += "Bob" ˆ If you declare people as a var, instead of a val, however, then the collection can be “updated” with a += operation, even though it is immutable. First, a new collection will be created, and then people will be reassigned to refer to the new collection: scala> var people = Set("Nancy", "Jane") people: scala.collection.immutable.Set[java.lang.String] = Set(Nancy, Jane) scala> people += "Bob" scala> people res34: scala.collection.immutable.Set[java.lang.String] = Set(Nancy, Jane, Bob) After this series of statements, the people variable refers to a new immutable set, which contains the added string, "Bob". The same idea applies to any method ending in =, not just the += method. Here’s the same syntax used with the -= operator, which removes an element from a set, and the ++= operator, which adds a collection of elements to a set: scala> people -= "Jane" scala> people ++= List("Tom", "Harry") scala> people res37: scala.collection.immutable.Set[java.lang.String] = Set(Nancy, Bob, Tom, Harry) To see how this is useful, consider again the following Map example from Section 1.1: var capital = Map("US" -> "Washington", "France" -> "Paris") capital += ("Japan" -> "Tokyo") println(capital("France")) This code uses immutable collections. If you want to try using mutable col- lections instead, all that is necessary is to import the mutable version of Map, thus overriding the default import of the immutable Map: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.4 Chapter 17 · Collections 392 import scala.collection.mutable.Map // only change needed! var capital = Map("US" -> "Washington", "France" -> "Paris") capital += ("Japan" -> "Tokyo") println(capital("France")) Not all examples are quite that easy to convert, but the special treatment of methods ending in an equals sign will often reduce the amount of code that needs changing. By the way, this syntactic treatment works on any kind of value, not just collections. For example, here it is being used on floating-point numbers: scala> var roughlyPi = 3.0 roughlyPi: Double = 3.0 scala> roughlyPi += 0.1 scala> roughlyPi += 0.04 scala> roughlyPi res40: Double = 3.14 The effect of this expansion is similar to Java’s assignment operators +=, -=, *=, etc., but it is more general because every operator ending in = can be converted. 17.4 Initializing collections As you’ve seen previously, the most common way to create and initialize a collection is to pass the initial elements to a factory method on the companion object of your chosen collection. You just place the elements in parentheses after the companion object name, and the Scala compiler will transform that to an invocation of an apply method on that companion object: scala> List(1, 2, 3) res41: List[Int] = List(1, 2, 3) scala> Set('a', 'b', 'c') res42: scala.collection.immutable.Set[Char] = Set(a, b, c) scala> import scala.collection.mutable import scala.collection.mutable Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.4 Chapter 17 · Collections 393 scala> mutable.Map("hi" -> 2, "there" -> 5) res43: scala.collection.mutable.Map[java.lang.String,Int] = Map(hi -> 2, there -> 5) scala> Array(1.0, 2.0, 3.0) res44: Array[Double] = Array(1.0, 2.0, 3.0) Although most often you can let the Scala compiler infer the element type of a collection from the elements passed to its factory method, some- times you may want to create a collection but specify a different type from the one the compiler would choose. This is especially an issue with mutable collections. Here’s an example: scala> import scala.collection.mutable import scala.collection.mutable scala> val stuff = mutable.Set(42) stuff: scala.collection.mutable.Set[Int] = Set(42) scala> stuff += "abracadabra" :15: error: type mismatch; found : java.lang.String("abracadabra") required: Int stuff += "abracadabra" ˆ The problem here is that stuff was given an element type of Int. If you want it to have an element type of Any, you need to say so explicitly by putting the element type in square brackets, like this: scala> val stuff = mutable.Set[Any](42) stuff: scala.collection.mutable.Set[Any] = Set(42) Another special situation is if you want to initialize a collection with another collection. For example, imagine you have a list, but you want a TreeSet containing the elements in the list. Here’s the list: scala> val colors = List("blue", "yellow", "red", "green") colors: List[java.lang.String] = List(blue, yellow, red, green) You cannot pass the colors list to the factory method for TreeSet: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.4 Chapter 17 · Collections 394 scala> import scala.collection.immutable.TreeSet import scala.collection.immutable.TreeSet scala> val treeSet = TreeSet(colors) :15: error: could not find implicit value for parameter ord: Ordering[List[java.lang.String]] val treeSet = TreeSet(colors) ˆ Instead, you’ll need to create an empty TreeSet[String] and add to it the elements of the list with the TreeSet’s ++ operator: scala> val treeSet = TreeSet[String]() ++ colors treeSet: scala.collection.immutable.TreeSet[String] = TreeSet(blue, green, red, yellow) Converting to array or list If you need to initialize a list or array with another collection, on the other hand, it is quite straightforward. As you’ve seen previously, to initialize a new list with another collection, simply invoke toList on that collection: scala> treeSet.toList res50: List[String] = List(blue, green, red, yellow) Or, if you need an array, invoke toArray: scala> treeSet.toArray res51: Array[String] = Array(blue, green, red, yellow) Note that although the original colors list was not sorted, the elements in the list produced by invoking toList on the TreeSet are in alphabetical order. When you invoke toList or toArray on a collection, the order of the elements in the resulting list or array will be the same as the order of elements produced by an iterator obtained by invoking elements on that collection. Because a TreeSet[String]’s iterator will produce strings in alphabetical order, those strings will appear in alphabetical order in the list resulting from invoking toList on that TreeSet. Keep in mind, however, that conversion to lists or arrays usually requires copying all of the elements of the collection, and thus may be slow for large collections. Sometimes you need to do it, though, due to an existing API. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.4 Chapter 17 · Collections 395 Further, many collections only have a few elements anyway, in which case there is only a small speed penalty. Converting between mutable and immutable sets and maps Another situation that arises occasionally is the need to convert a mutable set or map to an immutable one, or vice versa. To accomplish this, you can use the technique shown on the previous page to initialize a TreeSet with the elements of a list. Create a collection of the new type using the empty method and then add the new elements using either ++ or ++=, whichever is appropriate for the target collection type. Here’s how you’d convert the immutable TreeSet from the previous example to a mutable set, and back again to an immutable one: scala> import scala.collection.mutable import scala.collection.mutable scala> treeSet res52: scala.collection.immutable.TreeSet[String] = TreeSet(blue, green, red, yellow) scala> val mutaSet = mutable.Set.empty ++= treeSet mutaSet: scala.collection.mutable.Set[String] = Set(yellow, blue, red, green) scala> val immutaSet = Set.empty ++ mutaSet immutaSet: scala.collection.immutable.Set[String] = Set(yellow, blue, red, green) You can use the same technique to convert between mutable and im- mutable maps: scala> val muta = mutable.Map("i" -> 1, "ii" -> 2) muta: scala.collection.mutable.Map[java.lang.String,Int] = Map(ii -> 2, i -> 1) scala> val immu = Map.empty ++ muta immu: scala.collection.immutable.Map[java.lang.String,Int] = Map(ii -> 2, i -> 1) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.5 Chapter 17 · Collections 396 17.5 Tuples As described in Step 9 in Chapter 3, a tuple combines a fixed number of items together so that they can be passed around as a whole. Unlike an array or list, a tuple can hold objects with different types. Here is an example of a tuple holding an integer, a string, and the console: (1, "hello", Console) Tuples save you the tedium of defining simplistic data-heavy classes. Even though defining a class is already easy, it does require a certain minimum effort, which sometimes serves no purpose. Tuples save you the effort of choosing a name for the class, choosing a scope to define the class in, and choosing names for the members of the class. If your class simply holds an integer and a string, there is no clarity added by defining a class named AnIntegerAndAString. Because tuples can combine objects of different types, tuples do not in- herit from Traversable. If you find yourself wanting to group exactly one integer and exactly one string, then you want a tuple, not a List or Array. A common application of tuples is returning multiple values from a method. For example, here is a method that finds the longest word in a collection and also returns its index: def longestWord(words: Array[String]) = { var word = words(0) var idx = 0 for (i <- 1 until words.length) if (words(i).length > word.length) { word = words(i) idx = i } (word, idx) } Here is an example use of the method: scala> val longest = longestWord("The quick brown fox".split("")) longest: (String, Int) = (quick,1) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.5 Chapter 17 · Collections 397 The longestWord function here computes two items: word, the longest word in the array, and idx, the index of that word. To keep things sim- ple, the function assumes there is at least one word in the list, and it breaks ties by choosing the word that comes earlier in the list. Once the function has chosen which word and index to return, it returns both of them together using the tuple syntax (word, idx). To access elements of a tuple, you can use method _1 to access the first element, _2 to access the second, and so on: scala> longest._1 res53: String = quick scala> longest._2 res54: Int = 1 Additionally, you can assign each element of the tuple to its own vari- able,5 like this: scala> val (word, idx) = longest word: String = quick idx: Int = 1 scala> word res55: String = quick By the way, if you leave off the parentheses you get a different result: scala> val word, idx = longest word: (String, Int) = (quick,1) idx: (String, Int) = (quick,1) This syntax gives multiple definitions of the same expression. Each variable is initialized with its own evaluation of the expression on the right-hand side. That the expression evaluates to a tuple in this case does not matter. Both variables are initialized to the tuple in its entirety. See Chapter 18 for some examples where multiple definitions are convenient. As a note of warning, tuples are almost too easy to use. Tuples are great when you combine data that has no meaning beyond “an A and a B.” How- ever, whenever the combination has some meaning, or you want to add some 5This syntax is actually a special case of pattern matching, as described in detail in Section 15.7. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 17.6 Chapter 17 · Collections 398 methods to the combination, it is better to go ahead and create a class. For example, do not use a 3-tuple for the combination of a month, a day, and a year. Make a Date class. It makes your intentions explicit, which both clears up the code for human readers and gives the compiler and language opportunities to help you catch mistakes. 17.6 Conclusion This chapter has given an overview of the Scala collections library and the most important classes and traits in it. With this foundation you should be able to work effectively with Scala collections, and know where to look in Scaladoc when you need more information. For more detailed information about Scala collections, look ahead to Chapter 24 and Chapter 25. For now, in the next chapter, we’ll turn our attention from the Scala library back to the language and discuss Scala’s support for mutable objects. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 18 Stateful Objects In previous chapters, we put the spotlight on functional (immutable) objects. We did so because the idea of objects without any mutable state deserves to be better known. However, it is also perfectly possible to define objects with mutable state in Scala. Such stateful objects often come up naturally when you want to model objects in the real world that change over time. This chapter explains what stateful objects are, and what Scala provides in terms of syntax to express them. The second part of this chapter intro- duces a larger case study on discrete event simulation, which involves state- ful objects as well as building an internal domain specific language (DSL) for defining digital circuits to simulate. 18.1 What makes an object stateful? You can observe the principal difference between a purely functional object and a stateful one even without looking at the object’s implementation. When you invoke a method or dereference a field on some purely functional object, you will always get the same result. For instance, given a list of characters: val cs = List('a', 'b', 'c') an application of cs.head will always return 'a'. This is the case even if there is an arbitrary number of operations on the list cs between the point where it is defined and the point where the access cs.head is made. For a stateful object, on the other hand, the result of a method call or field access may depend on what operations were previously performed on the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.1 Chapter 18 · Stateful Objects 400 object. A good example of a stateful object is a bank account. Listing 18.1 shows a simplified implementation of bank accounts: class BankAccount{ private var bal: Int = 0 def balance: Int = bal def deposit(amount: Int){ require(amount > 0) bal += amount } def withdraw(amount: Int): Boolean = if (amount > bal) false else { bal -= amount true } } Listing 18.1· A mutable bank account class. The BankAccount class defines a private variable, bal, and three pub- lic methods: balance returns the current balance; deposit adds a given amount to bal; and withdraw tries to subtract a given amount from bal while assuring that the remaining balance won’t be negative. The return value of withdraw is a Boolean indicating whether the requested funds were successfully withdrawn. Even if you know nothing about the inner workings of the BankAccount class, you can still tell that BankAccounts are stateful objects: scala> val account = new BankAccount account: BankAccount = BankAccount@bf5bb7 scala> account deposit 100 scala> account withdraw 80 res1: Boolean = true scala> account withdraw 80 res2: Boolean = false Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.1 Chapter 18 · Stateful Objects 401 Note that the two final withdrawals in the previous interaction returned dif- ferent results. The first withdraw operation returned true because the bank account contained sufficient funds to allow the withdrawal. The second oper- ation, although the same as the first one, returned false, because the balance of the account had been reduced so that it no longer covered the requested funds. So, clearly bank accounts have mutable state, because the same oper- ation can return different results at different times. You might think that the statefulness of BankAccount is immediately ap- parent because it contains a var definition. State and vars usually go hand in hand, but things are not always so clear-cut. For instance, a class might be stateful without defining or inheriting any vars because it forwards method calls to other objects that have mutable state. The reverse is also possible: A class might contain vars and still be purely functional. An example would be a class that caches the result of an expensive operation in a field for opti- mization purposes. To pick an example, assume the following unoptimized class Keyed with an expensive operation computeKey: class Keyed { def computeKey: Int = ... // this will take some time ... } Provided that computeKey neither reads nor writes any vars, you can make Keyed more efficient by adding a cache: class MemoKeyed extends Keyed { private var keyCache: Option[Int] = None override def computeKey: Int = { if (!keyCache.isDefined) keyCache = Some(super.computeKey) keyCache.get } } Using MemoKeyed instead of Keyed can speed up things, because the sec- ond time the result of the computeKey operation is requested, the value stored in the keyCache field can be returned instead of running computeKey once again. But except for this speed gain, the behavior of class Keyed and MemoKeyed is exactly the same. Consequently, if Keyed is purely functional, then so is MemoKeyed, even though it contains a reassignable variable. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.2 Chapter 18 · Stateful Objects 402 18.2 Reassignable variables and properties You can perform two fundamental operations on a reassignable variable: get its value or set it to a new value. In libraries such as JavaBeans, these op- erations are often encapsulated in separate getter and setter methods, which need to be defined explicitly. In Scala, every var that is a non-private mem- ber of some object implicitly defines a getter and a setter method with it. These getters and setters are named differently from the Java convention, however. The getter of a var x is just named “x”, while its setter is named “x_=”. For example, if it appears in a class, the var definition: var hour = 12 generates a getter, “hour”, and setter, “hour_=”, in addition to a reassignable field. The field is always marked private[this], which means it can be accessed only from the object that contains it. The getter and setter, on the other hand, get the same visibility as the original var. If the var definition is public, so are its getter and setter, if it is protected they are also protected, and so on. For instance, consider the class Time shown in Listing 18.2, which de- fines two public vars named hour and minute: class Time{ var hour = 12 var minute = 0 } Listing 18.2· A class with public vars. This implementation is exactly equivalent to the class definition shown in Listing 18.3. In the definitions shown in Listing 18.3, the names of the local fields h and m are arbitrarily chosen so as not to clash with any names already in use. An interesting aspect about this expansion of vars into getters and setters is that you can also choose to define a getter and a setter directly instead of defining a var. By defining these access methods directly you can interpret the operations of variable access and variable assignment as you like. For in- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.2 Chapter 18 · Stateful Objects 403 class Time{ private[this] varh= 12 private[this] var m = 0 def hour: Int = h def hour_=(x: Int) { h = x } def minute: Int = m def minute_=(x: Int) { m = x } } Listing 18.3· How public vars are expanded into getter and setter methods. stance, the variant of class Time shown in Listing 18.4 contains requirements that catch all assignments to hour and minute with illegal values. class Time{ private[this] varh= 12 private[this] var m = 0 def hour: Int = h def hour_= (x: Int){ require(0 <= x && x < 24) h = x } def minute = m def minute_= (x: Int){ require(0 <= x && x < 60) m = x } } Listing 18.4· Defining getter and setter methods directly. Some languages have a special syntactic construct for these variable- like quantities that are not plain variables in that their getter or setter can be redefined. For instance, C# has properties, which fulfill this role. Scala’s convention of always interpreting a variable as a pair of setter and getter methods gives you in effect the same capabilities as C# properties without Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.2 Chapter 18 · Stateful Objects 404 requiring special syntax. Properties can serve many different purposes. In the example shown in Listing 18.4, the setters enforced an invariant, thus protecting the variable from being assigned illegal values. You could also use a property to log all accesses to getters or setters of a variable. Or you could integrate variables with events, for instance by notifying some subscriber methods each time a variable is modified (you’ll see examples of this in Chapter 35). It is also possible, and sometimes useful, to define a getter and a setter without an associated field. An example is the following class Thermometer, which encapsulates a temperature variable that can be read and updated. Temperatures can be expressed in Celsius or Fahrenheit degrees. The class below allows you to get and set the temperature in either measure. class Thermometer{ var celsius: Float = _ def fahrenheit = celsius * 9 / 5 + 32 def fahrenheit_= (f: Float){ celsius = (f - 32) * 5 / 9 } override def toString = fahrenheit +"F/"+ celsius +"C" } Listing 18.5· Defining a getter and setter without an associated field. The first line in the body of this class defines a var, celsius, which will contain the temperature in degrees Celsius. The celsius variable is initially set to a default value by specifying ‘_’ as the “initializing value” of the variable. More precisely, an initializer “= _” of a field assigns a zero value to that field. The zero value depends on the field’s type. It is 0 for numeric types, false for booleans, and null for reference types. This is the same as if the same variable was defined in Java without an initializer. Note that you cannot simply leave off the “= _” initializer in Scala. If you had written: var celsius: Float this would declare an abstract variable, not an uninitialized one.1 1Abstract variables will be explained in Chapter 20. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.3 Chapter 18 · Stateful Objects 405 The celsius variable definition is followed by a getter, “fahrenheit”, and a setter, “fahrenheit_=”, which access the same temperature, but in de- grees Fahrenheit. There is no separate field that contains the current temper- ature value in Fahrenheit. Instead the getter and setter methods for Fahren- heit values automatically convert from and to degrees Celsius, respectively. Here’s an example of interacting with a Thermometer object: scala> val t = new Thermometer t: Thermometer = 32.0F/0.0C scala> t.celsius = 100 scala> t res3: Thermometer = 212.0F/100.0C scala> t.fahrenheit = -40 scala> t res4: Thermometer = -40.0F/-40.0C 18.3 Case study: Discrete event simulation The rest of this chapter shows by way of an extended example how state- ful objects can be combined with first-class function values in interesting ways. You’ll see the design and implementation of a simulator for digital circuits. This task is decomposed into several subproblems, each of which is interesting individually: First, you’ll see a little language for digital circuits. The definition of this language will highlight a general method for embed- ding domain-specific languages in a host language like Scala. Second, we’ll present a simple but general framework for discrete event simulation. The main task of this framework will be to keep track of actions that are per- formed in simulated time. Finally, we’ll show how discrete simulation pro- grams can be structured and built. The idea of such simulations is to model physical objects by simulated objects, and to use the simulation framework to model physical time. The example is taken from the classic textbook Structure and Interpreta- tion of Computer Programs by Abelson and Sussman [Abe96]. What’s dif- ferent here is that the implementation language is Scala instead of Scheme, and that the various aspects of the example are structured into four software Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.4 Chapter 18 · Stateful Objects 406 and-gate or-gateinverter Figure 18.1· Basic gates. layers: one for the simulation framework, another for the basic circuit simu- lation package, a third for a library of user-defined circuits, and the last layer for each simulated circuit itself. Each layer is expressed as a class, and more specific layers inherit from more general ones. The fast track Understanding the discrete event simulation example presented in this chapter will take some time. If you feel you want to get on with learning more Scala instead, it’s safe to skip ahead to the next chapter. 18.4 A language for digital circuits We’ll start with a “little language” to describe digital circuits. A digital cir- cuit is built from wires and function boxes. Wires carry signals, which are transformed by function boxes. Signals are represented by booleans: true for signal-on and false for signal-off. Figure 18.1 shows three basic function boxes (or gates): • An inverter, which negates its signal. • An and-gate, which sets its output to the conjunction of its inputs. • An or-gate, which sets its output to the disjunction of its inputs. These gates are sufficient to build all other function boxes. Gates have de- lays, so an output of a gate will change only some time after its inputs change. We’ll describe the elements of a digital circuit by the following set of Scala classes and functions. First, there is a class Wire for wires. We can construct wires like this: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.4 Chapter 18 · Stateful Objects 407 val a = new Wire val b = new Wire val c = new Wire or, equivalent but shorter, like this: val a, b, c = new Wire Second, there are three procedures which “make” the basic gates we need: def inverter(input: Wire, output: Wire) def andGate(a1: Wire, a2: Wire, output: Wire) def orGate(o1: Wire, o2: Wire, output: Wire) What’s unusual, given the functional emphasis of Scala, is that these proce- dures construct the gates as a side-effect, instead of returning the constructed gates as a result. For instance, an invocation of inverter(a, b) places an inverter between the wires a and b. It turns out that this side-effecting con- struction makes it easier to construct complicated circuits gradually. Also, although methods most often have verb names, these have noun names that indicate which gate they are making. This reflects the declarative nature of the DSL: it should describe a circuit, not the actions of making one. More complicated function boxes can be built from the basic gates. For instance, the method shown in Listing 18.6 constructs a half-adder. The halfAdder method takes two inputs, a and b, and produces a sum, s, defined by “s = (a + b) % 2” and a carry, c, defined by “c = (a + b) / 2”. A diagram of the half-adder is shown in Figure 18.2. def halfAdder(a: Wire, b: Wire, s: Wire, c: Wire){ val d, e = new Wire orGate(a, b, d) andGate(a, b, c) inverter(c, e) andGate(d, e, s) } Listing 18.6· The halfAdder method. Note that halfAdder is a parameterized function box just like the three methods that construct the primitive gates. You can use the halfAdder Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.4 Chapter 18 · Stateful Objects 408 a b s c d e Figure 18.2· A half-adder circuit. method to construct more complicated circuits. For instance, Listing 18.7 defines a full, one-bit adder, shown in Figure 18.3, which takes two inputs, a and b, as well as a carry-in, cin, and which produces a sum output de- fined by “sum = (a + b + cin) % 2” and a carry-out output defined by “cout = (a + b + cin) / 2”. def fullAdder(a: Wire, b: Wire, cin: Wire, sum: Wire, cout: Wire){ val s, c1, c2 = new Wire halfAdder(a, cin, s, c1) halfAdder(b, s, sum, c2) orGate(c1, c2, cout) } Listing 18.7· The fullAdder method. Class Wire and functions inverter, andGate, and orGate represent a little language with which users can define digital circuits. It’s a good example of an internal DSL, a domain specific language defined as a library in a host language instead of being implemented on its own. The implementation of the circuit DSL still needs to be worked out. Since the purpose of defining a circuit in the DSL is simulating the circuit, it makes sense to base the DSL implementation on a general API for discrete event simulation. The next two sections will present first the simulation API and then the implementation of the circuit DSL on top of it. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.5 Chapter 18 · Stateful Objects 409 a b cout sum c2 half adder half adder c1 cin s Figure 18.3· A full-adder circuit. 18.5 The Simulation API The simulation API is shown in Listing 18.8. It consists of class Simulation in package org.stairwaybook.simulation. Concrete simulation libraries inherit this class and augment it with domain-specific functionality. The elements of the Simulation class are presented in this section. A discrete event simulation performs user-defined actions at specified times. The actions, which are defined by concrete simulation subclasses, all share a common type: type Action = () => Unit This statement defines Action to be an alias of the type of procedure that takes an empty parameter list and returns Unit. Action is a type member of class Simulation. You can think of it as a more readable name for type () => Unit. Type members will be described in detail in Section 20.6. The time at which an action is performed is simulated time; it has nothing to do with the actual “wall clock” time. Simulated times are represented simply as integers. The current simulated time is kept in a private variable: private var curtime: Int = 0 The variable has a public accessor method, which retrieves the current time: def currentTime: Int = curtime This combination of private variable with public accessor is used to make sure that the current time cannot be modified outside the Simulation class. After all, you don’t usually want your simulation objects to manipulate the current time, except possibly if your simulation models time travel. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.5 Chapter 18 · Stateful Objects 410 abstract class Simulation { type Action = () => Unit case class WorkItem(time: Int, action: Action) private var curtime = 0 def currentTime: Int = curtime private var agenda: List[WorkItem] = List() private def insert(ag: List[WorkItem], item: WorkItem): List[WorkItem] = { if (ag.isEmpty || item.time < ag.head.time) item :: ag else ag.head :: insert(ag.tail, item) } def afterDelay(delay: Int)(block: => Unit){ val item = WorkItem(currentTime + delay, () => block) agenda = insert(agenda, item) } private def next() { (agenda: @unchecked) match { case item :: rest => agenda = rest curtime = item.time item.action() } } def run() { afterDelay(0){ println("*** simulation started, time = "+ currentTime +" ***") } while (!agenda.isEmpty) next() } } Listing 18.8· The Simulation class. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.5 Chapter 18 · Stateful Objects 411 An action that needs to be executed at a specified time is called a work item. Work items are implemented by the following class: case class WorkItem(time: Int, action: Action) We made the WorkItem class a case class because of the syntactic conve- niences this entails: you can use the factory method, WorkItem, to create instances of the class, and you get accessors for the constructor parameters time and action for free. Note also that class WorkItem is nested inside class Simulation. Nested classes in Scala are treated similarly to Java. Sec- tion 20.7 will give more details. The Simulation class keeps an agenda of all remaining work items that have not yet been executed. The work items are sorted by the simulated time at which they have to be run: private var agenda: List[WorkItem] = List() The agenda list will be kept in the proper sorted order by the insert method, which updates it. You can see insert being called from afterDelay, which is the only way to add a work item to the agenda: def afterDelay(delay: Int)(block: => Unit){ val item = WorkItem(currentTime + delay, () => block) agenda = insert(agenda, item) } As the name implies, this method inserts an action (given by block) into the agenda so that it is scheduled for execution delay time units after the current simulation time. For instance, the following invocation would create a new work item to be executed at the simulated time, currentTime + delay: afterDelay(delay) { count += 1 } The code to be executed is contained in the method’s second argument. The formal parameter for this argument has type “=> Unit”, i.e., it is a computa- tion of type Unit which is passed by name. Recall that by-name parameters are not evaluated when passed to a method. So in the call above, count would be incremented only when the simulation framework calls the action stored in the work item. Note that afterDelay is a curried function. It’s a good example of the principle set forward in Section 9.5 that currying can be used to make method calls look more like built-in syntax. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.5 Chapter 18 · Stateful Objects 412 The created work item still needs to be inserted into the agenda. This is done by the insert method, which maintains the invariant that the agenda is time-sorted: private def insert(ag: List[WorkItem], item: WorkItem): List[WorkItem] = { if (ag.isEmpty || item.time < ag.head.time) item :: ag else ag.head :: insert(ag.tail, item) } The core of the Simulation class is defined by the run method: def run() { afterDelay(0){ println("*** simulation started, time = "+ currentTime +" ***") } while (!agenda.isEmpty) next() } This method repeatedly takes the first item in the agenda, removes it from the agenda and executes it. It does this until there are no more items left in the agenda to execute. Each step is performed by calling the next method, which is defined as follows: private def next() { (agenda: @unchecked) match { case item :: rest => agenda = rest curtime = item.time item.action() } } The next method decomposes the current agenda with a pattern match into a front item, item, and a remaining list of work items, rest. It removes the front item from the current agenda, sets the simulated time curtime to the work item’s time, and executes the work item’s action. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.6 Chapter 18 · Stateful Objects 413 Note that next can be called only if the agenda is non-empty. There’s no case for an empty list, so you would get a MatchError exception if you tried to run next on an empty agenda. In fact, the Scala compiler would normally warn you that you missed one of the possible patterns for a list: Simulator.scala:19: warning: match is not exhaustive! missing combination Nil agenda match { ˆ one warning found In this case, the missing case is not a problem, because you know that next is called only on a non-empty agenda. Therefore, you might want to dis- able the warning. You saw in Section 15.5 that this can be done by adding an @unchecked annotation to the selector expression of the pattern match. That’s why the Simulation code uses “(agenda: @unchecked) match”, not “agenda match”. That’s it. This seems surprisingly little code for a simulation framework. You might wonder how this framework could possibly support interesting simulations, if all it does is execute a list of work items? In fact the power of the simulation framework comes from the fact that actions stored in work items can themselves install further work items into the agenda when they are executed. That makes it possible to have long-running simulations evolve from simple beginnings. 18.6 Circuit Simulation The next step is to use the simulation framework to implement the domain- specific language for circuits shown in Section 18.4. Recall that the cir- cuit DSL consists of a class for wires and methods that create and-gates, or- gates, and inverters. These are all contained in a BasicCircuitSimulation class, which extends the simulation framework. This class is shown in List- ings 18.9 and 18.10. Class BasicCircuitSimulation declares three abstract methods that represent the delays of the basic gates: InverterDelay, AndGateDelay, and OrGateDelay. The actual delays are not known at the level of this class, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.6 Chapter 18 · Stateful Objects 414 package org.stairwaybook.simulation abstract class BasicCircuitSimulation extends Simulation { def InverterDelay: Int def AndGateDelay: Int def OrGateDelay: Int class Wire { private var sigVal = false private var actions: List[Action] = List() def getSignal = sigVal def setSignal(s: Boolean) = if (s != sigVal) { sigVal = s actions foreach (_ ()) } def addAction(a: Action) = { actions = a :: actions a() } } def inverter(input: Wire, output: Wire) = { def invertAction() { val inputSig = input.getSignal afterDelay(InverterDelay){ output setSignal !inputSig } } input addAction invertAction } // continued in Listing 18.10... Listing 18.9· The first half of the BasicCircuitSimulation class. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.6 Chapter 18 · Stateful Objects 415 // ...continued from Listing 18.9 def andGate(a1: Wire, a2: Wire, output: Wire) = { def andAction() = { val a1Sig = a1.getSignal val a2Sig = a2.getSignal afterDelay(AndGateDelay){ output setSignal (a1Sig & a2Sig) } } a1 addAction andAction a2 addAction andAction } def orGate(o1: Wire, o2: Wire, output: Wire){ def orAction() { val o1Sig = o1.getSignal val o2Sig = o2.getSignal afterDelay(OrGateDelay){ output setSignal (o1Sig | o2Sig) } } o1 addAction orAction o2 addAction orAction } def probe(name: String, wire: Wire){ def probeAction() { println(name +""+ currentTime + " new-value = "+ wire.getSignal) } wire addAction probeAction } } Listing 18.10· The second half of the BasicCircuitSimulation class. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.6 Chapter 18 · Stateful Objects 416 because they depend on the technology of circuits that are simulated. That’s why the delays are left abstract in class BasicCircuitSimulation, so that their concrete definition is delegated to a subclass.2 The implementation of class BasicCircuitSimulation’s other members is described next. The Wire class A wire needs to support three basic actions: getSignal: Boolean: returns the current signal on the wire. setSignal(sig: Boolean): sets the wire’s signal to sig. addAction(p: Action): attaches the specified procedure p to the ac- tions of the wire. The idea is that all action procedures attached to some wire will be executed every time the signal of the wire changes. Typically actions are added to a wire by components connected to the wire. An attached action is executed once at the time it is added to a wire, and after that, every time the signal of the wire changes. Here is the implementation of the Wire class: class Wire { private var sigVal = false private var actions: List[Action] = List() def getSignal = sigVal def setSignal(s: Boolean) = if (s != sigVal) { sigVal = s actions foreach (_ ()) } def addAction(a: Action) = { actions = a :: actions a() } } 2The names of these “delay” methods start with a capital letter because they represent constants. They are methods so they can be overridden in subclasses. You’ll find out how to do the same thing with vals in Section 20.3. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.6 Chapter 18 · Stateful Objects 417 Two private variables make up the state of a wire. The variable sigVal rep- resents the current signal, and the variable actions represents the action procedures currently attached to the wire. The only interesting method im- plementation is the one for setSignal: When the signal of a wire changes, the new value is stored in the variable sigVal. Furthermore, all actions at- tached to a wire are executed. Note the shorthand syntax for doing this: “actions foreach (_ ())” applies the function, “_ ()”, to each element in the actions list. As described in Section 8.5, the function “_ ()” is a shorthand for “f => f ()”, i.e., it takes a function (we’ll call it f) and applies it to the empty parameter list. The inverter method The only effect of creating an inverter is that an action is installed on its input wire. This action is invoked once at the time the action is installed, and thereafter every time the signal on the input changes. The effect of the action is that the value of the inverter’s output value is set (via setSignal) to the inverse of its input value. Since inverter gates have delays, this change should take effect only InverterDelay units of simulated time after the input value has changed and the action was executed. This suggests the following implementation: def inverter(input: Wire, output: Wire) = { def invertAction() { val inputSig = input.getSignal afterDelay(InverterDelay){ output setSignal !inputSig } } input addAction invertAction } The effect of the inverter method is to add invertAction to the input wire. This action, when invoked, gets the input signal and installs another action that inverts the output signal into the simulation agenda. This other action is to be executed after InverterDelay units of simulated time. Note how the method uses the afterDelay method of the simulation framework to create a new work item that’s going to be executed in the future. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.6 Chapter 18 · Stateful Objects 418 The andGate and orGate methods The implementation of and-gates is analogous to the implementation of in- verters. The purpose of an and-gate is to output the conjunction of its input signals. This should happen at AndGateDelay simulated time units after any one of its two inputs changes. Hence, the following implementation: def andGate(a1: Wire, a2: Wire, output: Wire) = { def andAction() = { val a1Sig = a1.getSignal val a2Sig = a2.getSignal afterDelay(AndGateDelay){ output setSignal (a1Sig & a2Sig) } } a1 addAction andAction a2 addAction andAction } The effect of the andGate method is to add andAction to both of its input wires a1 and a2. This action, when invoked, gets both input signals and installs another action that sets the output signal to the conjunction of both input signals. This other action is to be executed after AndGateDelay units of simulated time. Note that the output has to be recomputed if either of the input wires changes. That’s why the same andAction is installed on each of the two input wires a1 and a2. The orGate method is implemented similarly, except it performs a logical-or instead of a logical-and. Simulation output To run the simulator, you need a way to inspect changes of signals on wires. To accomplish this, you can simulate the action of putting a probe on a wire: def probe(name: String, wire: Wire){ def probeAction() { println(name +""+ currentTime + " new-value = "+ wire.getSignal) } wire addAction probeAction } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.6 Chapter 18 · Stateful Objects 419 The effect of the probe procedure is to install a probeAction on a given wire. As usual, the installed action is executed every time the wire’s signal changes. In this case it simply prints the name of the wire (which is passed as first parameter to probe), as well as the current simulated time and the wire’s new value. Running the simulator After all these preparations, it’s time to see the simulator in action. To de- fine a concrete simulation, you need to inherit from a simulation framework class. To see something interesting, we’ll create an abstract simulation class that extends BasicCircuitSimulation and contains method definitions for half-adders and full-adders as they were presented earlier in this chapter in Listings 18.6 and 18.7. This class, which we’ll call CircuitSimulation, is shown in Listing 18.11: package org.stairwaybook.simulation abstract class CircuitSimulation extends BasicCircuitSimulation{ def halfAdder(a: Wire, b: Wire, s: Wire, c: Wire){ val d, e = new Wire orGate(a, b, d) andGate(a, b, c) inverter(c, e) andGate(d, e, s) } def fullAdder(a: Wire, b: Wire, cin: Wire, sum: Wire, cout: Wire){ val s, c1, c2 = new Wire halfAdder(a, cin, s, c1) halfAdder(b, s, sum, c2) orGate(c1, c2, cout) } } Listing 18.11· The CircuitSimulation class. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.6 Chapter 18 · Stateful Objects 420 A concrete circuit simulation will be an object that inherits from class CircuitSimulation. The object still needs to fix the gate delays according to the circuit implementation technology that’s simulated. Finally, you will also need to define the concrete circuit that’s going to be simulated. You can do these steps interactively in the Scala interpreter: scala> import org.stairwaybook.simulation._ import org.stairwaybook.simulation._ First, the gate delays. Define an object (call it MySimulation) that provides some numbers: scala> object MySimulation extends CircuitSimulation { def InverterDelay = 1 def AndGateDelay = 3 def OrGateDelay = 5 } defined module MySimulation Because you are going to access the members of the MySimulation object repeatedly, an import of the object keeps the subsequent code shorter: scala> import MySimulation._ import MySimulation._ Next, the circuit. Define four wires, and place probes on two of them: scala> val input1, input2, sum, carry = new Wire input1: MySimulation.Wire = BasicCircuitSimulation$Wire@111089b input2: MySimulation.Wire = BasicCircuitSimulation$Wire@14c352e sum: MySimulation.Wire = BasicCircuitSimulation$Wire@37a04c carry: MySimulation.Wire = BasicCircuitSimulation$Wire@1fd10fa scala> probe("sum", sum) sum 0 new-value = false scala> probe("carry", carry) carry 0 new-value = false Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 18.7 Chapter 18 · Stateful Objects 421 Note that the probes immediately print an output. This is a consequence of the fact that every action installed on a wire is executed a first time when the action is installed. Now define a half-adder connecting the wires: scala> halfAdder(input1, input2, sum, carry) Finally, set the signals, one after another, on the two input wires to true and run the simulation: scala> input1 setSignal true scala> run() *** simulation started, time = 0 *** sum 8 new-value = true scala> input2 setSignal true scala> run() *** simulation started, time = 8 *** carry 11 new-value = true sum 15 new-value = false 18.7 Conclusion This chapter has brought together two techniques that seem at first disparate: mutable state and higher-order functions. Mutable state was used to simulate physical entities whose state changes over time. Higher-order functions were used in the simulation framework to execute actions at specified points in simulated time. They were also used in the circuit simulations as triggers that associate actions with state changes. Along the way, you saw a simple way to define a domain specific language as a library. That’s probably enough for one chapter! If you feel like staying a bit longer, you might want to try more simula- tion examples. You can combine half-adders and full-adders to create larger circuits, or design new circuits from the basic gates defined so far and sim- ulate them. In the next chapter, you’ll learn about type parameterization in Scala, and see another example in which a combination of functional and imperative approaches yields a good solution. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 19 Type Parameterization In this chapter, we’ll explain the details of type parameterization in Scala. Along the way we’ll demonstrate some of the techniques for information hiding introduced in Chapter 13 by means of a concrete example: the design of a class for purely functional queues. We’re presenting type parameteri- zation and information hiding together, because information hiding can be used to obtain more general type parameterization variance annotations. Type parameterization allows you to write generic classes and traits. For example, sets are generic and take a type parameter: they are defined as Set[T]. As a result, any particular set instance might be a Set[String], a Set[Int], etc.—but it must be a set of something. Unlike Java, which allows raw types, Scala requires that you specify type parameters. Variance defines inheritance relationships of parameterized types, such as whether a Set[String], for example, is a subtype of Set[AnyRef]. The chapter contains three parts. The first part develops a data struc- ture for purely functional queues. The second part develops techniques to hide internal representation details of this structure. The final part explains variance of type parameters and how it interacts with information hiding. 19.1 Functional queues A functional queue is a data structure with three operations: head returns the first element of the queue tail returns a queue without its first element enqueue returns a new queue with a given element appended at the end Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.1 Chapter 19 · Type Parameterization 423 Unlike a mutable queue, a functional queue does not change its contents when an element is appended. Instead, a new queue is returned that contains the element. The goal of this chapter will be to create a class, which we’ll name Queue, that works like this: scala> val q = Queue(1, 2, 3) q: Queue[Int] = Queue(1, 2, 3) scala> val q1 = q enqueue 4 q1: Queue[Int] = Queue(1, 2, 3, 4) scala> q res0: Queue[Int] = Queue(1, 2, 3) If Queue were a mutable implementation, the enqueue operation in the sec- ond input line above would affect the contents of q; in fact both the result, q1, and the original queue, q, would contain the sequence 1, 2, 3, 4 after the operation. But for a functional queue, the appended value shows up only in the result, q1, not in the queue, q, being operated on. Purely functional queues also have some similarity with lists. Both are so called fully persistent data structures, where old versions remain available even after extensions or modifications. Both support head and tail opera- tions. But where a list is usually extended at the front, using a :: operation, a queue is extended at the end, using enqueue. How can this be implemented efficiently? Ideally, a functional (im- mutable) queue should not have a fundamentally higher overhead than an imperative (mutable) one. That is, all three operations head, tail, and enqueue should operate in constant time. One simple approach to implement a functional queue would be to use a list as representation type. Then head and tail would just translate into the same operations on the list, whereas enqueue would be concatenation. This would give the following implementation: class SlowAppendQueue[T](elems: List[T]){// Not efficient def head = elems.head def tail = new SlowAppendQueue(elems.tail) def enqueue(x: T) = new SlowAppendQueue(elems ::: List(x)) } The problem with this implementation is in the enqueue operation. It takes time proportional to the number of elements stored in the queue. If you want Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.1 Chapter 19 · Type Parameterization 424 constant time append, you could also try to reverse the order of the elements in the representation list, so that the last element that’s appended comes first in the list. This would lead to the following implementation: class SlowHeadQueue[T](smele: List[T]){// Not efficient // smele is elems reversed def head = smele.last def tail = new SlowHeadQueue(smele.init) def enqueue(x: T) = new SlowHeadQueue(x :: smele) } Now enqueue is constant time, but head and tail are not. They now take time proportional to the number of elements stored in the queue. Looking at these two examples, it does not seem easy to come up with an implementation that’s constant time for all three operations. In fact, it looks doubtful that this is even possible! However, by combining the two operations you can get very close. The idea is to represent a queue by two lists, called leading and trailing. The leading list contains elements towards the front, whereas the trailing list contains elements towards the back of the queue in reversed order. The contents of the whole queue are at each instant equal to “leading ::: trailing.reverse”. Now, to append an element, you just cons it to the trailing list using the :: operator, so enqueue is constant time. This means that, when an initially empty queue is constructed from successive enqueue operations, the trailing list will grow whereas the leading list will stay empty. Then, before the first head or tail operation is performed on an empty leading list, the whole trailing list is copied to leading, reversing the order of the elements. This is done in an operation called mirror. Listing 19.1 shows an implementation of queues that uses this approach. What is the complexity of this implementation of queues? The mirror operation might take time proportional to the number of queue elements, but only if list leading is empty. It returns directly if leading is non-empty. Because head and tail call mirror, their complexity might be linear in the size of the queue, too. However, the longer the queue gets, the less often mirror is called. Indeed, assume a queue of length n with an empty leading list. Then mirror has to reverse-copy a list of length n. However, the next time mirror will have to do any work is once the leading list is empty again, which will be the case after n tail operations. This means you can “charge” each of these n tail operations with one n’th of the complexity Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.1 Chapter 19 · Type Parameterization 425 class Queue[T]( private val leading: List[T], private val trailing: List[T] ){ private def mirror = if (leading.isEmpty) new Queue(trailing.reverse, Nil) else this def head = mirror.leading.head def tail = { val q = mirror new Queue(q.leading.tail, q.trailing) } def enqueue(x: T) = new Queue(leading, x :: trailing) } Listing 19.1· A basic functional queue. of mirror, which means a constant amount of work. Assuming that head, tail, and enqueue operations appear with about the same frequency, the amortized complexity is hence constant for each operation. So functional queues are asymptotically just as efficient as mutable ones. Now, there are some caveats that need to be attached to this argument. First, the discussion only was about asymptotic behavior, the constant factors might well be somewhat different. Second, the argument rested on the fact that head, tail and enqueue are called with about the same frequency. If head is called much more often than the other two operations, the argument is not valid, as each call to head might involve a costly re-organization of the list with mirror. The second caveat can be avoided; it is possible to design functional queues so that in a sequence of successive head operations only the first one might require a re-organization. You will find out at the end of this chapter how this is done. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.2 Chapter 19 · Type Parameterization 426 19.2 Information hiding The implementation of Queue shown in Listing 19.1 is now quite good with regards to efficiency. You might object, though, that this efficiency is paid for by exposing a needlessly detailed implementation. The Queue construc- tor, which is globally accessible, takes two lists as parameters, where one is reversed—hardly an intuitive representation of a queue. What’s needed is a way to hide this constructor from client code. In this section, we’ll show you some ways to accomplish this in Scala. Private constructors and factory methods In Java, you can hide a constructor by making it private. In Scala, the pri- mary constructor does not have an explicit definition; it is defined implicitly by the class parameters and body. Nevertheless, it is still possible to hide the primary constructor by adding a private modifier in front of the class parameter list, as shown in Listing 19.2: class Queue[T] private ( private val leading: List[T], private val trailing: List[T] ) Listing 19.2· Hiding a primary constructor by making it private. The private modifier between the class name and its parameters indi- cates that the constructor of Queue is private: it can be accessed only from within the class itself and its companion object. The class name Queue is still public, so you can use it as a type, but you cannot call its constructor: scala> new Queue(List(1, 2), List(3)) :6: error: constructor Queue cannot be accessed in object $iw new Queue(List(1, 2), List(3)) ˆ Now that the primary constructor of class Queue can no longer be called from client code, there needs to be some other way to create new queues. One possibility is to add an auxiliary constructor, like this: def this() = this(Nil, Nil) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.2 Chapter 19 · Type Parameterization 427 The auxiliary constructor shown in the previous example builds an empty queue. As a refinement, the auxiliary constructor could take a list of initial queue elements: def this(elems: T*) = this(elems.toList, Nil) Recall that T* is the notation for repeated parameters, as described in Sec- tion 8.8. Another possibility is to add a factory method that builds a queue from such a sequence of initial elements. A neat way to do this is to define an object Queue that has the same name as the class being defined and contains an apply method, as shown in Listing 19.3: object Queue{ // constructs a queue with initial elements ‘xs’ def apply[T](xs: T*) = new Queue[T](xs.toList, Nil) } Listing 19.3· An apply factory method in a companion object. By placing this object in the same source file as class Queue, you make the object a companion object of the class. You saw in Section 13.5 that a companion object has the same access rights as its class. Because of this, the apply method in object Queue can create a new Queue object, even though the constructor of class Queue is private. Note that, because the factory method is called apply, clients can create queues with an expression such as Queue(1, 2, 3). This expression expands to Queue.apply(1, 2, 3) since Queue is an object instead of a function. As a result, Queue looks to clients as if it was a globally defined factory method. In reality, Scala has no globally visible methods; every method must be contained in an object or a class. However, using methods named apply inside global objects, you can support usage patterns that look like invocations of global methods. An alternative: private classes Private constructors and private members are one way to hide the initial- ization and representation of a class. Another, more radical way is to hide the class itself and only export a trait that reveals the public interface of the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.2 Chapter 19 · Type Parameterization 428 trait Queue[T]{ def head: T def tail: Queue[T] def enqueue(x: T): Queue[T] } object Queue { def apply[T](xs: T*): Queue[T] = new QueueImpl[T](xs.toList, Nil) private class QueueImpl[T]( private val leading: List[T], private val trailing: List[T] ) extends Queue[T] { def mirror = if (leading.isEmpty) new QueueImpl(trailing.reverse, Nil) else this def head: T = mirror.leading.head def tail: QueueImpl[T] = { val q = mirror new QueueImpl(q.leading.tail, q.trailing) } def enqueue(x: T) = new QueueImpl(leading, x :: trailing) } } Listing 19.4· Type abstraction for functional queues. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.3 Chapter 19 · Type Parameterization 429 class. The code in Listing 19.4 implements this design. There’s a trait Queue, which declares the methods head, tail, and enqueue. All three methods are implemented in a subclass QueueImpl, which is itself a private inner class of object Queue. This exposes to clients the same information as before, but using a different technique. Instead of hiding individual constructors and methods, this version hides the whole implementation class. 19.3 Variance annotations Queue, as defined in Listing 19.4, is a trait, but not a type. Queue is not a type because it takes a type parameter. As a result, you cannot create variables of type Queue: scala> def doesNotCompile(q: Queue) {} :5: error: trait Queue takes type parameters def doesNotCompile(q: Queue) {} ˆ Instead, trait Queue enables you to specify parameterized types, such as Queue[String], Queue[Int], or Queue[AnyRef]: scala> def doesCompile(q: Queue[AnyRef]) {} doesCompile: (Queue[AnyRef])Unit Thus, Queue is a trait, and Queue[String] is a type. Queue is also called a type constructor, because with it you can construct a type by speci- fying a type parameter. (This is analogous to constructing an object instance with a plain-old constructor by specifying a value parameter.) The type con- structor Queue “generates” a family of types, which includes Queue[Int], Queue[String], and Queue[AnyRef]. You can also say that Queue is a generic trait. (Classes and traits that take type parameters are “generic,” but the types they generate are “param- eterized,” not generic.) The term “generic” means that you are defining many specific types with one generically written class or trait. For exam- ple, trait Queue in Listing 19.4 defines a generic queue. Queue[Int] and Queue[String], etc., would be the specific queues. The combination of type parameters and subtyping poses some interest- ing questions. For example, are there any special subtyping relationships be- tween members of the family of types generated by Queue[T]? More specifi- cally, should a Queue[String] be considered a subtype of Queue[AnyRef]? Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.3 Chapter 19 · Type Parameterization 430 Or more generally, if S is a subtype of type T, then should Queue[S] be considered a subtype of Queue[T]? If so, you could say that trait Queue is covariant (or “flexible”) in its type parameter T. Or, since it just has one type parameter, you could say simply that Queues are covariant. Covariant Queues would mean, for example, that you could pass a Queue[String] to the doesCompile method shown previously, which takes a value parameter of type Queue[AnyRef]. Intuitively, all this seems OK, since a queue of Strings looks like a spe- cial case of a queue of AnyRefs. In Scala, however, generic types have by default nonvariant (or, “rigid”) subtyping. That is, with Queue defined as in Listing 19.4, queues with different element types would never be in a subtype relationship. A Queue[String] would not be usable as a Queue[AnyRef]. However, you can demand covariant (flexible) subtyping of queues by chang- ing the first line of the definition of class Queue like this: trait Queue[+T] { ... } Prefixing a formal type parameter with a + indicates that subtyping is co- variant (flexible) in that parameter. By adding this single character, you are telling Scala that you want Queue[String], for example, to be considered a subtype of Queue[AnyRef]. The compiler will check that Queue is defined in a way that this subtyping is sound. Besides +, there is also a prefix -, which indicates contravariant subtyp- ing. If Queue were defined like this: trait Queue[-T] { ... } then if T is a subtype of type S, this would imply that Queue[S] is a sub- type of Queue[T] (which in the case of queues would be rather surprising!). Whether a type parameter is covariant, contravariant, or nonvariant is called the parameter’s variance . The + and - symbols you can place next to type parameters are called variance annotations. In a purely functional world, many types are naturally covariant (flexi- ble). However, the situation changes once you introduce mutable data. To find out why, consider the simple type of one-element cells that can be read or written, shown in Listing 19.5. The Cell type of Listing 19.5 is declared nonvariant (rigid). For the sake of argument, assume for a moment that Cell was declared covariant instead—i.e., it was declared class Cell[+T]—and that this passed the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.3 Chapter 19 · Type Parameterization 431 class Cell[T](init: T) { private[this] var current = init def get = current def set(x: T) { current = x } } Listing 19.5· A nonvariant (rigid) Cell class. Scala compiler. (It doesn’t, and we’ll explain why shortly.) Then you could construct the following problematic statement sequence: val c1 = new Cell[String]("abc") val c2: Cell[Any] = c1 c2.set(1) val s: String = c1.get Seen by itself, each of these four lines looks OK. The first line creates a cell of strings and stores it in a val named c1. The second line defines a new val, c2, of type Cell[Any], which initialized with c1. This is OK, since Cells are assumed to be covariant. The third line sets the value of cell c2 to 1. This is also OK, because the assigned value 1 is an instance of c2’s element type Any. Finally, the last line assigns the element value of c1 into a string. Nothing strange here, as both the sides are of the same type. But taken together, these four lines end up assigning the integer 1 to the string s. This is clearly a violation of type soundness. Which operation is to blame for the runtime fault? It must be the second one, which uses covariant subtyping. The other statements are too simple and fundamental. Thus, a Cell of String is not also a Cell of Any, because there are things you can do with a Cell of Any that you cannot do with a Cell of String. You cannot use set with an Int argument on a Cell of String, for example. In fact, were you to pass the covariant version of Cell to the Scala com- piler, you would get a compile-time error: Cell.scala:7: error: covariant type T occurs in contravariant position in type T of value x def set(x: T) = current = x ˆ Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.3 Chapter 19 · Type Parameterization 432 Variance and arrays It’s interesting to compare this behavior with arrays in Java. In principle, arrays are just like cells except that they can have more than one element. Nevertheless, arrays are treated as covariant in Java. You can try an example analogous to the cell interaction above with Java arrays: // this is Java String[] a1 = { "abc" }; Object[] a2 = a1; a2[0] = new Integer(17); String s = a1[0]; If you try out this example, you will find that it compiles, but executing the program will cause an ArrayStore exception to be thrown when a2[0] is assigned to an Integer: Exception in thread "main" java.lang.ArrayStoreException: java.lang.Integer at JavaArrays.main(JavaArrays.java:8) What happens here is that Java stores the element type of the array at run- time. Then, every time an array element is updated, the new element value is checked against the stored type. If it is not an instance of that type, an ArrayStore exception is thrown. You might ask why Java adopted this design, which seems both unsafe and expensive. When asked this question, James Gosling, the principal in- ventor of the Java language, answered that they wanted to have a simple means to treat arrays generically. For instance, they wanted to be able to write a method to sort all elements of an array, using a signature like the following that takes an array of Object: void sort(Object[] a, Comparator cmp) { ... } Covariance of arrays was needed so that arrays of arbitrary reference types could be passed to this sort method. Of course, with the arrival of Java generics, such a sort method can now be written with a type parameter, so the covariance of arrays is no longer necessary. For compatibility reasons, though, it has persisted in Java to this day. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.4 Chapter 19 · Type Parameterization 433 Scala tries to be purer than Java in not treating arrays as covariant. Here’s what you get if you translate the first two lines of the array example to Scala: scala> val a1 = Array("abc") a1: Array[java.lang.String] = Array(abc) scala> val a2: Array[Any] = a1 :5: error: type mismatch; found : Array[java.lang.String] required: Array[Any] val a2: Array[Any] = a1 ˆ What happened here is that Scala treats arrays as nonvariant (rigid), so an Array[String] is not considered to conform to an Array[Any]. However, sometimes it is necessary to interact with legacy methods in Java that use an Object array as a means to emulate a generic array. For instance, you might want to call a sort method like the one described previously with an array of Strings as argument. To make this possible, Scala lets you cast an array of Ts to an array of any supertype of T: scala> val a2: Array[Object] = a1.asInstanceOf[Array[Object]] a2: Array[java.lang.Object] = Array(abc) The cast is always legal at compile-time, and it will always succeed at run- time, because the JVM’s underlying run-time model treats arrays as covari- ant, just as Java the language does. But you might get ArrayStore excep- tions afterwards, again just as you would in Java. 19.4 Checking variance annotations Now that you have seen some examples where variance is unsound, you may be wondering which kind of class definitions need to be rejected and which can be accepted. So far, all violations of type soundness involved some re- assignable field or array element. The purely functional implementation of queues, on the other hand, looks like a good candidate for covariance. How- ever, the following example shows that you can “engineer” an unsound situ- ation even if there is no reassignable field. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.4 Chapter 19 · Type Parameterization 434 To set up the example, assume that queues as defined in Listing 19.4 are covariant. Then, create a subclass of queues that specializes the element type to Int and overrides the enqueue method: class StrangeIntQueue extends Queue[Int] { override def enqueue(x: Int) = { println(math.sqrt(x)) super.enqueue(x) } } The enqueue method in StrangeIntQueue prints out the square root of its (integer) argument before doing the append proper. Now, you can write a counterexample in two lines: val x: Queue[Any] = new StrangeIntQueue x.enqueue("abc") The first of these two lines is valid, because StrangeIntQueue is a subclass of Queue[Int], and, assuming covariance of queues, Queue[Int] is a sub- type of Queue[Any]. The second line is valid because you can append a String to a Queue[Any]. However, taken together these two lines have the effect of applying a square root method to a string, which makes no sense. Clearly it’s not just mutable fields that make covariant types unsound. The problem is more general. It turns out that as soon as a generic parameter type appears as the type of a method parameter, the containing class or trait may not be covariant in that type parameter. For queues, the enqueue method violates this condition: class Queue[+T] { def enqueue(x: T) = ... } Running a modified queue class like the one above through a Scala compiler would yield: Queues.scala:11: error: covariant type T occurs in contravariant position in type T of value x def enqueue(x: T) = ˆ Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.4 Chapter 19 · Type Parameterization 435 Reassignable fields are a special case of the rule that disallows type parame- ters annotated with + from being used as method parameter types. As men- tioned in Section 18.2, a reassignable field, “var x: T”, is treated in Scala as a getter method, “def x: T”, and a setter method, “def x_=(y: T)”. As you can see, the setter method has a parameter of the field’s type T. So that type may not be covariant. The fast track In the rest of this section, we’ll describe the mechanism by which the Scala compiler checks variance annotations. If you’re not interested in such detail right now, you can safely skip to Section 19.5. The most important thing to understand is that the Scala compiler will check any variance annotations you place on type parameters. For example, if you try to declare a type parameter to be covariant (by adding a +), but that could lead to potential runtime errors, your program won’t compile. To verify correctness of variance annotations, the Scala compiler classi- fies all positions in a class or trait body as positive, negative, or neutral.A “position” is any location in the class (or trait, but from now on we’ll just write “class”) body where a type parameter may be used. Every method value parameter is a position, for example, because a method value parame- ter has a type, and therefore a type parameter could appear in that position. The compiler checks each use of each of the class’s type parameters. Type parameters annotated with + may only be used in positive positions, while type parameters annotated with - may only be used in negative positions. A type parameter with no variance annotation may be used in any position, and is, therefore, the only kind of type parameter that can be used in neutral positions of the class body. To classify the positions, the compiler starts from the declaration of a type parameter and then moves inward through deeper nesting levels. Po- sitions at the top level of the declaring class are classified as positive. By default, positions at deeper nesting levels are classified the same as that at enclosing levels, but there are a handful of exceptions where the classifica- tion changes. Method value parameter positions are classified to the flipped classification relative to positions outside the method, where the flip of a pos- itive classification is negative, the flip of a negative classification is positive, and the flip of a neutral classification is still neutral. Besides method value parameter positions, the current classification is also flipped at the type parameters of methods. A classification is sometimes Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.5 Chapter 19 · Type Parameterization 436 flipped at the type argument position of a type, such as the Arg in C[Arg], depending on the variance of the corresponding type parameter. If C’s type parameter is annotated with a + then the classification stays the same. If C’s type parameter is annotated with a -, then the current classification is flipped. If C’s type parameter has no variance annotation then the current classification is changed to neutral. As a somewhat contrived example, consider the following class defini- tion, where the variance of several positions is annotated with + (for positive) or − (for negative): abstract class Cat[-T, +U] { def meow[W−](volume: T−, listener: Cat[U+,T−]−) : Cat[Cat[U+,T−]−,U+]+ } The positions of the type parameter, W, and the two value parameters, volume and listener, are all negative. Looking at the result type of meow, the position of the first Cat[U, T] argument is negative, because Cat’s first type parameter, T, is annotated with a -. The type U inside this argument is again in positive position (two flips), whereas the type T inside that argument is still in negative position. You see from this discussion that it’s quite hard to keep track of variance positions. That’s why it’s a welcome relief that the Scala compiler does this job for you. Once the variances are computed, the compiler checks that each type parameter is only used in positions that are classified appropriately. In this case, T is only used in negative positions, and U is only used in positive positions. So class Cat is type correct. 19.5 Lower bounds Back to the Queue class. You saw that the previous definition of Queue[T] shown in Listing 19.4 cannot be made covariant in T because T appears as a type of a parameter of the enqueue method, and that’s a negative position. Fortunately, there’s a way to get unstuck: you can generalize enqueue by making it polymorphic (i.e., giving the enqueue method itself a type pa- rameter) and using a lower bound for its type parameter. Listing 19.6 shows a new formulation of Queue that implements this idea. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.5 Chapter 19 · Type Parameterization 437 class Queue[+T](private val leading: List[T], private val trailing: List[T] ){ def enqueue[U >: T](x: U) = new Queue[U](leading, x :: trailing) // ... } Listing 19.6· A type parameter with a lower bound. The new definition gives enqueue a type parameter U, and with the syntax, “U >: T”, defines T as the lower bound for U. As a result, U is required to be a supertype of T.1 The parameter to enqueue is now of type U instead of type T, and the return value of the method is now Queue[U] instead of Queue[T]. As an example, suppose there is a class Fruit with two subclasses, Apple and Orange. With the new definition of class Queue, it is possible to append an Orange to a Queue[Apple]. The result will be a Queue[Fruit]. This revised definition of enqueue is type correct. Intuitively, if T is a more specific type than expected (for example, Apple instead of Fruit), a call to enqueue will still work, because U (Fruit) will still be a supertype of T (Apple).2 The new definition of enqueue is arguably better than the old, because it is more general. Unlike the old version, the new definition allows you to append an arbitrary supertype U of the queue element type T. The result is then a Queue[U]. Together with queue covariance, this gives the right kind of flexibility for modeling queues of different element types in a natural way. This shows that variance annotations and lower bounds play well to- gether. They are a good example of type-driven design, where the types of an interface guide its detailed design and implementation. In the case of queues, you would probably not have thought of the refined implementation of enqueue with a lower bound, but you might have decided to make queues covariant. In that case, the compiler would have pointed out the variance error for enqueue. Correcting the variance error by adding a lower bound makes enqueue more general and queues as a whole more usable. 1Supertype and subtype relationships are reflexive, which means a type is both a super- type and a subtype of itself. Even though T is a lower bound for U, you could still pass in a T to enqueue. 2Technically, what happens is a flip occurs for lower bounds. The type parameter U is in a negative position (1 flip), while the lower bound (>: T) is in a positive position (2 flips). Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.6 Chapter 19 · Type Parameterization 438 This observation is also the main reason that Scala prefers declaration- site variance over use-site variance as it is found in Java’s wildcards. With use-site variance, you are on your own designing a class. It will be the clients of the class that need to put in the wildcards, and if they get it wrong, some important instance methods will no longer be applicable. Variance being a tricky business, users usually get it wrong, and they come away thinking that wildcards and generics are overly complicated. With definition-side vari- ance, you express your intent to the compiler, and the compiler will double check that the methods you want available will indeed be available. 19.6 Contravariance So far in this chapter, all examples you’ve seen were either covariant or non- variant. But there are also cases where contravariance is natural. For in- stance, consider the trait of output channels shown in Listing 19.7: trait OutputChannel[-T]{ def write(x: T) } Listing 19.7· A contravariant output channel. Here, OutputChannel is defined to be contravariant in T. So an output chan- nel of AnyRefs, say, is a subtype of an output channel of Strings. Al- though it may seem non-intuitive, it actually makes sense. To see why, con- sider what you can do with an OutputChannel[String]. The only sup- ported operation is writing a String to it. The same operation can also be done on an OutputChannel[AnyRef]. So it is safe to substitute an OutputChannel[AnyRef] for an OutputChannel[String]. By contrast, it would not be safe to substitute an OutputChannel[String] where an OutputChannel[AnyRef] is required. After all, you can send any object to an OutputChannel[AnyRef], whereas an OutputChannel[String] re- quires that the written values are all strings. This reasoning points to a general principle in type system design: it is safe to assume that a type T is a subtype of a type U if you can sub- stitute a value of type T wherever a value of type U is required. This is called the Liskov Substitution Principle. The principle holds if T supports the same operations as U and all of T’s operations require less and provide more Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.6 Chapter 19 · Type Parameterization 439 trait Function1[-S, +T] { def apply(x: S): T } Listing 19.8· Covariance and contravariance of Function1s. than the corresponding operations in U. In the case of output channels, an OutputChannel[AnyRef] can be a subtype of an OutputChannel[String] because the two support the same write operation, and this operation re- quires less in OutputChannel[AnyRef] than in OutputChannel[String]. “Less” means the argument is only required to be an AnyRef in the first case, whereas it is required to be a String in the second case. Sometimes covariance and contravariance are mixed in the same type. A prominent example is Scala’s function traits. For instance, whenever you write the function type A => B, Scala expands this to Function1[A, B]. The definition of Function1 in the standard library uses both covariance and contravariance: the Function1 trait is contravariant in the function argument type S and covariant in the result type T, as shown in Listing 19.8. This satisfies the Liskov substitution principle, because arguments are something that’s required, whereas results are something that’s provided. As an example, consider the application shown in Listing 19.9. In this example, class Publication contains one parametric field, title, of type String. Class Book extends Publication and forwards its string title parameter to the constructor of its superclass. The Library singleton object defines a set of books and a method printBookList, which takes a function, named info, of type Book => AnyRef. In other words, the type of the lone parameter to printBookList is a function that takes one Book argument and returns an AnyRef. The Customer application defines a method, getTitle, which takes a Publication as its lone parameter and returns a String, the title of the passed Publication. Now take a look at the last line in Customer. This line invokes Library’s printBookList method and passes getTitle, wrapped in a function value: Library.printBookList(getTitle) This line of code type checks even though String, the function’s result type, is a subtype of AnyRef, the result type of printBookList’s info param- eter. This code passes the compiler because function result types are de- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.6 Chapter 19 · Type Parameterization 440 class Publication(val title: String) class Book(title: String) extends Publication(title) object Library { val books: Set[Book] = Set( new Book("Programming in Scala"), new Book("Walden") ) def printBookList(info: Book => AnyRef){ for (book <- books) println(info(book)) } } object Customer extends Application { def getTitle(p: Publication): String = p.title Library.printBookList(getTitle) } Listing 19.9· Demonstration of function type parameter variance. clared to be covariant (the +T in Listing 19.8). If you look inside the body of printBookList, you can get a glimpse of why this makes sense. The printBookList method iterates through its book list, and invokes the passed function on each book. It passes the AnyRef result returned by info to println, which invokes toString on it and prints the result. This activity will work with String as well as any other subclass of AnyRef, which is what covariance of function result types means. Now consider the parameter type of the function being passed to the printBookList method. Although printBookList’s parameter type is de- clared as Book, the getTitle we’re passing in takes a Publication, a su- pertype of Book. The reason this works is that since printBookList’s pa- rameter type is Book, the body of the printBookList method will only be allowed to pass a Book into the function. And because getTitle’s parameter type is Publication, the body of that function will only be able to access on its parameter, p, members that are declared in class Publication. Because any method declared in Publication is also available on its subclass Book, everything should work, which is what contravariance of function parameter Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.7 Chapter 19 · Type Parameterization 441 Publication => String Book => AnyRef AnyRef String Book Publication argument type result type Figure 19.1· Covariance and contravariance in function type parameters. types means. You can see all this graphically in Figure 19.1. The code in Listing 19.9 compiles because Publication => String is a subtype of Book => AnyRef, as shown in the center of the Figure 19.1. Be- cause the result type of a Function1 is defined as covariant, the inheritance relationship of the two result types, shown at the right of the diagram, is in the same direction as that of the two functions shown in the center. By con- trast, because the parameter type of a Function1 is defined as contravariant, the inheritance relationship of the two parameter types, shown at the left of the diagram, is in the opposite direction as that of the two functions. 19.7 Object private data The Queue class seen so far has a problem in that the mirror operation might repeatedly copy the trailing into the leading list if head is called several times in a row on a list where leading is empty. The wasteful copying could be avoided by adding some judicious side effects. Listing 19.10 presents a new implementation of Queue, which performs at most one trailing to leading adjustment for any sequence of head operations. What’s different with respect to the previous version is that now leading and trailing are reassignable variables, and mirror performs the reverse copy from trailing to leading as a side-effect on the current queue instead of returning a new queue. This side-effect is purely internal to the imple- mentation of the Queue operation; since leading and trailing are private variables, the effect is not visible to clients of Queue. So by the terminology established in Chapter 18, the new version of Queue still defines purely func- tional objects, in spite of the fact that they now contain reassignable fields. You might wonder whether this code passes the Scala type checker. After Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.7 Chapter 19 · Type Parameterization 442 class Queue[+T] private ( private[this] var leading: List[T], private[this] var trailing: List[T] ){ private def mirror() = if (leading.isEmpty) { while (!trailing.isEmpty) { leading = trailing.head :: leading trailing = trailing.tail } } def head: T = { mirror() leading.head } def tail: Queue[T] = { mirror() new Queue(leading.tail, trailing) } def enqueue[U >: T](x: U) = new Queue[U](leading, x :: trailing) } Listing 19.10· An optimized functional queue. all, queues now contain two reassignable fields of the covariant parameter type T. Is this not a violation of the variance rules? It would be indeed, except for the detail that leading and trailing have a private[this] modifier and are thus declared to be object private. As mentioned in Section 13.5, object private members can be accessed only from within the object in which they are defined. It turns out that ac- cesses to variables from the same object in which they are defined do not cause problems with variance. The intuitive explanation is that, in order to construct a case where variance would lead to type errors, you need to have a reference to a containing object that has a statically weaker type than the type the object was defined with. For accesses to object private values, however, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.8 Chapter 19 · Type Parameterization 443 this is impossible. Scala’s variance checking rules contain a special case for object private definitions. Such definitions are omitted when it is checked that a type pa- rameter with either a + or - annotation occurs only in positions that have the same variance classification. Therefore, the code in Listing 19.10 compiles without error. On the other hand, if you had left out the [this] qualifiers from the two private modifiers, you would see two type errors: Queues.scala:1: error: covariant type T occurs in contravariant position in type List[T] of parameter of setter leading_= class Queue[+T] private (private var leading: List[T], ˆ Queues.scala:1: error: covariant type T occurs in contravariant position in type List[T] of parameter of setter trailing_= private var trailing: List[T]) { ˆ 19.8 Upper bounds In Listing 16.1 on page 360, we showed a merge sort function for lists that took a comparison function as a first argument and a list to sort as a sec- ond, curried argument. Another way you might want to organize such a sort function is by requiring the type of the list to mix in the Ordered trait. As mentioned in Section 12.4, by mixing Ordered into a class and implement- ing Ordered’s one abstract method, compare, you enable clients to compare instances of that class with <, >, <=, and >=. For example, Listing 19.11 shows Ordered being mixed into a Person class. As a result, you can com- pare two persons like this: scala> val robert = new Person("Robert", "Jones") robert: Person = Robert Jones scala> val sally = new Person("Sally", "Smith") sally: Person = Sally Smith scala> robert < sally res0: Boolean = true Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.8 Chapter 19 · Type Parameterization 444 class Person(val firstName: String, val lastName: String) extends Ordered[Person] { def compare(that: Person) = { val lastNameComparison = lastName.compareToIgnoreCase(that.lastName) if (lastNameComparison != 0) lastNameComparison else firstName.compareToIgnoreCase(that.firstName) } override def toString = firstName +""+ lastName } Listing 19.11· A Person class that mixes in the Ordered trait. def orderedMergeSort[T <: Ordered[T]](xs: List[T]): List[T] = { def merge(xs: List[T], ys: List[T]): List[T] = (xs, ys) match { case (Nil, _) => ys case (_, Nil) => xs case (x :: xs1, y :: ys1) => if (x < y) x :: merge(xs1, ys) else y :: merge(xs, ys1) } val n = xs.length / 2 if (n == 0) xs else { val (ys, zs) = xs splitAt n merge(orderedMergeSort(ys), orderedMergeSort(zs)) } } Listing 19.12· A merge sort function with an upper bound. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.8 Chapter 19 · Type Parameterization 445 To require that the type of the list passed to your new sort function mixes in Ordered, you need to use an upper bound. An upper bound is specified similar to a lower bound, except instead of the >: symbol used for lower bounds, you use a <: symbol, as shown in Listing 19.12. With the “T <: Ordered[T]” syntax, you indicate that the type parameter, T, has an upper bound, Ordered[T]. This means that the element type of the list passed to orderedMergeSort must be a subtype of Ordered. Thus, you could pass a List[Person] to orderedMergeSort, because Person mixes in Ordered. For example, consider this list: scala> val people = List( new Person("Larry", "Wall"), new Person("Anders", "Hejlsberg"), new Person("Guido", "van Rossum"), new Person("Alan", "Kay"), new Person("Yukihiro", "Matsumoto") ) people: List[Person] = List(Larry Wall, Anders Hejlsberg, Guido van Rossum, Alan Kay, Yukihiro Matsumoto) Because the element type of this list, Person, mixes in (and is therefore a subtype of) Ordered[People], you can pass the list to orderedMergeSort: scala> val sortedPeople = orderedMergeSort(people) sortedPeople: List[Person] = List(Anders Hejlsberg, Alan Kay, Yukihiro Matsumoto, Guido van Rossum, Larry Wall) Now, although the sort function shown in Listing 19.12 serves as a useful illustration of upper bounds, it isn’t actually the most general way in Scala to design a sort function that takes advantage of the Ordered trait. For example, you couldn’t use the orderedMergeSort function to sort a list of integers, because class Int is not a subtype of Ordered[Int]: scala> val wontCompile = orderedMergeSort(List(3, 2, 1)) :5: error: inferred type arguments [Int] do not conform to method orderedMergeSort's type parameter bounds [T <: Ordered[T]] val wontCompile = orderedMergeSort(List(3, 2, 1)) ˆ Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 19.9 Chapter 19 · Type Parameterization 446 In Section 21.6, we’ll show you how to use implicit parameters and view bounds to achieve a more general solution. 19.9 Conclusion In this chapter you saw several techniques for information hiding: private constructors, factory methods, type abstraction, and object private members. You also learned how to specify data type variance and what it implies for class implementation. Finally, you saw two techniques which help in obtain- ing flexible variance annotations: lower bounds for method type parameters, and private[this] annotations for local fields and methods. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 20 Abstract Members A member of a class or trait is abstract if the member does not have a com- plete definition in the class. Abstract members are intended to be imple- mented in subclasses of the class in which they are declared. This idea is found in many object-oriented languages. For instance, Java lets you declare abstract methods. Scala also lets you declare such methods, as you saw in Section 10.2. But Scala goes beyond that and implements the idea in its full generality: besides methods, you can also declare abstract fields and even abstract types as members of classes and traits. In this chapter we’ll describe all four kinds of abstract member: vals, vars, methods, and types. Along the way we’ll discuss pre-initialized fields, lazy vals, path-dependent types, and enumerations. 20.1 A quick tour of abstract members The following trait declares one of each kind of abstract member: an abstract type (T), method (transform), val (initial), and var (current): trait Abstract { type T def transform(x: T): T val initial: T var current: T } A concrete implementation of Abstract needs to fill in definitions for each of its abstract members. Here is an example implementation that provides Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.2 Chapter 20 · Abstract Members 448 these definitions: class Concrete extends Abstract { type T = String def transform(x: String) = x + x val initial = "hi" var current = initial } The implementation gives a concrete meaning to the type name T by defining it as an alias of type String. The transform operation concatenates a given string with itself, and the initial and current values are both set to "hi". This example gives you a rough first idea of what kinds of abstract mem- bers exist in Scala. The remainder of the chapter will present the details and explain what the new forms of abstract members, as well as type members in general, are good for. 20.2 Type members As you can see from the example in the previous section, the term abstract type in Scala means a type declared (with the “type” keyword) to be a mem- ber of a class or trait, without specifying a definition. Classes themselves may be abstract, and traits are by definition abstract, but neither of these are what are referred to as abstract types in Scala. An abstract type in Scala is always a member of some class or trait, such as type T in trait Abstract. You can think of a non-abstract (or, “concrete”) type member, such as type T in class Concrete, as a way to define a new name, or alias, for a type. In class Concrete, for example, the type String is given the alias T. As a result, anywhere T appears in the definition of class Concrete, it means String. This includes the parameter and result types of transform, initial, and current, which mention T when they are declared in super- trait Abstract. Thus, when class Concrete implements these methods, those Ts are interpreted to mean String. One reason to use a type member is to define a short, descriptive alias for a type whose real name is more verbose, or less obvious in meaning, than the alias. Such type members can help clarify the code of a class or trait. The other main use of type members is to declare abstract types that must Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.3 Chapter 20 · Abstract Members 449 be defined in subclasses. This use, which was demonstrated in the previous section, will be described in detail later in this chapter. 20.3 Abstract vals An abstract val declaration has a form like: val initial: String It gives a name and type for a val, but not its value. This value has to be provided by a concrete val definition in a subclass. For instance, class Concrete implemented the val using: val initial = "hi" You use an abstract val declaration in a class when you do not know the correct value in the class, but you do know that the variable will have an unchangeable value in each instance of the class. An abstract val declaration resembles an abstract parameterless method declaration such as: def initial: String Client code would refer to both the val and the method in exactly the same way, i.e., obj.initial. However, if initial is an abstract val, the client is guaranteed that obj.initial will yield the same value every time it is referenced. If initial were an abstract method, that guarantee would not hold, because in that case initial could be implemented by a concrete method that returns a different value every time it’s called. In other words, an abstract val constrains its legal implementation: any implementation must be a val definition; it may not be a var or a def. Abstract method declarations, on the other hand, may be implemented by both concrete method definitions and concrete val definitions. Given the abstract class Fruit shown in Listing 20.1, class Apple would be a legal subclass implementation, but class BadApple would not. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.4 Chapter 20 · Abstract Members 450 abstract class Fruit { val v: String // ‘v’ for value def m: String // ‘m’ for method } abstract class Apple extends Fruit { val v: String val m: String // OK to override a ‘def’ with a ‘val’ } abstract class BadApple extends Fruit { def v: String // ERROR: cannot override a ‘val’ with a ‘def’ def m: String } Listing 20.1· Overriding abstract vals and parameterless methods. 20.4 Abstract vars Like an abstract val, an abstract var declares just a name and a type, but not an initial value. For instance, Listing 20.2 shows a trait AbstractTime, which declares two abstract variables named hour and minute: trait AbstractTime{ var hour: Int var minute: Int } Listing 20.2· Declaring abstract vars. What is the meaning of abstract vars like hour and minute? You saw in Section 18.2 that vars declared as members of classes come equipped with getter and setter methods. This holds for abstract vars as well. If you declare an abstract var named hour, for example, you implicitly declare an abstract getter method, hour, and an abstract setter method, hour_=. There’s no reassignable field to be defined—that will come in subclasses that define the concrete implementation of the abstract var. For instance, the definition of AbstractTime shown in Listing 20.2 is exactly equivalent to the definition shown in Listing 20.3. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.5 Chapter 20 · Abstract Members 451 trait AbstractTime{ def hour: Int // getter for ‘hour’ def hour_=(x: Int) // setter for ‘hour’ def minute: Int // getter for ‘minute’ def minute_=(x: Int) // setter for ‘minute’ } Listing 20.3· How abstract vars are expanded into getters and setters. 20.5 Initializing abstract vals Abstract vals sometimes play a role analogous to superclass parameters: they let you provide details in a subclass that are missing in a superclass. This is particularly important for traits, because traits don’t have a constructor to which you could pass parameters. So the usual notion of parameterizing a trait works via abstract vals that are implemented in subclasses. As an example, consider a reformulation of class Rational from Chapter 6, as shown in Listing 6.5 on page 155, as a trait: trait RationalTrait { val numerArg: Int val denomArg: Int } The Rational class from Chapter 6 had two parameters: n for the numerator of the rational number, and d for the denominator. The RationalTrait trait given here defines instead two abstract vals: numerArg and denomArg. To instantiate a concrete instance of that trait, you need to implement the abstract val definitions. Here’s an example: new RationalTrait { val numerArg = 1 val denomArg = 2 } Here the keyword new appears in front of a trait name, RationalTrait, which is followed by a class body in curly braces. This expression yields an instance of an anonymous class that mixes in the trait and is defined by the body. This particular anonymous class instantiation has an effect analogous Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.5 Chapter 20 · Abstract Members 452 to the instance creation new Rational(1, 2). The analogy is not perfect, however. There’s a subtle difference concerning the order in which expres- sions are initialized. When you write: new Rational(expr1, expr2) the two expressions, expr1 and expr2, are evaluated before class Rational is initialized, so the values of expr1 and expr2 are available for the initial- ization of class Rational. For traits, however, the situation is the opposite. When you write: new RationalTrait { val numerArg = expr1 val denomArg = expr2 } the expressions, expr1 and expr2, are evaluated as part of the initializa- tion of the anonymous class, but the anonymous class is initialized after the RationalTrait. So the values of numerArg and denomArg are not avail- able during the initialization of RationalTrait (more precisely, a selection of either value would yield the default value for type Int, 0). For the def- inition of RationalTrait given previously, this is not a problem, because the trait’s initialization does not make use of values numerArg or denomArg. However, it does become a problem in the variant of RationalTrait shown in Listing 20.4, which defines normalized numerators and denominators: trait RationalTrait{ val numerArg: Int val denomArg: Int require(denomArg !=0) private val g = gcd(numerArg, denomArg) val numer = numerArg / g val denom = denomArg / g private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b) override def toString = numer +"/"+ denom } Listing 20.4· A trait that uses its abstract vals. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.5 Chapter 20 · Abstract Members 453 If you try to instantiate this trait with some numerator and denominator expressions that are not simple literals, you’ll get an exception: scala> val x = 2 x: Int = 2 scala> new RationalTrait { val numerArg = 1 * x val denomArg = 2 * x } java.lang.IllegalArgumentException: requirement failed at scala.Predef$.require(Predef.scala:134) at RationalTrait$class.$init$(:8) at $anon$1.(:8) ... The exception in this example was thrown because denomArg still had its default value of 0 when class RationalTrait was initialized, which caused the require invocation to fail. This example demonstrates that initialization order is not the same for class parameters and abstract fields. A class parameter argument is evaluated before it is passed to the class constructor (unless the parameter is by-name). An implementing val definition in a subclass, by contrast, is evaluated only after the superclass has been initialized. Now that you understand why abstract vals behave differently from pa- rameters, it would be good to know what can be done about this. Is it possible to define a RationalTrait that can be initialized robustly, without fearing errors due to uninitialized fields? In fact, Scala offers two alternative solu- tions to this problem, pre-initialized fields and lazy vals. They are presented in the remainder of this section. Pre-initialized fields The first solution, pre-initialized fields, lets you initialize a field of a subclass before the superclass is called. To do this, simply place the field definition in braces before the superclass constructor call. As an example, Listing 20.5 shows another attempt to create an instance of RationalTrait. As you see from this example, the initialization section comes before the mention of the supertrait RationalTrait. Both are separated by a with. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.5 Chapter 20 · Abstract Members 454 scala> new{ val numerArg = 1 * x val denomArg = 2 * x } with RationalTrait res1: java.lang.Object with RationalTrait = 1/2 Listing 20.5· Pre-initialized fields in an anonymous class expression. object twoThirds extends { val numerArg = 2 val denomArg = 3 } with RationalTrait Listing 20.6· Pre-initialized fields in an object definition. Pre-initialized fields are not restricted to anonymous classes; they can also be used in objects or named subclasses. Two examples are shown in Listings 20.6 and 20.7. As you can see from these examples, the pre- initialization section comes in each case after the extends keyword of the defined object or class. Class RationalClass, shown in Listing 20.7, exem- plifies a general schema of how class parameters can be made available for the initialization of a supertrait. Because pre-initialized fields are initialized before the superclass con- structor is called, their initializers cannot refer to the object that’s being con- structed. Consequently, if such an initializer refers to this, the reference goes to the object containing the class or object that’s being constructed, not the constructed object itself. Here’s an example: scala> new { val numerArg = 1 val denomArg = this.numerArg * 2 } with RationalTrait :9: error: value numerArg is not a member of object $iw val denomArg = this.numerArg * 2 ˆ The example did not compile because the reference this.numerArg was looking for a numerArg field in the object containing the new (which in this Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.5 Chapter 20 · Abstract Members 455 class RationalClass(n: Int, d: Int) extends { val numerArg = n val denomArg = d } with RationalTrait { def + (that: RationalClass) = new RationalClass( numer * that.denom + that.numer * denom, denom * that.denom ) } Listing 20.7· Pre-initialized fields in a class definition. case was the synthetic object named $iw, into which the interpreter puts user input lines). Once more, pre-initialized fields behave in this respect like class constructor arguments. Lazy vals You can use pre-initialized fields to simulate precisely the initialization be- havior of class constructor arguments. Sometimes, however, you might pre- fer to let the system itself sort out how things should be initialized. This can be achieved by making your val definitions lazy. If you prefix a val defini- tion with a lazy modifier, the initializing expression on the right-hand side will only be evaluated the first time the val is used. For an example, define an object Demo with a val as follows: scala> object Demo { val x = { println("initializing x"); "done" } } defined module Demo Now, first refer to Demo, then to Demo.x: scala> Demo initializing x res3: Demo.type = Demo$@17469af scala> Demo.x res4: java.lang.String = done Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.5 Chapter 20 · Abstract Members 456 As you can see, the moment you use Demo, its x field becomes initialized. The initialization of x forms part of the initialization of Demo. The situation changes, however, if you define the x field to be lazy: scala> object Demo { lazy val x = { println("initializing x"); "done" } } defined module Demo scala> Demo res5: Demo.type = Demo$@11dda2d scala> Demo.x initializing x res6: java.lang.String = done Now, initializing Demo does not involve initializing x. The initialization of x will be deferred until the first time x is used. This is similar to the situation where x is defined as a parameterless method, using a def. However, unlike a def a lazy val is never evaluated more than once. In fact, after the first evaluation of a lazy val the result of the evaluation is stored, to be reused when the same val is used subsequently. trait LazyRationalTrait{ val numerArg: Int val denomArg: Int lazy val numer = numerArg / g lazy val denom = denomArg / g override def toString = numer +"/"+ denom private lazy val g = { require(denomArg != 0) gcd(numerArg, denomArg) } private def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b) } Listing 20.8· Initializing a trait with lazy vals. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.5 Chapter 20 · Abstract Members 457 Looking at this example, it seems that objects like Demo themselves be- have like lazy vals, in that they are also initialized on demand, the first time they are used. This is correct. In fact an object definition can be seen as a shorthand for the definition of a lazy val with an anonymous class that describes the object’s contents. Using lazy vals, you could reformulate RationalTrait as shown in Listing 20.8. In the new trait definition, all concrete fields are defined lazy. Another change with respect to the previous definition of RationalTrait, shown in Listing 20.4, is that the require clause was moved from the body of the trait to the initializer of the private field, g, which computes the greatest common divisor of numerArg and denomArg. With these changes, there’s nothing that remains to be done when LazyRationalTrait is initialized; all initialization code is now part of the right-hand side of a lazy val. Therefore, it is safe to initialize the abstract fields of LazyRationalTrait after the class is defined. Here’s an example: scala> val x = 2 x: Int = 2 scala> new LazyRationalTrait { val numerArg = 1 * x val denomArg = 2 * x } res7: java.lang.Object with LazyRationalTrait = 1/2 No pre-initialization is needed. It’s instructive to trace the sequence of ini- tializations that lead to the string 1/2 to be printed in the code above: 1. First, a fresh instance of LazyRationalTrait gets created, and the initialization code of LazyRationalTrait is run. This initialization code is empty—none of the fields of LazyRationalTrait is as yet initialized. 2. Next, the primary constructor of the anonymous subclass defined by the new expression is executed. This involves the initialization of numerArg with 2 and denomArg with 4. 3. Next, the toString method is invoked on the constructed object by the interpreter, so that the resulting value can be printed. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.5 Chapter 20 · Abstract Members 458 4. Next, the numer field is accessed for the first time by the toString method in trait LazyRationalTrait, so its initializer is evaluated. 5. The initializer of numer accesses the private field, g, so g is evaluated next. This evaluation accesses numerArg and denomArg, which were defined in Step 2. 6. Next, the toString method accesses the value of denom, which causes denom’s evaluation. The evaluation of denom accesses the values of denomArg and g. The initializer of the g field is not re-evaluated, be- cause it was already evaluated in Step 5. 7. Finally, the result string "1/2" is constructed and printed. Note that the definition of g comes textually after the definitions of numer and denom in class LazyRationalTrait. Nevertheless, because all three values are lazy, g gets initialized before the initialization of numer and denom is completed. This shows an important property of lazy vals: the textual order of their definitions does not matter, because values get initialized on demand. Therefore, lazy vals can free you as a programmer from having to think hard how to arrange val definitions to ensure that everything is defined when it is needed. However, this advantage holds only as long as the initialization of lazy vals neither produces side effects nor depends on them. In the presence of side effects, initialization order starts to matter. And then it can be quite difficult to trace in what order initialization code is run, as the previous ex- ample has demonstrated. So lazy vals are an ideal complement to functional objects, where the order of initializations does not matter, as long as every- thing gets initialized eventually. They are less well suited for code that’s predominantly imperative. Lazy functional languages Scala is by no means the first language to have exploited the perfect match of lazy definitions and functional code. In fact, there is a cate- gory of “lazy functional programming languages” in which every value and parameter is initialized lazily. The best known member of this class of languages is Haskell [SPJ02]. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.6 Chapter 20 · Abstract Members 459 20.6 Abstract types In the beginning of this chapter, you saw, “type T”, an abstract type decla- ration. The rest of this chapter discusses what such an abstract type decla- ration means and what it’s good for. Like all other abstract declarations, an abstract type declaration is a placeholder for something that will be defined concretely in subclasses. In this case, it is a type that will be defined further down the class hierarchy. So T above refers to a type that is at yet unknown at the point where it is declared. Different subclasses can provide different realizations of T. Here is a well-known example where abstract types show up naturally. Suppose you are given the task of modeling the eating habits of animals. You might start with a class Food and a class Animal with an eat method: class Food abstract class Animal { def eat(food: Food) } You might then attempt to specialize these two classes to a class of Cows that eat Grass: class Grass extends Food class Cow extends Animal { override def eat(food: Grass) {} // This won’t compile } However, if you tried to compile the new classes, you’d get the following compilation errors: BuggyAnimals.scala:7: error: class Cow needs to be abstract, since method eat in class Animal of type (Food)Unit is not defined class Cow extends Animal { ˆ BuggyAnimals.scala:8: error: method eat overrides nothing override def eat(food: Grass) {} ˆ Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.6 Chapter 20 · Abstract Members 460 What happened is that the eat method in class Cow does not override the eat method in class Animal, because its parameter type is different—it’s Grass in class Cow vs. Food in class Animal. Some people have argued that the type system is unnecessarily strict in refusing these classes. They have said that it should be OK to specialize a parameter of a method in a subclass. However, if the classes were allowed as written, you could get yourself in unsafe situations very quickly. For instance, the following script would pass the type checker: class Food abstract class Animal { def eat(food: Food) } class Grass extends Food class Cow extends Animal { override def eat(food: Grass) {} // This won’t compile, } // but if it did,... class Fish extends Food val bessy: Animal = new Cow bessy eat (new Fish) // ...you could feed fish to cows. The program would compile if the restriction were eased, because Cows are Animals and Animals do have an eat method that accepts any kind of Food, including Fish. But surely it would do a cow no good to eat a fish! What you need to do instead is apply some more precise modeling. Animals do eat Food, but what kind of Food each Animal eats depends on the Animal. This can be neatly expressed with an abstract type, as shown in Listing 20.9: class Food abstract class Animal { type SuitableFood <: Food def eat(food: SuitableFood) } Listing 20.9· Modeling suitable food with an abstract type. With the new class definition, an Animal can eat only food that’s suitable. What food is suitable cannot be determined at the level of the Animal class. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.7 Chapter 20 · Abstract Members 461 That’s why SuitableFood is modeled as an abstract type. The type has an upper bound, Food, which is expressed by the “<: Food” clause. This means that any concrete instantiation of SuitableFood (in a subclass of Animal) must be a subclass of Food. For example, you would not be able to instantiate SuitableFood with class IOException. class Grass extends Food class Cow extends Animal { type SuitableFood = Grass override def eat(food: Grass) {} } Listing 20.10· Implementing an abstract type in a subclass. With Animal defined, you can now progress to cows, as shown in List- ing 20.10. Class Cow fixes its SuitableFood to be Grass and also defines a concrete eat method for this kind of food. These new class definitions com- pile without errors. If you tried to run the “cows-that-eat-fish” counterex- ample with the new class definitions, you would get the following compiler error: scala> class Fish extends Food defined class Fish scala> val bessy: Animal = new Cow bessy: Animal = Cow@2e3919 scala> bessy eat (new Fish) :12: error: type mismatch; found : Fish required: bessy.SuitableFood bessy eat (new Fish) ˆ 20.7 Path-dependent types Have a look at the last error message: What’s interesting about it is the type required by the eat method: bessy.SuitableFood. This type consists of an object reference, bessy, which is followed by a type field, SuitableFood, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.7 Chapter 20 · Abstract Members 462 of the object. So this shows that objects in Scala can have types as members. The meaning of bessy.SuitableFood is “the type SuitableFood that is a member of the object referenced from bessy,” or alternatively, the type of food that’s suitable for bessy. A type like bessy.SuitableFood is called a path-dependent type. The word “path” here means a reference to an object. It could be a single name, such as bessy, or a longer access path, such as farm.barn.bessy.SuitableFood, where each of farm, barn, and bessy are variables (or singleton object names) that refer to objects. As the term “path-dependent type” says, the type depends on the path: in general, different paths give rise to different types. For instance, say you defined classes DogFood and Dog, like this: class DogFood extends Food class Dog extends Animal { type SuitableFood = DogFood override def eat(food: DogFood) {} } If you attempted to feed a dog with food fit for a cow, your code would not compile: scala> val bessy = new Cow bessy: Cow = Cow@e7bbeb scala> val lassie = new Dog lassie: Dog = Dog@ce38f1 scala> lassie eat (new bessy.SuitableFood) :14: error: type mismatch; found : Grass required: DogFood lassie eat (new bessy.SuitableFood) ˆ The problem here is that the type of the SuitableFood object passed to the eat method, bessy.SuitableFood, is incompatible with the parameter type of eat, lassie.SuitableFood. The case would be different for two Dogs however. Because Dog’s SuitableFood type is defined to be an alias for class DogFood, the SuitableFood types of two Dogs are in fact the same. As a result, the Dog instance named lassie could actually eat the suitable food of a different Dog instance (which we’ll name bootsie): Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.7 Chapter 20 · Abstract Members 463 scala> val bootsie = new Dog bootsie: Dog = Dog@66db21 scala> lassie eat (new bootsie.SuitableFood) A path-dependent type resembles the syntax for an inner class type in Java, but there is a crucial difference: a path-dependent type names an outer object, whereas an inner class type names an outer class. Java-style inner class types can also be expressed in Scala, but they are written differently. Consider these two classes, Outer and Inner: class Outer { class Inner } In Scala, the inner class is addressed using the expression Outer#Inner in- stead of Java’s Outer.Inner. The ‘.’ syntax is reserved for objects. For example, imagine you instantiate two objects of type Outer, like this: val o1 = new Outer val o2 = new Outer Here o1.Inner and o2.Inner are two path-dependent types (and they are different types). Both of these types conform to (are subtypes of) the more general type Outer#Inner, which represents the Inner class with an arbi- trary outer object of type Outer. By contrast, type o1.Inner refers to the Inner class with a specific outer object (the one referenced from o1). Like- wise, type o2.Inner refers to the Inner class with a different, specific outer object (the one referenced from o2). In Scala, as in Java, inner class instances hold a reference to an enclosing outer class instance. This allows an inner class, for example, to access mem- bers of its outer class. Thus you can’t instantiate an inner class without in some way specifying an outer class instance. One way to do this is to instan- tiate the inner class inside the body of the outer class. In this case, the current outer class instance (referenced from this) will be used. Another way is to use a path-dependent type. For example, because the type, o1.Inner, names a specific outer object, you can instantiate it: scala> new o1.Inner res11: o1.Inner = Outer$Inner@1df6ed6 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.8 Chapter 20 · Abstract Members 464 The resulting inner object will contain a reference to its outer object, the object referenced from o1. By contrast, because the type Outer#Inner does not name any specific instance of Outer, you can’t create an instance of it: scala> new Outer#Inner :7: error: Outer is not a legal prefix for a constructor new Outer#Inner ˆ 20.8 Structural subtyping When a class inherits from another, the first class is said to be a nominal sub- type of the other one. It’s a nominal subtype because each type has a name, and the names are explicitly declared to have a subtyping relationship. Scala additionally supports structural subtyping, where you get a subtyping rela- tionship simply because two types have the same members. To get structural subtyping in Scala, use Scala’s refinement types. Nominal subtyping is usually more convenient, so you should try nom- inal types first with any new design. A name is a single short identifier and thus is more concise than an explicit listing of member types. Fur- ther, structural subtyping is often more flexible than you want. A widget can draw(), and a Western cowboy can draw(), but they aren’t really sub- stitutable. You’d typically prefer to get a compilation error if you tried to substitute a cowboy for a widget. Nonetheless, structural subtyping has its own advantages. One is that sometimes there really is no more to a type than its members. For example, suppose you want to define a Pasture class that can contain animals that eat grass. One option would be to define a trait AnimalThatEatsGrass and mix it into every class where it applies. It would be verbose, however. Class Cow has already declared that it’s an animal and that it eats grass, and now it would have to declare that it is also an animal-that-eats-grass. Instead of defining AnimalThatEatsGrass, you can use a refinement type. Simply write the base type, Animal, followed by a sequence of mem- bers listed in curly braces. The members in the curly braces further specify— or refine, if you will—the types of members from the base class. Here is how you write the type, “animal that eats grass”: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.8 Chapter 20 · Abstract Members 465 Animal { type SuitableFood = Grass } Given this type, you can now write the pasture class like this: class Pasture { var animals: List[Animal { type SuitableFood = Grass }] = Nil // ... } Another place structural subtyping is helpful is if you want to group to- gether a number of classes that were written by someone else. For example, suppose you want to generalize the loan pattern example from Section 9.4. The original example worked only for type PrintWriter, and you might want to have it work for any type with a close method. That is, one caller might use the routine to clean up an open file: using(new PrintWriter("date.txt")) { writer => writer.println(new Date) } Another caller, meanwhile, might want to clean up an open socket: using(serverSocket.accept()) { socket => socket.getOutputStream().write("hello, world\n".getBytes) } Implementing using is mostly straightforward. The method performs an operation and then closes an object, so it must take two arguments: the operation and the object. The operation is a function from any type to any other type, so using must have two type parameters as well. Here is a first try at implementing this method: def using[T, S](obj: T)(operation: T => S) = { val result = operation(obj) obj.close() // type error! result } This attempt almost works, but it will get a type error where close() is called. The problem is that, as written, T can be any type at all. To indicate that it only really supports types with close() methods, the <: notation can Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.9 Chapter 20 · Abstract Members 466 be used to give an upper bound to T. In this case, the desired upper bound is { def close(): Unit }. Here’s a complete working definition: def using[T <: { def close(): Unit }, S](obj: T) (operation: T => S) = { val result = operation(obj) obj.close() result } Note two small differences in this refinement type from the one for ani- mals that eat grass. One is that no base type is specified. If no base type is specified, Scala uses AnyRef automatically. The other difference is that the close method does not appear at all in the base type. Class AnyRef simply doesn’t have a close method. Technically speaking, that means the second type is a structural type. 20.9 Enumerations An interesting application of path-dependent types is found in Scala’s sup- port for enumerations. Some other languages, including Java and C#, have enumerations as a built-in language construct to define new types. Scala does not need special syntax for enumerations. Instead, there’s a class in its stan- dard library, scala.Enumeration. To create a new enumeration, you define an object that extends this class, as in the following example, which defines a new enumeration of Colors: object Color extends Enumeration { val Red = Value val Green = Value val Blue = Value } Scala lets you also shorten several successive val or var definitions with the same right-hand side. Equivalently to the above you could write: object Color extends Enumeration { val Red, Green, Blue = Value } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.9 Chapter 20 · Abstract Members 467 This object definition provides three values: Color.Red, Color.Green, and Color.Blue. You could also import everything in Color with: import Color._ and then just use Red, Green, and Blue. But what is the type of these values? Enumeration defines an inner class named Value, and the same-named pa- rameterless Value method returns a fresh instance of that class. This means that a value such as Color.Red is of type Color.Value. Color.Value is the type of all enumeration values defined in object Color. It’s a path-dependent type, with Color being the path and Value being the dependent type. What’s significant about this is that it is a completely new type, different from all other types. In particular, if you would define another enumeration, such as: object Direction extends Enumeration { val North, East, South, West = Value } then Direction.Value would be different from Color.Value because the path parts of the two types differ. Scala’s Enumeration class also offers many other features found in the enumeration designs of other languages. You can associate names with enu- meration values by using a different overloaded variant of the Value method: object Direction extends Enumeration { val North = Value("North") val East = Value("East") val South = Value("South") val West = Value("West") } You can iterate over the values of an enumeration via the set returned by the enumeration’s values method: scala> for (d <- Direction.values) print(d +"") North East South West Values of an enumeration are numbered from 0, and you can find out the number of an enumeration value by its id method: scala> Direction.East.id res14: Int = 1 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 468 It’s also possible to go the other way, from a non-negative integer number to the value that has this number as id in an enumeration: scala> Direction(1) res15: Direction.Value = East This should be enough to get you started with enumerations. You can find more information in the Scaladoc comments of class scala.Enumeration. 20.10 Case study: Currencies The rest of this chapter presents a case study that explains how abstract types can be used in Scala. The task is to design a class Currency. A typical instance of Currency would represent an amount of money in dollars, euros, yen, or some other currency. It should be possible to do some arithmetic on currencies. For instance, you should be able to add two amounts of the same currency. Or you should be able to multiply a currency amount by a factor representing an interest rate. These thoughts lead to the following first design for a currency class: // A first (faulty) design of the Currency class abstract class Currency { val amount: Long def designation: String override def toString = amount +""+ designation def + (that: Currency): Currency = ... def * (x: Double): Currency = ... } The amount of a currency is the number of currency units it represents. This is a field of type Long so that very large amounts of money such as the market capitalization of Google or Microsoft can be represented. It’s left abstract here, waiting to be defined when a subclass talks about concrete amounts of money. The designation of a currency is a string that identifies it. The toString method of class Currency indicates an amount and a designation. It would yield results such as: 79 USD 11000 Yen 99 Euro Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 469 Finally, there are methods +, for adding currencies, and *, for multiplying a currency with a floating-point number. You can create a concrete currency value by supplying concrete amount and designation values, like this: new Currency{ val amount = 79L def designation = "USD" } This design would be OK if all we wanted to model was a single currency such as only dollars or only euros. But it fails once we need to deal with several currencies. Assume you model dollars and euros as two subclasses of class currency: abstract class Dollar extends Currency { def designation = "USD" } abstract class Euro extends Currency { def designation = "Euro" } At first glance this looks reasonable. But it would let you add dollars to euros. The result of such an addition would be of type Currency. But it would be a funny currency that was made up of a mix of euros and dollars. What you want instead is a more specialized version of the + method: when implemented in class Dollar, it should take Dollar arguments and yield a Dollar result; when implemented in class Euro, it should take Euro argu- ments and yield a Euro result. So the type of the addition method would change depending on which class you are in. Nonetheless, you would like to write the addition method just once, not each time a new currency is defined. In Scala, there’s a simple technique to deal with situations like this: if something is not known at the point where a class is defined, make it abstract in the class. This applies to both values and types. In the case of currencies, the exact argument and result type of the addition method are not known, so it is a good candidate for an abstract type. This would lead to the following sketch of class AbstractCurrency: // A second (still imperfect) design of the Currency class abstract class AbstractCurrency { type Currency <: AbstractCurrency Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 470 val amount: Long def designation: String override def toString = amount +""+ designation def + (that: Currency): Currency = ... def * (x: Double): Currency = ... } The only differences from the previous situation are that the class is now called AbstractCurrency, and that it contains an abstract type Currency, which represents the real currency in question. Each concrete subclass of AbstractCurrency would need to fix the Currency type to refer to the concrete subclass itself, thereby “tying the knot.” For instance, here is a new version of class Dollar, which now extends class AbstractCurrency: abstract class Dollar extends AbstractCurrency { type Currency = Dollar def designation = "USD" } This design is workable, but it is still not perfect. One problem is hidden by the ellipses that indicate the missing method definitions of + and * in class AbstractCurrency. In particular, how should addition be implemented in this class? It’s easy enough to calculate the correct amount of the new currency as this.amount + that.amount, but how would you convert the amount into a currency of the right type? You might try something like: def + (that: Currency): Currency = new Currency { val amount = this.amount + that.amount } However, this would not compile: error: class type required def + (that: Currency): Currency = new Currency { ˆ One of the restrictions of Scala’s treatment of abstract types is that you can neither create an instance of an abstract type, nor have an abstract type as a Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 471 supertype of another class.1 So the compiler would refuse the example code above that attempted to instantiate Currency. However, you can work around this restriction using a factory method. Instead of creating an instance of an abstract type directly, declare an abstract method that does it. Then, wherever the abstract type is fixed to be some concrete type, you also need to give a concrete implementation of the factory method. For class AbstractCurrency, this would look as follows: abstract class AbstractCurrency { type Currency <: AbstractCurrency // abstract type def make(amount: Long): Currency // factory method ... // rest of class } A design like this could be made to work, but it looks rather suspicious. Why place the factory method inside class AbstractCurrency? This looks dubious, for at least two reasons. First, if you have some amount of currency (say, one dollar), you also hold in your hand the ability to make more of the same currency, using code such as: myDollar.make(100) // here are a hundred more! In the age of color copying this might be a tempting scenario, but hopefully not one which you would be able to do for very long without being caught. The second problem with this code is that you can make more Currency objects if you already have a reference to a Currency object, but how do you get the first object of a given Currency? You’d need another creation method, which does essentially the same job as make. So you have a case of code duplication, which is a sure sign of a code smell. The solution, of course, is to move the abstract type and the factory method outside class AbstractCurrency. You need to create another class that contains the AbstractCurrency class, the Currency type, and the make factory method. We’ll call this a CurrencyZone: abstract class CurrencyZone { type Currency <: AbstractCurrency def make(x: Long): Currency 1 There’s some promising recent research on virtual classes, which would allow this, but virtual classes are not currently supported in Scala. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 472 abstract class AbstractCurrency { val amount: Long def designation: String override def toString = amount +""+ designation def + (that: Currency): Currency = make(this.amount + that.amount) def * (x: Double): Currency = make((this.amount * x).toLong) } } An example concrete CurrencyZone is the US, which could be defined as: object US extends CurrencyZone { abstract class Dollar extends AbstractCurrency { def designation = "USD" } type Currency = Dollar def make(x: Long) = new Dollar { val amount = x } } Here, US is an object that extends CurrencyZone. It defines a class Dollar, which is a subclass of AbstractCurrency. So the type of money in this zone is US.Dollar. The US object also fixes the type Currency to be an alias for Dollar, and it gives an implementation of the make factory method to return a dollar amount. This is a workable design. There are only a few refinements to be added. The first refinement concerns subunits. So far, every currency was measured in a single unit: dollars, euros, or yen. However, most currencies have sub- units: for instance, in the US, it’s dollars and cents. The most straightforward way to model cents is to have the amount field in US.Currency represent cents instead of dollars. To convert back to dollars, it’s useful to introduce a field CurrencyUnit into class CurrencyZone, which contains the amount of one standard unit in that currency: class CurrencyZone { ... val CurrencyUnit: Currency } Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 473 The US object could define the quantities Cent, Dollar, and CurrencyUnit as shown in Listing 20.11. This definition is just like the previous definition of the US object, except that it adds three new fields. The field Cent repre- sents an amount of 1 US.Currency. It’s an object analogous to a one-cent coin. The field Dollar represents an amount of 100 US.Currency. So the US object now defines the name Dollar in two ways. The type Dollar (defined by the abstract inner class named Dollar) represents the generic name of the Currency valid in the US currency zone. By contrast, the value Dollar (referenced from the val field named Dollar) represents a single US dollar, analogous to a one-dollar bill. The third field definition of CurrencyUnit specifies that the standard currency unit in the US zone is the Dollar (i.e., the value Dollar, referenced from the field, not the type Dollar). objectUS extends CurrencyZone { abstract class Dollar extends AbstractCurrency { def designation = "USD" } type Currency = Dollar def make(cents: Long) = new Dollar { val amount = cents } val Cent = make(1) val Dollar = make(100) val CurrencyUnit = Dollar } Listing 20.11· The US currency zone. The toString method in class Currency also needs to be adapted to take subunits into account. For instance, the sum of ten dollars and twenty three cents should print as a decimal number: 10.23 USD. To achieve this, you could implement Currency’s toString method as follows: override def toString = ((amount.toDouble / CurrencyUnit.amount.toDouble) formatted ("%."+ decimals(CurrencyUnit.amount) +"f") +""+ designation) Here, formatted is a method that Scala makes available on several classes, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 474 including Double.2 The formatted method returns the string that results from formatting the original string on which formatted was invoked ac- cording to a format string passed as the formatted method’s right-hand operand. The syntax of format strings passed to formatted is the same as that of Java’s String.format method. For instance, the format string %.2f formats a number with two decimal digits. The format string used in the toString shown previously is assembled by calling the decimals method on CurrencyUnit.amount. This method returns the number of dec- imal digits of a decimal power minus one. For instance, decimals(10) is 1, decimals(100) is 2, and so on. The decimals method is implemented by a simple recursion: private def decimals(n: Long): Int = if (n == 1) 0 else 1 + decimals(n / 10) Listing 20.12 shows some other currency zones. As another refinement you can add a currency conversion feature to the model. As a first step, you could write a Converter object that contains applicable exchange rates be- tween currencies, as shown in Listing 20.13. Then, you could add a conver- sion method, from, to class Currency, which converts from a given source currency into the current Currency object: def from(other: CurrencyZone#AbstractCurrency): Currency = make(math.round( other.amount.toDouble * Converter.exchangeRate (other.designation)(this.designation))) The from method takes an arbitrary currency as argument. This is expressed by its formal parameter type, CurrencyZone#AbstractCurrency, which indicates that the argument passed as other must be an AbstractCurrency type in some arbitrary and unknown CurrencyZone. It produces its result by multiplying the amount of the other currency with the exchange rate between the other and the current currency.3 The final version of the CurrencyZone class is shown in Listing 20.14. You can test the class in the Scala command shell. We’ll assume that the 2Scala uses rich wrappers, described in Section 5.9, to make formatted available. 3By the way, in case you think you’re getting a bad deal on Japanese yen, the exchange rates convert currencies based on their CurrencyZone amounts. Thus, 1.211 is the exchange rate between US cents to Japanese yen. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 475 object Europe extends CurrencyZone { abstract class Euro extends AbstractCurrency { def designation = "EUR" } type Currency = Euro def make(cents: Long) = new Euro { val amount = cents } val Cent = make(1) val Euro = make(100) val CurrencyUnit = Euro } object Japan extends CurrencyZone { abstract class Yen extends AbstractCurrency { def designation = "JPY" } type Currency = Yen def make(yen: Long) = new Yen { val amount = yen } val Yen = make(1) val CurrencyUnit = Yen } Listing 20.12· Currency zones for Europe and Japan. CurrencyZone class and all concrete CurrencyZone objects are defined in a package org.stairwaybook.currencies. The first step is to import ev- erything in this package into the command shell: scala> import org.stairwaybook.currencies._ You can then do some currency conversions: scala> Japan.Yen from US.Dollar * 100 res16: Japan.Currency = 12110 JPY scala> Europe.Euro from res16 res17: Europe.Currency = 75.95 EUR Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 476 object Converter{ var exchangeRate = Map( "USD" -> Map("USD" -> 1.0 , "EUR" -> 0.7596, "JPY" -> 1.211 , "CHF" -> 1.223), "EUR" -> Map("USD" -> 1.316 , "EUR" -> 1.0 , "JPY" -> 1.594 , "CHF" -> 1.623), "JPY" -> Map("USD" -> 0.8257, "EUR" -> 0.6272, "JPY" -> 1.0 , "CHF" -> 1.018), "CHF" -> Map("USD" -> 0.8108, "EUR" -> 0.6160, "JPY" -> 0.982 , "CHF" -> 1.0 ) ) } Listing 20.13· A converter object with an exchange rates map. scala> US.Dollar from res17 res18: US.Currency = 99.95 USD The fact that we obtain almost the same amount after three conversions im- plies that these are some pretty good exchange rates! You can also add up values of the same currency: scala> US.Dollar * 100 + res18 res19: US.Currency = 199.95 USD On the other hand, you cannot add amounts of different currencies: scala> US.Dollar + Europe.Euro :10: error: type mismatch; found : Europe.Euro required: US.Currency US.Dollar + Europe.Euro ˆ By preventing the addition of two values with different units (in this case, currencies), the type abstraction has done its job. It prevents us from per- forming calculations that are unsound. Failures to convert correctly between different units may seem like trivial bugs, but they have caused many seri- ous systems faults. An example is the crash of the Mars Climate Orbiter Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.10 Chapter 20 · Abstract Members 477 abstract class CurrencyZone { type Currency <: AbstractCurrency def make(x: Long): Currency abstract class AbstractCurrency { val amount: Long def designation: String def + (that: Currency): Currency = make(this.amount + that.amount) def * (x: Double): Currency = make((this.amount * x).toLong) def - (that: Currency): Currency = make(this.amount - that.amount) def / (that: Double) = make((this.amount / that).toLong) def / (that: Currency) = this.amount.toDouble / that.amount def from(other: CurrencyZone#AbstractCurrency): Currency = make(math.round( other.amount.toDouble * Converter.exchangeRate (other.designation)(this.designation))) private def decimals(n: Long): Int = if (n == 1) 0 else 1 + decimals(n / 10) override def toString = ((amount.toDouble / CurrencyUnit.amount.toDouble) formatted ("%."+ decimals(CurrencyUnit.amount) +"f") +""+ designation) } val CurrencyUnit: Currency } Listing 20.14· The full code of class CurrencyZone. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 20.11 Chapter 20 · Abstract Members 478 spacecraft on September 23, 1999, which was caused because one engineer- ing team used metric units while another used English units. If units had been coded in the same way as currencies are coded in this chapter, this error would have been detected by a simple compilation run. Instead, it caused the crash of the orbiter after a near ten-month voyage. 20.11 Conclusion Scala offers systematic and very general support for object-oriented abstrac- tion. It enables you to not only abstract over methods, but also over values, variables, and types. This chapter has shown how to take advantage of ab- stract members. They support a simple yet effective principle for systems structuring: when designing a class, make everything that is not yet known into an abstract member. The type system will then drive the development of your model, just as you saw with the currency case study. It does not matter whether the unknown is a type, method, variable or value. In Scala, all of these can be declared abstract. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 21 Implicit Conversions and Parameters There’s a fundamental difference between your own code and libraries of other people: you can change or extend your own code as you wish, but if you want to use someone else’s libraries, you usually have to take them as they are. A number of constructs have sprung up in programming languages to alleviate this problem. Ruby has modules, and Smalltalk lets packages add to each other’s classes. These are very powerful, but also dangerous, in that you modify the behavior of a class for an entire application, some parts of which you might not know. C# 3.0 has static extension methods, which are more local, but also more restrictive in that you can only add methods, not fields, to a class, and you can’t make a class implement new interfaces. Scala’s answer is implicit conversions and parameters. These can make existing libraries much more pleasant to deal with by letting you leave out tedious, obvious details that obscure the interesting parts of your code. Used tastefully, this results in code that is focused on the interesting, non-trivial parts of your program. This chapter shows you how implicits work, and it presents some of the most common ways they are used. 21.1 Implicit conversions Before delving into the details of implicit conversions, take a look at a typical example of their use. Implicit conversions are often helpful for working with two bodies of software that were developed without each other in mind. Each library has its own way to encode a concept that is essentially the same thing. Implicit conversions help by reducing the number of explicit conversions that Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.1 Chapter 21 · Implicit Conversions and Parameters 480 are needed from one type to another. Java includes a library named Swing for implementing cross-platform user interfaces. One of the things Swing does is process events from the operating system, convert them to platform-independent event objects, and pass those events to parts of an application called event listeners. If Swing had been written with Scala in mind, event listeners would prob- ably have been represented by a function type. Callers could then use the function literal syntax as a lightweight way to specify what should happen for a certain class of events. Since Java doesn’t have function literals, Swing uses the next best thing, an inner class that implements a one-method inter- face. In the case of action listeners, the interface is ActionListener. Without the use of implicit conversions, a Scala program that uses Swing must use inner classes just like in Java. Here’s an example that creates a but- ton and hooks up an action listener to it. The action listener is invoked when- ever the button is pressed, at which point it prints the string "pressed!": val button = new JButton button.addActionListener( new ActionListener { def actionPerformed(event: ActionEvent){ println("pressed!") } } ) This code has a lot of information-free boilerplate. The fact that this lis- tener is an ActionListener, the fact that the callback method is named actionPerformed, and the fact that the argument is an ActionListener are all implied for any argument to addActionListener. The only new information here is the code to be performed, namely the call to println. This new information is drowned out by the boilerplate. Someone reading this code must have an eagle’s eye to pick through the noise and find the informative part. A more Scala-friendly version would take a function as an argument, greatly reducing the amount of boilerplate. button.addActionListener( // Type mismatch! (_: ActionEvent) => println("pressed!") ) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.1 Chapter 21 · Implicit Conversions and Parameters 481 As written so far, this code doesn’t work. The addActionListener method wants an action listener but is getting a function. With implicit conversions, however, this code can be made to work. The first step is to write an implicit conversion between the two types. Here is an implicit conversion from functions to action listeners: implicit def function2ActionListener(f: ActionEvent => Unit) = new ActionListener { def actionPerformed(event: ActionEvent) = f(event) } This is a one-argument method that takes a function and returns an action listener. Like any other one-argument method, it can be called directly and have its result passed on to another expression: button.addActionListener( function2ActionListener( (_: ActionEvent) => println("pressed!") ) ) This much is already an improvement on the version with the inner class. Note how arbitrary amounts of boilerplate end up replaced by a function literal and a call to a method. It gets better, though, with implicit conversions. Because function2ActionListener is marked as implicit, it can be left out and the compiler will insert it automatically. The result is the following, very tight code: // Now this works button.addActionListener( (_: ActionEvent) => println("pressed!") ) The way this code works is that the compiler first tries to compile it as is, but it sees a type error. Before giving up, it looks for an implicit conversion that can repair the problem. In this case, it finds function2ActionListener. It tries that conversion method, sees that it works, and moves on. The compiler works hard here so that the developer can ignore one more fiddly detail. Action listener? Action event function? Either one will work—use the one that’s more convenient. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.2 Chapter 21 · Implicit Conversions and Parameters 482 This section has shown you some of the power of implicit conversions, and how they let you dress up existing libraries. In the next sections you’ll learn the rules that determine when implicit conversions are tried and how they are found. 21.2 Rules for implicits Implicit definitions are those that the compiler is allowed to insert into a program in order to fix any of its type errors. For example, if x + y does not type check, then the compiler might change it to convert(x) + y, where convert is some available implicit conversion. If convert changes x into something that has a + method, then this change might fix a program so that it type checks and runs correctly. If convert really is just a simple conversion function, then leaving it out of the source code can be a clarification. Implicit conversions are governed by the following general rules: Marking Rule: Only definitions marked implicit are available. The implicit keyword is used to mark which declarations the compiler may use as implicits. You can use it to mark any variable, function, or object definition. Here’s an example of an implicit function definition:1 implicit def intToString(x: Int) = x.toString The compiler will only change x + y to convert(x) + y if convert is marked as implicit. This way, you avoid the confusion that would result if the compiler picked random functions that happen to be in scope and inserted them as “conversions.” The compiler will only select among the definitions you have explicitly marked as implicit. Scope Rule: An inserted implicit conversion must be in scope as a single identifier, or be associated with the source or target type of the conver- sion. The Scala compiler will only consider implicit conversions that are in scope. To make an implicit conversion available, therefore, you must in some way bring it into scope. Moreover, with one exception, the implicit conversion must be in scope as a single identifier. The compiler will not in- sert a conversion of the form someVariable.convert. For example, it will 1Variables and singleton objects marked implicit can be used as implicit parameters. This use case will be described later in this chapter. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.2 Chapter 21 · Implicit Conversions and Parameters 483 not expand x + y to someVariable.convert(x) + y. If you want to make someVariable.convert available as an implicit, therefore, you would need to import it, which would make it available as a single identifier. Once im- ported, the compiler would be free to apply it as convert(x) + y. In fact, it is common for libraries to include a Preamble object including a number of useful implicit conversions. Code that uses the library can then do a single “import Preamble._” to access the library’s implicit conversions. There’s one exception to the “single identifier” rule. The compiler will also look for implicit definitions in the companion object of the source or expected target types of the conversion. For example, if you’re attempting to pass a Dollar object to a method that takes a Euro, the source type is Dollar and the target type is Euro. You could, therefore, package an implicit conversion from Dollar to Euro in the companion object of either class, Dollar or Euro. Here’s an example in which the implicit definition is placed in Dollar’s companion object: object Dollar { implicit def dollarToEuro(x: Dollar): Euro = ... } class Dollar { ... } In this case, the conversion dollarToEuro is said to be associated to the type Dollar. The compiler will find such an associated conversion every time it needs to convert from an instance of type Dollar. There’s no need to import the conversion separately into your program. The Scope Rule helps with modular reasoning. When you read code in a file, the only things you need to consider from other files are those that are either imported or are explicitly referenced through a fully qualified name. This benefit is at least as important for implicits as for explicitly written code. If implicits took effect system-wide, then to understand a file you would have to know about every implicit introduced anywhere in the program! One-at-a-time Rule: Only one implicit is tried. The compiler will never rewrite x + y to convert1(convert2(x)) + y. Doing so would cause com- pile times to increase dramatically on erroneous code, and it would increase the difference between what the programmer writes and what the program actually does. For sanity’s sake, the compiler does not insert further im- plicit conversions when it is already in the middle of trying another implicit. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.2 Chapter 21 · Implicit Conversions and Parameters 484 However, it’s possible to circumvent this restriction by having implicits take implicit parameters, which will be described later in this chapter. Explicits-First Rule: Whenever code type checks as it is written, no implicits are attempted. The compiler will not change code that already works. A corollary of this rule is that you can always replace implicit iden- tifiers by explicit ones, thus making the code longer but with less apparent ambiguity. You can trade between these choices on a case-by-case basis. Whenever you see code that seems repetitive and verbose, implicit conver- sions can help you decrease the tedium. Whenever code seems terse to the point of obscurity, you can insert conversions explicitly. The amount of im- plicits you leave the compiler to insert is ultimately a matter of style. Naming an implicit conversion. Implicit conversions can have arbitrary names. The name of an implicit conversion matters only in two situations: if you want to write it explicitly in a method application, and for determining which implicit conversions are available at any place in the program. To illustrate the second point, say you have an object with two implicit conversions: object MyConversions { implicit def stringWrapper(s: String): IndexedSeq[Char] = ... implicit def intToString(x: Int): String = ... } In your application, you want to make use of the stringWrapper conver- sion, but you don’t want integers to be converted automatically to strings by means of the intToString conversion. You can achieve this by importing only one conversion, but not the other: import MyConversions.stringWrapper ... // code making use of stringWrapper In this example, it was important that the implicit conversions had names, because only that way could you selectively import one and not the other. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.3 Chapter 21 · Implicit Conversions and Parameters 485 Where implicits are tried. There are three places implicits are used in the language: conversions to an expected type, conversions of the receiver of a selection, and implicit parameters. Implicit conversions to an expected type let you use one type in a context where a different type is expected. For example, you might have a String and want to pass it to a method that requires an IndexedSeq[Char]. Conversions of the receiver let you adapt the receiver of a method call, i.e., the object on which a method is invoked, if the method is not applicable on the original type. An example is "abc".exists, which is converted to stringWrapper("abc").exists because the exists method is not available on Strings but is available on IndexedSeqs. Implicit parameters, on the other hand, are usually used to provide more information to the called function about what the caller wants. Implicit parameters are especially useful with generic functions, where the called function might otherwise know nothing at all about the type of one or more arguments. Each of the following three sections will discuss one of these three kinds of implicits. 21.3 Implicit conversion to an expected type Implicit conversion to an expected type is the first place the compiler will use implicits. The rule is simple. Whenever the compiler sees an X, but needs a Y, it will look for an implicit function that converts X to Y. For example, normally a double cannot be used as an integer, because it loses precision: scala> val i: Int = 3.5 :4: error: type mismatch; found : Double(3.5) required: Int val i: Int = 3.5 ˆ However, you can define an implicit conversion to smooth this over: scala> implicit def doubleToInt(x: Double) = x.toInt doubleToInt: (x: Double)Int scala> val i: Int = 3.5 i: Int = 3 What happens here is that the compiler sees a Double, specifically 3.5, in a context where it requires an Int. So far, the compiler is looking at an Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.4 Chapter 21 · Implicit Conversions and Parameters 486 ordinary type error. Before giving up, though, it searches for an implicit conversion from Double to Int. In this case, it finds one: doubleToInt, be- cause doubleToInt is in scope as a single identifier. (Outside the interpreter, you might bring doubleToInt into scope via an import or possibly through inheritance.) The compiler then inserts a call to doubleToInt automatically. Behind the scenes, the code becomes: val i: Int = doubleToInt(3.5) This is literally an implicit conversion. You did not explicitly ask for conver- sion. Instead, you marked doubleToInt as an available implicit conversion by bringing it into scope as a single identifier, and then the compiler auto- matically used it when it needed to convert from a Double to an Int. Converting Doubles to Ints might raise some eyebrows, because it’s a dubious idea to have something that causes a loss in precision happen in- visibly. So this is not really a conversion we recommend. It makes much more sense to go the other way, from some more constrained type to a more general one. For instance, an Int can be converted without loss of precision to a Double, so an implicit conversion from Int to Double makes sense. In fact, that’s exactly what happens. The scala.Predef object, which is im- plicitly imported into every Scala program, defines implicit conversions that convert “smaller” numeric types to “larger” ones. For instance, you will find in Predef the following conversion: implicit def int2double(x: Int): Double = x.toDouble That’s why in Scala Int values can be stored in variables of type Double. There’s no special rule in the type system for this; it’s just an implicit con- version that gets applied.2 21.4 Converting the receiver Implicit conversions also apply to the receiver of a method call, the object on which the method is invoked. This kind of implicit conversion has two main uses. First, receiver conversions allow smoother integration of a new class into an existing class hierarchy. And second, they support writing domain- specific languages (DSLs) within the language. 2The Scala compiler backend will treat the conversion specially, however, translating it to a special “i2d” bytecode. So the compiled image is the same as in Java. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.4 Chapter 21 · Implicit Conversions and Parameters 487 To see how it works, suppose you write down obj.doIt, and obj does not have a member named doIt. The compiler will try to insert conversions before giving up. In this case, the conversion needs to apply to the receiver, obj. The compiler will act as if the expected “type” of obj were “has a member named doIt.” This “has a doIt” type is not a normal Scala type, but it is there conceptually and is why the compiler will insert an implicit conversion in this case. Interoperating with new types As mentioned previously, one major use of receiver conversions is allowing smoother integration of new with existing types. In particular, they allow you to enable client programmers to use instances of existing types as if they were instances of your new type. Take, for example, class Rational shown in Listing 6.5 on page 155. Here’s a snippet of that class again: class Rational(n: Int, d: Int){ ... def + (that: Rational): Rational = ... def + (that: Int): Rational = ... } Class Rational has two overloaded variants of the + method, which take Rationals and Ints, respectively, as arguments. So you can either add two rational numbers or a rational number and an integer: scala> val oneHalf = new Rational(1, 2) oneHalf: Rational = 1/2 scala> oneHalf + oneHalf res0: Rational = 1/1 scala> oneHalf + 1 res1: Rational = 3/2 What about an expression like 1 + oneHalf, however? This expression is tricky because the receiver, 1, does not have a suitable + method. So the following gives an error: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.4 Chapter 21 · Implicit Conversions and Parameters 488 scala> 1 + oneHalf :6: error: overloaded method value + with alternatives (Double)Double ... cannot be applied to (Rational) 1 + oneHalf ˆ To allow this kind of mixed arithmetic, you need to define an implicit con- version from Int to Rational: scala> implicit def intToRational(x: Int) = new Rational(x, 1) intToRational: (x: Int)Rational With the conversion in place, converting the receiver does the trick: scala> 1 + oneHalf res2: Rational = 3/2 What happens behind the scenes here is that Scala compiler first tries to type check the expression 1 + oneHalf as it is. This fails because Int has several + methods, but none that takes a Rational argument. Next, the compiler searches for an implicit conversion from Int to another type that has a + method which can be applied to a Rational. It finds your conversion and applies it, which yields: intToRational(1) + oneHalf In this case, the compiler found the implicit conversion function because you entered its definition into the interpreter, which brought it into scope for the remainder of the interpreter session. Simulating new syntax The other major use of implicit conversions is to simulate adding new syntax. Recall that you can make a Map using syntax like this: Map(1 -> "one", 2 -> "two", 3 -> "three") Have you wondered how the -> is supported? It’s not syntax! Instead, -> is a method of the class ArrowAssoc, a class defined inside the standard Scala Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.5 Chapter 21 · Implicit Conversions and Parameters 489 preamble (scala.Predef). The preamble also defines an implicit conver- sion from Any to ArrowAssoc. When you write 1 -> "one", the compiler inserts a conversion from 1 to ArrowAssoc so that the -> method can be found. Here are the relevant definitions: package scala object Predef { class ArrowAssoc[A](x: A) { def -> [B](y: B): Tuple2[A, B] = Tuple2(x, y) } implicit def any2ArrowAssoc[A](x: A): ArrowAssoc[A] = new ArrowAssoc(x) ... } This “rich wrappers” pattern is common in libraries that provide syntax-like extensions to the language, so you should be ready to recognize the pattern when you see it. Whenever you see someone calling methods that appear not to exist in the receiver class, they are probably using implicits. Similarly, if you see a class named RichSomething, e.g., RichInt or RichBoolean, that class is likely adding syntax-like methods to type Something. You have already seen this rich wrappers pattern for the basic types de- scribed in Chapter 5. As you can now see, these rich wrappers apply more widely, often letting you get by with an internal DSL defined as a library where programmers in other languages might feel the need to develop an external DSL. 21.5 Implicit parameters The remaining place the compiler inserts implicits is within argument lists. The compiler will sometimes replace someCall(a) with someCall(a)(b), or new SomeClass(a) with new SomeClass(a)(b), thereby adding a miss- ing parameter list to complete a function call. It is the entire last curried parameter list that’s supplied, not just the last parameter. For example, if someCall’s missing last parameter list takes three parameters, the compiler might replace someCall(a) with someCall(a)(b, c, d). For this usage, not only must the inserted identifiers, such as b, c, and d in (b, c, d), be Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.5 Chapter 21 · Implicit Conversions and Parameters 490 marked implicit where they are defined, but also the last parameter list in someCall’s or someClass’s definition must be marked implicit. Here’s a simple example. Suppose you have a class PreferredPrompt, which encapsulates a shell prompt string (such as, say "$ " or "> ") that is preferred by a user: class PreferredPrompt(val preference: String) Also, suppose you have a Greeter object with a greet method, which takes two parameter lists. The first parameter list takes a string user name, and the second parameter list takes a PreferredPrompt: object Greeter { def greet(name: String)(implicit prompt: PreferredPrompt){ println("Welcome, "+ name +". The system is ready.") println(prompt.preference) } } The last parameter list is marked implicit, which means it can be supplied implicitly. But you can still provide the prompt explicitly, like this: scala> val bobsPrompt = new PreferredPrompt("relax> ") bobsPrompt: PreferredPrompt = PreferredPrompt@74a138 scala> Greeter.greet("Bob")(bobsPrompt) Welcome, Bob. The system is ready. relax> To let the compiler supply the parameter implicitly, you must first define a variable of the expected type, which in this case is PreferredPrompt. You could do this, for example, in a preferences object: object JoesPrefs { implicit val prompt = new PreferredPrompt("Yes, master> ") } Note that the val itself is marked implicit. If it wasn’t, the compiler would not use it to supply the missing parameter list. It will also not use it if it isn’t in scope as a single identifier. For example: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.5 Chapter 21 · Implicit Conversions and Parameters 491 scala> Greeter.greet("Joe") :10: error: could not find implicit value for parameter prompt: PreferredPrompt Greeter.greet("Joe") ˆ Once you bring it into scope via an import, however, it will be used to supply the missing parameter list: scala> import JoesPrefs._ import JoesPrefs._ scala> Greeter.greet("Joe") Welcome, Joe. The system is ready. Yes, master> Note that the implicit keyword applies to an entire parameter list, not to individual parameters. Listing 21.1 shows an example in which the last pa- rameter list of Greeter’s greet method, which is again marked implicit, has two parameters: prompt (of type PreferredPrompt) and drink (of type PreferredDrink): class PreferredPrompt(val preference: String) class PreferredDrink(val preference: String) object Greeter { def greet(name: String)(implicit prompt: PreferredPrompt, drink: PreferredDrink){ println("Welcome, "+ name +". The system is ready.") print("But while you work, ") println("why not enjoy a cup of "+ drink.preference +"?") println(prompt.preference) } } object JoesPrefs { implicit val prompt = new PreferredPrompt("Yes, master> ") implicit val drink = new PreferredDrink("tea") } Listing 21.1· An implicit parameter list with multiple parameters. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.5 Chapter 21 · Implicit Conversions and Parameters 492 Singleton object JoesPrefs in Listing 21.1 declares two implicit vals, prompt of type PreferredPrompt and drink of type PreferredDrink. As before, however, so long as these are not in scope as single identifiers, they won’t be used to fill in a missing parameter list to greet: scala> Greeter.greet("Joe") :14: error: could not find implicit value for parameter prompt: PreferredPrompt Greeter.greet("Joe") ˆ You can bring both implicit vals into scope with an import: scala> import JoesPrefs._ import JoesPrefs._ Because both prompt and drink are now in scope as single identifiers, you can use them to supply the last parameter list explicitly, like this: scala> Greeter.greet("Joe")(prompt, drink) Welcome, Joe. The system is ready. But while you work, why not enjoy a cup of tea? Yes, master> And because all the rules for implicit parameters are now met, you can alter- natively let the Scala compiler supply prompt and drink for you by leaving off the last parameter list: scala> Greeter.greet("Joe") Welcome, Joe. The system is ready. But while you work, why not enjoy a cup of tea? Yes, master> One thing to note about the previous examples is that we didn’t use String as the type of prompt or drink, even though ultimately it was a String that each of them provided through their preference fields. Be- cause the compiler selects implicit parameters by matching types of parame- ters against types of values in scope, implicit parameters usually have “rare” or “special” enough types that accidental matches are unlikely. For example, the types PreferredPrompt and PreferredDrink in Listing 21.1 were de- fined solely to serve as implicit parameter types. As a result, it is unlikely Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.5 Chapter 21 · Implicit Conversions and Parameters 493 that implicit variables of these types will be in scope if they aren’t intended to be used as implicit parameters to Greeter.greet. Another thing to know about implicit parameters is that they are perhaps most often used to provide information about a type mentioned explicitly in an earlier parameter list, similar to the type classes of Haskell. As an ex- ample, consider the maxListUpBound function shown in Listing 21.2, which returns the maximum element of the passed list: def maxListUpBound[T <: Ordered[T]](elements: List[T]): T = elements match { case List() => throw new IllegalArgumentException("empty list!") case List(x) => x case x :: rest => val maxRest = maxListUpBound(rest) if (x > maxRest) x else maxRest } Listing 21.2· A function with an upper bound. The signature of maxListUpBound is similar to that of orderedMergeSort, shown in Listing 19.12 on page 444: it takes a List[T] as its argument, and specifies via an upper bound that T must be a subtype of Ordered[T]. As mentioned at the end of Section 19.8, one weakness with this approach is that you can’t use the function with lists whose element type isn’t already a subtype of Ordered. For example, you couldn’t use the maxListUpBound function to find the maximum of a list of integers, because class Int is not a subtype of Ordered[Int]. Another, more general way to organize maxListUpBound would be to require a separate, second argument, in addition to the List[T] argument: a function that converts a T to an Ordered[T]. This approach is shown in Listing 21.3. In this example, the second argument, orderer, is placed in a separate argument list and marked implicit. The orderer parameter in this example is used to describe the ordering of Ts. In the body of maxListImpParm, this ordering is used in two places: a recursive call to maxListImpParm, and an if expression that checks whether the head of the list is larger than the maximum element of the rest of the list. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.5 Chapter 21 · Implicit Conversions and Parameters 494 def maxListImpParm[T](elements: List[T]) (implicit orderer: T => Ordered[T]): T = elements match { case List() => throw new IllegalArgumentException("empty list!") case List(x) => x case x :: rest => val maxRest = maxListImpParm(rest)(orderer) if (orderer(x) > maxRest) x else maxRest } Listing 21.3· A function with an implicit parameter. The maxListImpParm function, shown in Listing 21.3, is an example of an implicit parameter used to provide more information about a type men- tioned explicitly in an earlier parameter list. To be specific, the implicit parameter orderer, of type T => Ordered[T], provides more information about type T—in this case, how to order Ts. Type T is mentioned in List[T], the type of parameter elements, which appears in the earlier parameter list. Because elements must always be provided explicitly in any invocation of maxListImpParm, the compiler will know T at compile time, and can there- fore determine whether an implicit definition of type T => Ordered[T] is in scope. If so, it can pass in the second parameter list, orderer, implicitly. This pattern is so common that the standard Scala library provides im- plicit “orderer” methods for many common types. You could therefore use this maxListImpParm method with a variety of types: scala> maxListImpParm(List(1,5,10,3)) res9: Int = 10 scala> maxListImpParm(List(1.5, 5.2, 10.7, 3.14159)) res10: Double = 10.7 scala> maxListImpParm(List("one", "two", "three")) res11: java.lang.String = two In the first case, the compiler inserted an orderer function for Ints; in the second case, for Doubles; in the third case, for Strings. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.6 Chapter 21 · Implicit Conversions and Parameters 495 A style rule for implicit parameters As a style rule, it is best to use a custom named type in the types of implicit parameters. For example, the types of prompt and drink in the previous example was not String, but PreferredPrompt and PreferredDrink, respectively. As a counterexam- ple, consider that the maxListImpParm function could just as well have been written with the following type signature: def maxListPoorStyle[T](elements: List[T]) (implicit orderer: (T, T) => Boolean): T To use this version of the function, though, the caller would have to supply an orderer parameter of type (T, T) => Boolean. This is a fairly generic type that includes any function from two Ts to a Boolean. It does not indicate anything at all about what the type is for; it could be an equality test, a less- than test, a greater-than test, or something else entirely. The actual code for maxListImpParm, given in Listing 21.3, shows better style. It uses an orderer parameter of type T => Ordered[T]. The word Ordered in this type indicates exactly what the implicit parameter is used for: it is for ordering elements of T. Because this orderer type is more explicit, it becomes no trouble to add implicit conversions for this type in the standard library. To contrast, imagine the chaos that would ensue if you added an implicit of type (T, T) => Boolean in the standard library, and the compiler started sprinkling it around in people’s code. You would end up with code that compiles and runs, but that does fairly arbitrary tests against pairs of items! Thus the style rule: use at least one role-determining name within the type of an implicit parameter. 21.6 View bounds The previous example had an opportunity to use an implicit but did not. Note that when you use implicit on a parameter, then not only will the compiler try to supply that parameter with an implicit value, but the compiler will also use that parameter as an available implicit in the body of the method! Thus, both uses of orderer within the body of the method can be left out. When the compiler examines the code in Listing 21.4, it will see that the types do not match up. For example, x of type T does not have a > method, and so x > maxRest does not work. The compiler will not immediately stop, Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.6 Chapter 21 · Implicit Conversions and Parameters 496 def maxList[T](elements: List[T]) (implicit orderer: T => Ordered[T]): T = elements match { case List() => throw new IllegalArgumentException("empty list!") case List(x) => x case x :: rest => val maxRest = maxList(rest) // (orderer) is implicit if (x > maxRest) x // orderer(x) is implicit else maxRest } Listing 21.4· A function that uses an implicit parameter internally. however. It will first look for implicit conversions to repair the code. In this case, it will notice that orderer is available, so it can convert the code to orderer(x) > maxRest. Likewise for the expression maxList(rest), which can be converted to maxList(rest)(orderer). After these two in- sertions of implicits, the method fully type checks. Look closely at maxList. There is not a single mention of the orderer parameter in the text of the method. All uses of orderer are implicit. Sur- prisingly, this coding pattern is actually fairly common. The implicit param- eter is used only for conversions, and so it can itself be used implicitly. Now, because the parameter name is never used explicitly, the name could have been anything. For example, maxList would behave identically if you left its body alone but changed the parameter name: def maxList[T](elements: List[T]) (implicit converter: T => Ordered[T]): T = // same body... For that matter, it could just as well be: def maxList[T](elements: List[T]) (implicit iceCream: T => Ordered[T]): T = // same body... Because this pattern is common, Scala lets you leave out the name of this pa- rameter and shorten the method header by using a view bound. Using a view Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.6 Chapter 21 · Implicit Conversions and Parameters 497 def maxList[T <% Ordered[T]](elements: List[T]): T = elements match { case List() => throw new IllegalArgumentException("empty list!") case List(x) => x case x :: rest => val maxRest = maxList(rest) // (orderer) is implicit if (x > maxRest) x // orderer(x) is implicit else maxRest } Listing 21.5· A function with a view bound. bound, you would write the signature of maxList as shown in Listing 21.5. You can think of “T <% Ordered[T]” as saying, “I can use any T, so long as T can be treated as an Ordered[T].” This is different from saying that T is an Ordered[T], which is what an upper bound, “T <: Ordered[T]”, would say. For example, even though class Int is not a subtype of Ordered[Int], you could still pass a List[Int] to maxList so long as an implicit conver- sion from Int to Ordered[Int] is available. Moreover, if type T happens to already be an Ordered[T], you can still pass a List[T] to maxList. The compiler will use an implicit identity function, declared in Predef: implicit def identity[A](x: A): A = x In this case, the conversion is a no-op; it simply returns the object it is given. View bounds and upper bounds The maxListUpBound function, of Listing 21.2, specifies that T is an Ordered[T] with its upper bound, T <: Ordered[T]. By contrast, the maxList function, of Listing 21.5, specifies that T can be treated as an Ordered[T] with its view bound, T <% Ordered[T]. If you compare the code of maxListUpBound with that of maxList, you’ll find that the only non-cosmetic difference between the two is that the upper bound symbol, <:, is changed to a view bound symbol, <%. But maxList of Listing 21.5 can work with many more types. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.7 Chapter 21 · Implicit Conversions and Parameters 498 21.7 When multiple conversions apply It can happen that multiple implicit conversions are in scope that would each work. For the most part, Scala refuses to insert a conversion in such a case. Implicits work well when the conversion left out is completely obvious and thus is pure boilerplate. If multiple conversions apply, then the choice isn’t so obvious after all. Here’s a simple example. There is a method that takes a sequence, a conversion that turns an integer into a range, and a conversion that turns an integer into an array of digits: scala> def printLength(seq: Seq[Int]) = println(seq.length) printLength: (seq: Seq[Int])Unit scala> implicit def intToRange(i: Int) = 1 to i intToRange: (i: Int)scala.collection.immutable.Range.Inclusive with scala.collection.immutable.Range.ByOne scala> implicit def intToDigits(i: Int) = i.toString.toList.map(_.toInt) intToDigits: (i: Int)List[Int] scala> printLength(12) :21: error: type mismatch; found : Int(12) required: Seq[Int] Note that implicit conversions are not applicable because they are ambiguous: ... The ambiguity here is real. Converting an integer to a sequence of dig- its is completely different from converting it to a range. In this case, the programmer should specify which one is intended and be explicit. Up through Scala 2.7, that was the end of the story. Whenever mul- tiple implicit conversions applied, the compiler refused to choose between them. The situation was just as with method overloading. If you try to call foo(null), and there are two different foo overloads that accept null, the compiler will refuse. It will say that the method call’s target is ambiguous. Scala 2.8 loosens this rule. If one of the available conversions is strictly more specific than the others, then the compiler will choose the more specific one. The idea is that whenever there is a reason to believe a programmer Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.7 Chapter 21 · Implicit Conversions and Parameters 499 would always choose one of the conversions over the others, don’t require the programmer to write it explicitly. After all, method overloading has the same relaxation. Continuing the previous example, if one of the available foo methods takes a String while the other takes an Any, then choose the String version after all. It’s clearly more specific. To be more precise, one implicit conversion is more specific than another if one of the following applies: • The argument type of the former is a subtype of the latter’s. • Both conversions are methods, and the enclosing class of the former extends the enclosing class of the latter. The motivation to revisit this issue and revise the rule was to improve in- teroperation between Java collections, Scala collections, and strings. Here’s a simple example among many: val cba = "abc".reverse What is the type inferred for cba? Intuitively, the type should be String. Reversing a string should yield another string, right? However, in Scala 2.7, what happened is that "abc" was converted to a Scala collection. Reversing a Scala collection yields a Scala collection, so the type of cba would be a collection. There’s also an implicit conversion back to a string, but that didn’t patch up every problem. For example, in versions prior to Scala 2.8, "abc" == "abc".reverse.reverse was false! In Scala 2.8, the type of cba is String. The old implicit conversion to a Scala collection (now named WrappedString) is retained. However, there is a more specific conversion supplied from String to a new type called StringOps. StringOps has many methods such as reverse, but instead of returning a collection, they return a String. The conversion to StringOps is defined directly in Predef, whereas the conversion to a scala collection is defined in a new class, LowPriorityImplicits, which is extended by Predef. Whenever a choice exists between these two conversions, the com- piler chooses the conversion to StringOps, because it’s defined in a subclass of the class where the other conversion is defined. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.7 Chapter 21 · Implicit Conversions and Parameters 500 object Mocha extends Application { class PreferredDrink(val preference: String) implicit val pref = new PreferredDrink("mocha") def enjoy(name: String)(implicit drink: PreferredDrink){ print("Welcome, "+ name) print(". Enjoy a ") print(drink.preference) println("!") } enjoy("reader") } Listing 21.6· Sample code that uses an implicit parameter. $ scalac -Xprint:typer mocha.scala [[syntax trees at end of typer]]// Scala source: mocha.scala package { final object Mocha extends java.lang.Object with Application with ScalaObject { // ... private[this] val pref: Mocha.PreferredDrink = new Mocha.this.PreferredDrink("mocha"); implicit def pref: Mocha.PreferredDrink = Mocha.this.pref; def enjoy(name: String) (implicit drink: Mocha.PreferredDrink): Unit = { scala.this.Predef.print("Welcome, ".+(name)); scala.this.Predef.print(". Enjoy a "); scala.this.Predef.print(drink.preference); scala.this.Predef.println("!") }; Mocha.this.enjoy("reader")(Mocha.this.pref) } } Listing 21.7· Sample code after type checking and insertion of implicits. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.8 Chapter 21 · Implicit Conversions and Parameters 501 21.8 Debugging implicits Implicits are an powerful feature in Scala, but one which is sometimes diffi- cult to get right. This section contains a few tips for debugging implicits. Sometimes you might wonder why the compiler did not find an implicit conversion that you think should apply. In that case it helps to write the conversion out explicitly. If that also gives an error message, you then know why the compiler could not apply your implicit. For instance, assume that you mistakenly took wrapString to be a conversion from Strings to Lists, instead of IndexedSeqs. You would wonder why the following code does not work: scala> val chars: List[Char] = "xyz" :19: error: type mismatch; found : java.lang.String("xyz") required: List[Char] val chars: List[Char] = "xyz" ˆ In that case it helps to write the wrapString conversion explicitly, to find out what went wrong: scala> val chars: List[Char] = wrapString("xyz") :19: error: type mismatch; found : scala.collection.immutable.WrappedString required: List[Char] val chars: List[Char] = wrapString("xyz") ˆ With this, you have found the cause of the error: wrapString has the wrong return type. On the other hand, it’s also possible that inserting the conversion explicitly will make the error go away. In that case you know that one of the other rules (such as the Scope Rule) was preventing the implicit conversion from being applied. When you are debugging a program, it can sometimes help to see what implicit conversions the compiler is inserting. The -Xprint:typer option to the compiler is useful for this. If you run scalac with this option, then the compiler will show you what your code looks like after all implicit con- versions have been added by the type checker. An example is shown in Listing 21.6 and Listing 21.7. If you look at the last statement in each of these listings, you’ll see that the second parameter list to enjoy, which was Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 21.9 Chapter 21 · Implicit Conversions and Parameters 502 left off in the code in Listing 21.6,“enjoy("reader"),” was inserted by the compiler, as shown in Listing 21.7: Mocha.this.enjoy("reader")(Mocha.this.pref) If you are brave, try scala -Xprint:typer to get an interactive shell that prints out the post-typing source code it uses internally. If you do so, be prepared to see an enormous amount of boilerplate surrounding the meat of your code. 21.9 Conclusion Implicits are a powerful, code-condensing feature of Scala. This chapter has shown you Scala’s rules about implicits, and it has shown you several common programming situations where you can profit from using implicits. As a word of warning, implicits can make code confusing if they are used too frequently. Thus, before adding a new implicit conversion, first ask whether you can achieve a similar effect through other means, such as inheritance, mixin composition, or method overloading. If all of these fail, however, and you feel like a lot of your code is still tedious and redundant, then implicits might just be able to help you out. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 22 Implementing Lists Lists have been ubiquitous in this book. Class List is probably the most commonly used structured data type in Scala. Chapter 16 showed you how to use lists. This chapter “opens up the covers” and explains a bit how lists are implemented in Scala. Knowing the internals of the List class is useful for several reasons. You gain a better idea of the relative efficiency of list operations, which will help you in writing fast and compact code using lists. You also learn a toolbox of techniques that you can apply in the design of your own libraries. Finally, the List class is a sophisticated application of Scala’s type system in general and its genericity concepts in particular. So studying class List will deepen your knowledge in these areas. 22.1 The List class in principle Lists are not “built-in” as a language construct in Scala; they are defined by an abstract class List in the scala package, which comes with two sub- classes for :: and Nil. In the following we present a quick tour through class List. This section presents a somewhat simplified account of the class, compared to its real implementation in the Scala standard library, which is covered in Section 22.3. package scala abstract class List[+T] { List is an abstract class, so you cannot define elements by calling the empty List constructor. For instance the expression “new List” would be ille- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.1 Chapter 22 · Implementing Lists 504 scala ::[T] «final case» scala Nil «case object» scala List[+T] «sealed abstract» Figure 22.1· Class hierarchy for Scala lists. gal. The class has a type parameter T. The + in front of this type parameter specifies that lists are covariant, as discussed in Chapter 19. Because of this property, you can assign a value of type List[Int], say, to a variable of type List[Any]: scala> val xs = List(1, 2, 3) xs: List[Int] = List(1, 2, 3) scala> var ys: List[Any] = xs ys: List[Any] = List(1, 2, 3) All list operations can be defined in terms of three basic methods: def isEmpty: Boolean def head: T def tail: List[T] These three methods are all abstract in class List. They are defined in the subobject Nil and the subclass ::. The hierarchy for List is shown in Fig- ure 22.1. The Nil object The Nil object defines an empty list. Its definition is shown in Listing 22.1. The Nil object inherits from type List[Nothing]. Because of covariance, this means that Nil is compatible with every instance of the List type. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.1 Chapter 22 · Implementing Lists 505 case object Nil extends List[Nothing] { override def isEmpty = true def head: Nothing = throw new NoSuchElementException("head of empty list") def tail: List[Nothing] = throw new NoSuchElementException("tail of empty list") } Listing 22.1· The definition of the Nil singleton object. The three abstract methods of class List are implemented in the Nil object in a straightforward way: the isEmpty method returns true and the head and tail methods both throw an exception. Note that throwing an exception is not only reasonable, but practically the only possible thing to do for head: Because Nil is a List of Nothing, the result type of head must be Nothing. Since there is no value of this type, this means that head cannot return a normal value. It has to return abnormally by throwing an exception.1 The :: class Class ::, pronounced “cons” for “construct,” represents non-empty lists. It’s named that way in order to support pattern matching with the infix ::. You have seen in Section 16.5 that every infix operation in a pattern is treated as a constructor application of the infix operator to its arguments. So the pattern x :: xs is treated as ::(x, xs) where :: is a case class. Here is the definition of the :: class: final case class ::[T](hd: T, tl: List[T]) extends List[T] { def head = hd def tail = tl override def isEmpty: Boolean = false } The implementation of the :: class is straightforward. It takes two parame- ters hd and tl, representing the head and the tail of the list to be constructed. 1To be precise, the types would also permit for head to always go into an infinite loop instead of throwing an exception, but this is clearly not what’s wanted. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.1 Chapter 22 · Implementing Lists 506 The definitions of the head and tail method simply return the correspond- ing parameter. In fact, this pattern can be abbreviated by letting the parame- ters directly implement the head and tail methods of the superclass List, as in the following equivalent but shorter definition of the :: class: final case class ::[T](head: T, tail: List[T]) extends List[T] { override def isEmpty: Boolean = false } This works because every case class parameter is implicitly also a field of the class (it’s like the parameter declaration was prefixed with val). Recall from Section 20.3 that Scala allows you to implement an abstract parameterless method such as head or tail with a field. So the code above directly uses the parameters head and tail as implementations of the abstract methods head and tail that were inherited from class List. Some more methods All other List methods can be written using the basic three. For instance: def length: Int = if (isEmpty) 0 else 1 + tail.length or: def drop(n: Int): List[T] = if (isEmpty) Nil else if (n <= 0) this else tail.drop(n - 1) or: def map[U](f: T => U): List[U] = if (isEmpty) Nil else f(head) :: tail.map(f) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.1 Chapter 22 · Implementing Lists 507 List construction The list construction methods :: and ::: are special. Because they end in a colon, they are bound to their right operand. That is, an operation such as x :: xs is treated as the method call xs.::(x), not x.::(xs). In fact, x.::(xs) would not make sense, as x is of the list element type, which can be arbitrary, so we cannot assume that this type would have a :: method. For this reason, the :: method should take an element value and yield a new list. What is the required type of the element value? You might be tempted to say, it should be the same as the list’s element type, but in fact this is more restrictive than necessary. To see why, consider this class hierarchy: abstract class Fruit class Apple extends Fruit class Orange extends Fruit Listing 22.2 shows what happens when you construct lists of fruit: scala> val apples = new Apple :: Nil apples: List[Apple] = List(Apple@585fa9) scala> val fruits = new Orange :: apples fruits: List[Fruit] = List(Orange@cd6798, Apple@585fa9) Listing 22.2· Prepending a supertype element to a subtype list. The apples value is treated as a List of Apples, as expected. However, the definition of fruits shows that it’s still possible to add an element of a different type to that list. The element type of the resulting list is Fruit, which is the most precise common supertype of the original list element type (i.e., Apple) and the type of the element to be added (i.e., Orange). This flexibility is obtained by defining the :: method (cons) as shown in Listing 22.3: def ::[U >: T](x: U): List[U] = new scala.::(x, this) Listing 22.3· The definition of method :: (cons) in class List. Note that the method is itself polymorphic—it takes a type parameter named U. Furthermore, U is constrained in [U >: T] to be a supertype of the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.1 Chapter 22 · Implementing Lists 508 head apples Nil Apple :: tail head fruits Orange :: tail Figure 22.2· The structure of the Scala lists shown in Listing 22.2. list element type T. The element to be added is required to be of type U and the result is a List[U]. With the formulation of :: shown in Listing 22.3, you can check how the definition of fruits shown in Listing 22.2 works out type-wise: in that def- inition the type parameter U of :: is instantiated to Fruit. The lower-bound constraint of U is satisfied, because the list apples has type List[Apple] and Fruit is a supertype of Apple. The argument to the :: is new Orange, which conforms to type Fruit. Therefore, the method application is type- correct with result type List[Fruit]. Figure 22.2 illustrates the structure of the lists that result from executing the code shown in Listing 22.3. In fact, the polymorphic definition of :: with the lower bound T is not only convenient; it is also necessary to render the definition of class List type-correct. This is because Lists are defined to be covariant. Assume for a moment that we had defined :: like this: // A thought experiment (which wouldn’t work) def ::(x: T): List[T] = new scala.::(x, this) You saw in Chapter 19 that method parameters count as contravariant posi- tions, so the list element type T is in contravariant position in the definition above. But then List cannot be declared covariant in T. The lower bound [U >: T] thus kills two birds with one stone: it removes a typing problem, and it leads to a :: method that’s more flexible to use. The list concatenation method ::: is defined in a similar way to ::, as shown in Listing 22.4. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.2 Chapter 22 · Implementing Lists 509 def :::[U >: T](prefix: List[U]): List[U] = if (prefix.isEmpty) this else prefix.head :: prefix.tail ::: this Listing 22.4· The definition of method ::: in class List. Like cons, concatenation is polymorphic. The result type is “widened” as necessary to include the types of all list elements. Note also that again the order of the arguments is swapped between an infix operation and an explicit method call. Because both ::: and :: end in a colon, they both bind to the right and are both right associative. For instance, the else part of the definition of ::: shown in Listing 22.4 contains infix operations of both :: and :::. These infix operations can be expanded to equivalent method calls as follows: prefix.head :: prefix.tail ::: this equals (because :: and ::: are right-associative) prefix.head :: (prefix.tail ::: this) equals (because :: binds to the right) (prefix.tail ::: this).::(prefix.head) equals (because ::: binds to the right) this.:::(prefix.tail).::(prefix.head) 22.2 The ListBuffer class The typical access pattern for a list is recursive. For instance, to increment every element of a list without using map you could write: def incAll(xs: List[Int]): List[Int] = xs match { case List() => List() case x :: xs1 => x + 1 :: incAll(xs1) } One shortcoming of this program pattern is that it is not tail recursive. Note that the recursive call to incAll above occurs inside a :: operation. There- fore each recursive call requires a new stack frame. On today’s virtual ma- Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.2 Chapter 22 · Implementing Lists 510 chines this means that you cannot apply incAll to lists of much more than about 30,000 to 50,000 elements. This is a pity. How do you write a version of incAll that can work on lists of arbitrary size (as much as heap-capacity allows)? One approach is to use a loop: for (x <- xs) // ?? But what should go in the loop body? Note that where incAll above con- structs the list by prepending elements to the result of the recursive call, the loop needs to append new elements at the end of the result list. One, very inefficient possibility is to use :::, the list append operator: var result = List[Int]() // a very inefficient approach for (x <- xs) result = result ::: List(x + 1) result This has terrible efficiency, though. Because ::: takes time proportional to the length of its first operand, the whole operation takes time proportional to the square of the length of the list. This is clearly unacceptable. A better alternative is to use a list buffer. List buffers let you accumulate the elements of a list. To do this, you use an operation such as “buf += elem”, which appends the element elem at the end of the list buffer buf. Once you are done appending elements, you can turn the buffer into a list using the toList operation. ListBuffer is a class in package scala.collection.mutable. To use the simple name only, you can import ListBuffer from its package: import scala.collection.mutable.ListBuffer Using a list buffer, the body of incAll can now be written as follows: val buf = new ListBuffer[Int] for (x <- xs) buf += x + 1 buf.toList This is a very efficient way to build lists. In fact, the list buffer implemen- tation is organized so that both the append operation (+=) and the toList operation take (very short) constant time. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.3 Chapter 22 · Implementing Lists 511 22.3 The List class in practice The implementations of list methods given in Section 22.1 are concise and clear, but suffer from the same stack overflow problem as the non-tail re- cursive implementation of incAll. Therefore, most methods in the real im- plementation of class List avoid recursion and use loops with list buffers instead. For example, Listing 22.5 shows the real implementation of map in class List: final override def map[U](f: T => U): List[U] = { val b = new ListBuffer[U] var these = this while (!these.isEmpty) { b += f(these.head) these = these.tail } b.toList } Listing 22.5· The definition of method map in class List. This revised implementation traverses the list with a simple loop, which is highly efficient. A tail recursive implementation would be similarly ef- ficient, but a general recursive implementation would be slower and less scalable. But what about the operation b.toList at the end? What is its complexity? In fact, the call to the toList method takes only a small num- ber of cycles, which is independent of the length of the list. To understand why, take a second look at class ::, which constructs non- empty lists. In practice, this class does not quite correspond to its idealized definition given previously in Section 22.1. The real definition is shown in Listing 22.6. There’s one peculiarity: the tl argument is a var! This means that it is possible to modify the tail of a list after the list is constructed. However, be- cause the variable tl has the modifier private[scala], it can be accessed only from within package scala. Client code outside this package can nei- ther read nor write tl. Since the ListBuffer class is contained in a subpackage of package scala, scala.collection.mutable, ListBuffer can access the tl field Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.3 Chapter 22 · Implementing Lists 512 final case class ::[U](hd: U, private[scala] var tl: List[U]) extends List[U] { def head = hd def tail = tl override def isEmpty: Boolean = false } Listing 22.6· The definition of the :: subclass of List. of a cons cell. In fact the elements of a list buffer are represented as a list and appending new elements involves a modification of tl field of the last :: cell in that list. Here’s the start of class ListBuffer: package scala.collection.immutable final class ListBuffer[T] extends Buffer[T] { private var start: List[T] = Nil private var last0: ::[T] = _ private var exported: Boolean = false ... You see three private fields that characterize a ListBuffer: start points to the list of all elements stored in the buffer last0 points to the last :: cell in that list exported indicates whether the buffer has been turned into a list using a toList operation The toList operation is very simple: override def toList: List[T] = { exported = !start.isEmpty start } It returns the list of elements referred to by start and also sets exported to true if that list is nonempty. So toList is very efficient, because it does not copy the list which is stored in a ListBuffer. But what happens if the list is further extended after the toList operation? Of course, once a list Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.4 Chapter 22 · Implementing Lists 513 is returned from toList, it must be immutable. However, appending to the last0 element will modify the list which is referred to by start. To maintain the correctness of the list buffer operations, you need to work on a fresh list instead. This is achieved by the first line in the implementation of the += operation: override def += (x: T) { if (exported) copy() if (start.isEmpty) { last0 = new scala.::(x, Nil) start = last0 } else { val last1 = last0 last0 = new scala.::(x, Nil) last1.tl = last0 } } You see that += copies the list pointed to by start if exported is true. So, in the end, there is no free lunch. If you want to go from lists which can be extended at the end to immutable lists, there needs to be some copying. However, the implementation of ListBuffer is such that copying is neces- sary only for list buffers that are further extended after they have been turned into lists. This case is quite rare in practice. Most use cases of list buffers add elements incrementally and then do one toList operation at the end. In such cases, no copying is necessary. 22.4 Functional on the outside The previous section showed key elements of the implementation of Scala’s List and ListBuffer classes. You saw that lists are purely functional on the “outside” but have an imperative implementation using list buffers on the “inside.” This is a typical strategy in Scala programming: trying to com- bine purity with efficiency by carefully delimiting the effects of impure op- erations. You might ask, why insist on purity? Why not just open up the definition of lists, making the tail field, and maybe also the head field, mu- table? The disadvantage of such an approach is that it would make programs Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.5 Chapter 22 · Implementing Lists 514 much more fragile. Note that constructing lists with :: re-uses the tail of the constructed list. So when you write: val ys = 1 :: xs val zs = 2 :: xs the tails of lists ys and zs are shared; they point to the same data structure. This is essential for efficiency; if the list xs was copied every time you added a new element onto it, this would be much slower. Because sharing is per- vasive, changing list elements, if it were possible, would be quite dangerous. For instance, taking the code above, if you wanted to truncate list ys to its first two elements by writing: ys.drop(2).tail = Nil // can’t do this in Scala! you would also truncate lists zs and xs as a side effect. Clearly, it would be quite difficult to keep track of what gets changed. That’s why Scala opts for pervasive sharing and no mutation for lists. The ListBuffer class still al- lows you to build up lists imperatively and incrementally, if you wish to. But since list buffers are not lists, the types keep mutable buffers and immutable lists separate. The design of Scala’s List and ListBuffer is quite similar to what’s done in Java’s pair of classes String and StringBuffer. This is no coinci- dence. In both situations the designers wanted to maintain a pure immutable data structure but also wanted to provide an efficient way to construct this structure incrementally. For Java and Scala strings, StringBuffers (or, in Java 5, StringBuilders) provide a way to construct a string incrementally. For Scala’s lists, you have a choice: You can either construct lists incremen- tally by adding elements to the beginning of a list using ::, or you use a list buffer for adding elements to the end. Which one is preferable depends on the situation. Usually, :: lends itself well to recursive algorithms in the divide-and-conquer style. List buffers are often used in a more traditional loop-based style. 22.5 Conclusion In this chapter, you saw how lists are implemented in Scala. List is one of the most heavily used data structures in Scala, and it has a refined implemen- tation. List’s two subclasses, Nil and ::, are both case classes. Instead of Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 22.5 Chapter 22 · Implementing Lists 515 recursing through this structure, however, many core list methods are imple- mented using a ListBuffer. ListBuffer, in turn, is carefully implemented so that it can efficiently build lists without allocating extraneous memory. It is functional on the outside, but uses mutation internally to speed up the common case where a buffer is discarded after toList is been called. After studying all of this, you now know the list classes inside and out, and you might have learned an implementation trick or two. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 23 For Expressions Revisited Chapter 16 demonstrated that higher-order functions such as map, flatMap, and filter provide powerful constructions for dealing with lists. But some- times the level of abstraction required by these functions makes a program a bit hard to understand. Here’s an example. Say you are given a list of per- sons, each defined as an instance of a class Person. Class Person has fields indicating the person’s name, whether (s)he is male, and his/her children. Here’s the class definition: scala> case class Person(name: String, isMale: Boolean, children: Person*) Here’s a list of some sample persons: val lara = Person("Lara", false) val bob = Person("Bob", true) val julie = Person("Julie", false, lara, bob) val persons = List(lara, bob, julie) Now, say you want to find out the names of all pairs of mothers and their children in that list. Using map, flatMap and filter, you can formulate the following query: scala> persons filter (p => !p.isMale) flatMap (p => (p.children map (c => (p.name, c.name)))) res0: List[(String, String)] = List((Julie,Lara), (Julie,Bob)) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.1 Chapter 23 · For Expressions Revisited 517 You could optimize this example bit by using a withFilter call instead of filter. This would avoid the creation of an intermediate data structure for male persons: scala> persons withFilter (p => !p.isMale) flatMap (p => (p.children map (c => (p.name, c.name)))) res1: List[(String, String)] = List((Julie,Lara), (Julie,Bob)) These queries do their job, but they are not exactly trivial to write or un- derstand. Is there a simpler way? In fact, there is. Remember the for expressions in Section 7.3? Using a for expression, the same example can be written as follows: scala> for (p <- persons; if !p.isMale; c <- p.children) yield (p.name, c.name) res2: List[(String, String)] = List((Julie,Lara), (Julie,Bob)) The result of this expression is exactly the same as the result of the previous expression. What’s more, most readers of the code would likely find the for expression much clearer than the previous query, which used the higher- order functions, map, flatMap, and withFilter. However, the last two queries are not as dissimilar as it might seem. In fact, it turns out that the Scala compiler will translate the second query into the first one. More generally, all for expressions that yield a re- sult are translated by the compiler into combinations of invocations of the higher-order methods map, flatMap, and withFilter. All for loops with- out yield are translated into a smaller set of higher-order functions: just withFilter and foreach. In this chapter, you’ll find out first about the precise rules of writing for expressions. After that, you’ll see how they can make combinatorial prob- lems easier to solve. Finally, you’ll learn how for expressions are translated, and how as a result, for expressions can help you “grow” the Scala language into new application domains. 23.1 For expressions Generally, a for expression is of the form: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.1 Chapter 23 · For Expressions Revisited 518 for ( seq ) yield expr Here, seq is a sequence of generators, definitions, and filters, with semi- colons between successive elements. An example is the for expression: for (p <- persons; n = p.name; if (n startsWith "To")) yield n This for expression contains one generator, one definition, and one filter. As mentioned in Section 7.3 on page 167, you can also enclose the sequence in braces instead of parentheses. Then the semicolons become optional: for { p <- persons // a generator n = p.name // a definition if (n startsWith "To") // a filter } yield n A generator is of the form: pat <- expr The expression expr typically returns a list, even though you will see later that this can be generalized. The pattern pat gets matched one-by-one against all elements of that list. If the match succeeds, the variables in the pattern get bound to the corresponding parts of the element, just the way it is described in Chapter 15. But if the match fails, no MatchError is thrown. Instead, the element is simply discarded from the iteration. In the most common case, the pattern pat is just a variable x, as in x <- expr. In that case, the variable x simply iterates over all elements returned by expr. A definition is of the form: pat = expr This definition binds the pattern pat to the value of expr. So it has the same effect as a val definition: val x = expr The most common case is again where the pattern is a simple variable x, e.g., x = expr. This defines x as a name for the value expr. A filter is of the form: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.2 Chapter 23 · For Expressions Revisited 519 if expr Here, expr is an expression of type Boolean. The filter drops from the itera- tion all elements for which expr returns false. Every for expression starts with a generator. If there are several genera- tors in a for expression, later generators vary more rapidly than earlier ones. You can verify this easily with the following simple test: scala> for (x <- List(1, 2); y <- List("one", "two")) yield (x, y) res3: List[(Int, java.lang.String)] = List((1,one), (1,two), (2,one), (2,two)) 23.2 The n-queens problem A particularly suitable application area of for expressions are combinatorial puzzles. An example of such a puzzle is the 8-queens problem: Given a standard chess-board, place eight queens such that no queen is in check from any other (a queen can check another piece if they are on the same column, row, or diagonal). To find a solution to this problem, it’s actually simpler to generalize it to chess-boards of arbitrary size. Hence, the problem is to place N queens on a chess-board of N × N squares, where the size N is arbitrary. We’ll start numbering cells at one, so the upper-left cell of an N × N board has coordinate (1,1), and the lower-right cell has coordinate (N,N). To solve the N-queens problem, note that you need to place a queen in each row. So you could place queens in successive rows, each time checking that a newly placed queen is not in check from any other queens that have already been placed. In the course of this search, it might arrive that a queen that needs to be placed in row k would be in check in all fields of that row from queens in row 1 to k − 1. In that case, you need to abort that part of the search in order to continue with a different configuration of queens in columns 1 to k −1. An imperative solution to this problem would place queens one by one, moving them around on the board. But it looks difficult to come up with a scheme that really tries all possibilities. A more functional approach represents a solution directly, as a value. A solution consists of a list of coordinates, one for each queen placed on the Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.2 Chapter 23 · For Expressions Revisited 520 board. Note, however, that a full solution can not be found in a single step. It needs to be built up gradually, by occupying successive rows with queens. This suggests a recursive algorithm. Assume you have already generated all solutions of placing k queens on a board of size N ×N, where k is less than N. Each such solution can be presented by a list of length k of coordinates (row, column), where both row and column numbers range from 1 to N. It’s convenient to treat these partial solution lists as stacks, where the coordinates of the queen in row k come first in the list, followed by the coordinates of the queen in row k −1, and so on. The bottom of the stack is the coordinate of the queen placed in the first row of the board. All solutions together are represented as a list of lists, with one element for each solution. Now, to place the next queen in row k + 1, generate all possible exten- sions of each previous solution by one more queen. This yields another list of solution lists, this time of length k +1. Continue the process until you have obtained all solutions of the size of the chess-board N. This algorithmic idea is embodied in function placeQueens below: def queens(n: Int): List[List[(Int, Int)]] = { def placeQueens(k: Int): List[List[(Int, Int)]] = if (k == 0) List(List()) else for { queens <- placeQueens(k - 1) column <- 1 to n queen = (k, column) if isSafe(queen, queens) } yield queen :: queens placeQueens(n) } The outer function queens in the program above simply calls placeQueens with the size of the board n as its argument. The task of the function applica- tion placeQueens(k) is to generate all partial solutions of length k in a list. Every element of the list is one solution, represented by a list of length k. So placeQueens returns a list of lists. If the parameter k to placeQueens is 0, this means that it needs to gen- erate all solutions of placing zero queens on zero rows. There is exactly Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.2 Chapter 23 · For Expressions Revisited 521 one such solution: place no queen at all. This solution is represented by the empty list. So if k is zero, placeQueens returns List(List()), a list con- sisting of a single element that is the empty list. Note that this is quite differ- ent from the empty list List(). If placeQueens returns List(), this means no solutions, instead of a single solution consisting of no placed queens. In the other case, where k is not zero, all the work of placeQueens is done in a for expression. The first generator of that for expression iterates through all solutions of placing k - 1 queens on the board. The second gen- erator iterates through all possible columns on which the k’th queen might be placed. The third part of the for expression defines the newly consid- ered queen position to be the pair consisting of row k and each produced column. The fourth part of the for expression is a filter which checks with isSafe whether the new queen is safe from check of all previous queens (the definition of isSafe will be discussed a bit later). If the new queen is not in check from any other queens, it can form part of a partial solution, so placeQueens generates with queen :: queens a new solution. If the new queen is not safe from check, the filter returns false, so no solution is generated. The only remaining bit is the isSafe method, which is used to check whether a given queen is in check from any other element in a list of queens. Here is its definition: def isSafe(queen: (Int, Int), queens: List[(Int, Int)]) = queens forall (q => !inCheck(queen, q)) def inCheck(q1: (Int, Int), q2: (Int, Int)) = q1._1 == q2._1 || // same row q1._2 == q2._2 || // same column (q1._1 - q2._1).abs == (q1._2 - q2._2).abs // on diagonal The isSafe method expresses that a queen is safe with respect to some other queens if it is not in check from any other queen. The inCheck method expresses that queens q1 and q2 are mutually in check. It returns true in one of three cases: 1. If the two queens have the same row coordinate, 2. If the two queens have the same column coordinate, 3. If the two queens are on the same diagonal, i.e., the difference between their rows and the difference between their columns are the same. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.3 Chapter 23 · For Expressions Revisited 522 The first case, that the two queens have the same row coordinate, cannot happen in the application because placeQueens already takes care to place each queen in a different row. So you could remove the test without changing the functionality of the program as a whole. 23.3 Querying with for expressions The for notation is essentially equivalent to common operations of database query languages. For instance, say you are given a database named books, represented as a list of books, where Book is defined as follows: case class Book(title: String, authors: String*) Here is a small example database, represented as an in-memory list: val books: List[Book] = List( Book( "Structure and Interpretation of Computer Programs", "Abelson, Harold", "Sussman, Gerald J." ), Book( "Principles of Compiler Design", "Aho, Alfred", "Ullman, Jeffrey" ), Book( "Programming in Modula-2", "Wirth, Niklaus" ), Book( "Elements of ML Programming", "Ullman, Jeffrey" ), Book( "The Java Language Specification", "Gosling, James", "Joy, Bill", "Steele, Guy", "Bracha, Gilad" ) ) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.3 Chapter 23 · For Expressions Revisited 523 Then, to find the titles of all books whose author’s last name is “Gosling”: scala> for (b <- books; a <- b.authors if a startsWith "Gosling") yield b.title res4: List[String] = List(The Java Language Specification) Or, to find the titles of all books that have the string “Program” in their title: scala> for (b <- books if (b.title indexOf "Program") >= 0) yield b.title res5: List[String] = List(Structure and Interpretation of Computer Programs, Programming in Modula-2, Elements of ML Programming) Or, to find the names of all authors that have written at least two books in the database: scala> for (b1 <- books; b2 <- books if b1 != b2; a1 <- b1.authors; a2 <- b2.authors if a1 == a2) yield a1 res6: List[String] = List(Ullman, Jeffrey, Ullman, Jeffrey) The last solution is not yet perfect, because authors will appear several times in the list of results. You still need to remove duplicate authors from result lists. This can be achieved with the following function: scala> def removeDuplicates[A](xs: List[A]): List[A] = { if (xs.isEmpty) xs else xs.head :: removeDuplicates( xs.tail filter (x => x != xs.head) ) } removeDuplicates: [A](xs: List[A])List[A] scala> removeDuplicates(res6) res7: List[String] = List(Ullman, Jeffrey) It’s worth noting that the last expression in method removeDuplicates can be equivalently expressed using a for expression: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.4 Chapter 23 · For Expressions Revisited 524 xs.head :: removeDuplicates( for (x <- xs.tail if x != xs.head) yield x ) 23.4 Translation of for expressions Every for expression can be expressed in terms of the three higher-order functions map, flatMap, and withFilter. This section describes the trans- lation scheme, which is also used by the Scala compiler. Translating for expressions with one generator First, assume you have a simple for expression: for (x <- expr1) yield expr2 where x is a variable. Such an expression is translated to: expr1.map(x => expr2) Translating for expressions starting with a generator and a filter Now, consider for expressions that combine a leading generator with some other elements. A for expression of the form: for (x <- expr1 if expr2) yield expr3 is translated to: for (x <- expr1 withFilter (x => expr2)) yield expr3 This translation gives another for expression that is shorter by one element than the original, because an if element is transformed into an application of withFilter on the first generator expression. The translation then continues with this second expression, so in the end you obtain: expr1 withFilter (x => expr2) map (x => expr3) The same translation scheme also applies if there are further elements fol- lowing the filter. If seq is an arbitrary sequence of generators, definitions and filters, then: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.4 Chapter 23 · For Expressions Revisited 525 for (x <- expr1 if expr2; seq) yield expr3 is translated to: for (x <- expr1 withFilter expr2; seq) yield expr3 Then translation continues with the second expression, which is again shorter by one element than the original one. Translating for expressions starting with two generators The next case handles for expressions that start with two generators, as in: for (x <- expr1; y <- expr2; seq) yield expr3 Again, assume that seq is an arbitrary sequence of generators, definitions and filters. In fact, seq might also be empty, and in that case there would not be a semicolon after expr2. The translation scheme stays the same in each case. The for expression above is translated to an application of flatMap: expr1.flatMap(x => for (y <- expr2; seq) yield expr3) This time, there is another for expression in the function value passed to flatMap. That for expression (which is again simpler by one element than the original) is in turn translated with the same rules. The three translation schemes given so far are sufficient to translate all for expressions that contain just generators and filters, and where generators bind only simple variables. Take for instance the query, “find all authors who have published at least two books,” from Section 23.3: for (b1 <- books; b2 <- books if b1 != b2; a1 <- b1.authors; a2 <- b2.authors if a1 == a2) yield a1 This query translates to the following map/flatMap/filter combination: books flatMap (b1 => books withFilter (b2 => b1 != b2) flatMap (b2 => b1.authors flatMap (a1 => b2.authors withFilter (a2 => a1 == a2) map (a2 => a1)))) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.4 Chapter 23 · For Expressions Revisited 526 The translation scheme presented so far does not yet handle generators that bind whole patterns instead of simple variables. It also does not yet cover definitions. These two aspects will be explained in the next two sub-sections. Translating patterns in generators The translation scheme becomes more complicated if the left hand side of generator is a pattern, pat, other than a simple variable. Still relatively easy to handle is the case where the for expression binds a tuple of variables. In that case, almost the same scheme as for single variables applies. A for expression of the form: for ((x1, ..., xn) <- expr1) yield expr2 translates to: expr1.map { case (x1, ..., xn) => expr2 } Things become a bit more involved if the left hand side of the generator is an arbitrary pattern pat instead of a single variable or a tuple. In this case: for (pat <- expr1) yield expr2 translates to: expr1 withFilter { case pat => true case _ => false } map { case pat => expr2 } That is, the generated items are first filtered and only those that match pat are mapped. Therefore, it’s guaranteed that a pattern-matching generator will never throw a MatchError. The scheme above only treated the case where the for expression con- tains a single pattern-matching generator. Analogous rules apply if the for expression contains other generators, filters, or definitions. Because these additional rules don’t add much new insight, they are omitted from discus- sion here. If you are interested, you can look them up in the Scala Language Specification [Ode08]. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.4 Chapter 23 · For Expressions Revisited 527 Translating definitions The last missing situation is where a for expression contains embedded def- initions. Here’s a typical case: for (x <- expr1; y = expr2; seq) yield expr3 Assume again that seq is a (possibly empty) sequence of generators, defini- tions, and filters. This expression is translated to the following one: for ((x, y) <- for (x <- expr1) yield (x, expr2); seq) yield expr3 So you see that expr2 is evaluated each time there is a new x value being generated. This re-evaluation is necessary, because expr2 might refer to x and so needs to be re-evaluated for changing values of x. For you as a programmer the conclusion is that it’s probably not a good idea to have defi- nitions embedded in for expressions that do not refer to variables bound by some preceding generator, because re-evaluating such expressions would be wasteful. For instance, instead of: for (x <- 1 to 1000; y = expensiveComputationNotInvolvingX) yield x * y it’s usually better to write: val y = expensiveComputationNotInvolvingX for (x <- 1 to 1000) yield x * y Translating for loops The previous subsections showed how for expressions that contain a yield are translated. What about for loops that simply perform a side effect with- out returning anything? Their translation is similar, but simpler than for expressions. In principle, wherever the previous translation scheme used a map or a flatMap in the translation, the translation scheme for for loops uses just a foreach. For instance, the expression: for (x <- expr1) body translates to: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.5 Chapter 23 · For Expressions Revisited 528 expr1 foreach (x => body) A larger example is the expression: for (x <- expr1; if expr2; y <- expr3) body This expression translates to: expr1 withFilter (x => expr2) foreach (x => expr3 foreach (y => body)) For example, the following expression sums up all elements of a matrix rep- resented as a list of lists: var sum = 0 for (xs <- xss; x <- xs) sum += x This loop is translated into two nested foreach applications: var sum = 0 xss foreach (xs => xs foreach (x => sum += x)) 23.5 Going the other way The previous section showed that for expressions can be translated into ap- plications of the higher-order functions map, flatMap, and withFilter. In fact, you could equally well go the other way: every application of a map, flatMap, or filter can be represented as a for expression. Here are im- plementations of the three methods in terms of for expressions. The meth- ods are contained in an object Demo, to distinguish them from the standard operations on Lists. To be concrete, the three functions all take a List as parameter, but the translation scheme would work just as well with other collection types: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.6 Chapter 23 · For Expressions Revisited 529 object Demo { def map[A, B](xs: List[A], f: A => B): List[B] = for (x <- xs) yield f(x) def flatMap[A, B](xs: List[A], f: A => List[B]): List[B] = for (x <- xs; y <- f(x)) yield y def filter[A](xs: List[A], p: A => Boolean): List[A] = for (x <- xs if p(x)) yield x } Not surprisingly, the translation of the for expression used in the body of Demo.map will produce a call to map in class List. Similarly, Demo.flatMap and Demo.filter translate to flatMap and withFilter in class List. So this little demonstration has shown that for expressions really are equivalent in their expressiveness to applications of the three functions map, flatMap, and withFilter. 23.6 Generalizing for Because the translation of for expressions only relies on the presence of methods map, flatMap, and withFilter, it is possible to apply the for notation to a large class of data types. You have already seen for expressions over lists and arrays. These are supported because lists, as well as arrays, define operations map, flatMap, and withFilter. Because they define a foreach method as well, for loops over these data types are also possible. Besides lists and arrays, there are also many other types in the Scala stan- dard library that support the same four methods and therefore allow for ex- pressions. Examples are ranges, iterators, streams, and all implementations of sets. It’s also perfectly possible for your own data types to support for ex- pressions by defining the necessary methods. To support the full range of for expressions and for loops, you need to define map, flatMap, withFilter, and foreach as methods of your data type. But it’s also possible to define a subset of these methods, and thereby support a subset of all possible for expressions or loops. Here are the precise rules: • If your type defines just map, it allows for expressions consisting of a single generator. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.6 Chapter 23 · For Expressions Revisited 530 • If it defines flatMap as well as map, it allows for expressions consist- ing of several generators. • If it defines foreach, it allows for loops (both with single and multi- ple generators). • If it defines withFilter, it allows for filter expressions starting with an if in the for expression. The translation of for expressions happens before type checking. This al- lows for maximal flexibility, because it is only required that the result of expanding a for expression type checks. Scala defines no typing rules for the for expressions themselves, and does not require that methods map, flatMap, withFilter, or foreach to have any particular type signatures. Nevertheless, there is a typical setup that captures the most common intention of the higher order methods to which for expressions translate. Say you have a parameterized class, C, which typically would stand for some sort of collection. Then it’s quite natural to pick the following type signatures for map, flatMap, withFilter, and foreach: abstract class C[A] { def map[B](f: A => B): C[B] def flatMap[B](f: A => C[B]): C[B] def withFilter(p: A => Boolean): C[A] def foreach(b: A => Unit): Unit } That is, the map function takes a function from the collection’s element type A to some other type B. It produces a new collection of the same kind C, but with B as the element type. The flatMap method takes a function f from A to some C-collection of Bs and produces a C-collection of Bs. The withFilter method takes a predicate function from the collection’s element type A to Boolean. It produces a collection of the same type as the one on which it is invoked. Finally, the foreach method takes a function from A to Unit, and produces a Unit result. In class C above, the withFilter method produces a new collection of the same class. That means that every invocation of withFilter creates a new C object, just the same as filter would work. Now, in the translation of for expressions, any calls to withFilter are always followed by calls to one of the other three methods. Therefore, the object created by withFilter Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 23.7 Chapter 23 · For Expressions Revisited 531 will be immediately afterwards taken apart by one of the other methods. If objects of class C are large (think long sequences), you might want to avoid the creation of such an intermediate object. A standard technique is to let withFilter return not a C object but just a wrapper object that “remembers” that elements need to be filtered before being processed further. Concentrating on just the first three functions of class C, the following facts are noteworthy. In functional programming, there’s a general concept called a monad, which can explain a large number of types with computa- tions, ranging from collections, to computations with state and I/O, back- tracking computations, and transactions, to name but a few. You can for- mulate functions map, flatMap, and withFilter on a monad, and, if you do, they end up having exactly the types given above. Furthermore, you can characterize every monad by map, flatMap, and withFilter, plus a “unit” constructor that produces a monad from an element value. In an object- oriented language, this “unit” constructor is simply an instance constructor or a factory method. Therefore, map, flatMap and withFilter can be seen as an object-oriented version of the functional concept of monad. Because for expressions are equivalent to applications of these three methods, they can be seen as syntax for monads. All this suggests that the concept of for expression is more general than just iteration over a collection, and indeed it is. For instance, for expressions also play an important role in asynchronous I/O, or as an alternative notation for optional values. Watch out in the Scala libraries for occurrences of map, flatMap, and withFilter—when they are present, for expressions suggest themselves as a concise way of manipulating elements of the type. 23.7 Conclusion In this chapter, you were given a peek under the hood of for expressions and for loops. You learned that they translate into applications of a standard set of higher-order methods. As a consequence of this, you saw that for expres- sions are really much more general than mere iterations over collections, and that you can design your own classes to support them. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Chapter 24 The Scala Collections API In the eyes of many, the new collections framework is the most significant change in Scala 2.8. Scala had collections before (and in fact the new frame- work is largely compatible with them). But it’s only 2.8 that provides a common, uniform, and all-encompassing framework for collection types. Even though the additions to collections are subtle at first glance, the changes they can provoke in your programming style can be profound. In fact, quite often it’s as if you work on a higher level with the basic building blocks of a program being whole collections instead of their elements. This new style of programming requires some adaptation. Fortunately, the adap- tation is helped by several nice properties of the new Scala collections. They are easy to use, concise, safe, fast, and universal. Easy to use: A small vocabulary of twenty to fifty methods is enough to solve most collection problems in a couple of operations. No need to wrap your head around complicated looping structures or recur- sions. Persistent collections and side-effect-free operations mean that you need not worry about accidentally corrupting existing collections with new data. Interference between iterators and collection updates is eliminated. Concise: You can achieve with a single word what used to take one or sev- eral loops. You can express functional operations with lightweight syntax and combine operations effortlessly, so that the result feels like a custom algebra. Safe: This one has to be experienced to sink in. The statically typed and functional nature of Scala’s collections means that the overwhelming Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.1 Chapter 24 · The Scala Collections API 533 majority of errors you might make are caught at compile-time. The reason is that (1) the collection operations themselves are heavily used and therefore well tested. (2) the usages of the collection operation make inputs and output explicit as function parameters and results. (3) These explicit inputs and outputs are subject to static type checking. The bottom line is that the large majority of misuses will manifest themselves as type errors. It’s not at all uncommon to have programs of several hundred lines run at first try. Fast: Collection operations are tuned and optimized in the libraries. As a re- sult, using collections is typically quite efficient. You might be able to do a little bit better with carefully hand-tuned data structures and oper- ations, but you might also do a lot worse by making some suboptimal implementation decisions along the way. What’s more, collections are currently being adapted to parallel execution on multi-cores. Paral- lel collections will support the same operations as sequential ones, so no new operations need to be learned and no code needs to be rewrit- ten. You will be able to turn a sequential collection into a parallel one simply by invoking the par method. Universal: Collections provide the same operations on any type where it makes sense to do so. So you can achieve a lot with a fairly small vocabulary of operations. For instance, a string is conceptually a se- quence of characters. Consequently, in Scala collections, strings sup- port all sequence operations. The same holds for arrays. This chapter describes in depth the APIs of the Scala 2.8 collection classes from a user perspective. You’ve already seen a quick tour of the collections library, in Chapter 17. This chapter takes you on a more detailed tour, showing all the collection classes and all the methods they define, so it includes everything you need to know to use Scala collections. Looking ahead, Chapter 25 will concentrate on the architecture and extensibility as- pects of the library, for people implementing new collection types. 24.1 Mutable and immutable collections As is now familiar to you, Scala collections systematically distinguish be- tween mutable and immutable collections. A mutable collection can be up- dated or extended in place. This means you can change, add, or remove Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.1 Chapter 24 · The Scala Collections API 534 elements of a collection as a side effect. Immutable collections, by contrast, never change. You still have operations that simulate additions, removals, or updates, but those operations will in each case return a new collection and leave the old collection unchanged. All collection classes are found in the package scala.collection or one of its subpackages: mutable, immutable, and generic. Most collec- tion classes needed by client code exist in three variants, each of which has different characteristics with respect to mutability. The three variants are located in packages scala.collection, scala.collection.immutable, and scala.collection.mutable. A collection in package scala.collection.immutable is guaranteed to be immutable for everyone. Such a collection will never change after it is created. Therefore, you can rely on the fact that accessing the same collection value repeatedly at different points in time will always yield a collection with the same elements. A collection in package scala.collection.mutable is known to have some operations that change the collection in place. These operations let you write code to mutate the collection yourself. However, you must be careful to understand and defend against any updates performed by other parts of the code base. A collection in package scala.collection can be either mutable or im- mutable. For instance, scala.collection.IndexedSeq[T] is a supertrait of both scala.collection.immutable.IndexedSeq[T] and its mutable sibling scala.collection.mutable.IndexedSeq[T]. Generally, the root collections in package scala.collection define the same interface as the immutable collections. And typically, the mutable collections in package scala.collection.mutable add some side-effecting modification opera- tions to this immutable interface. The difference between root collections and immutable collections is that clients of an immutable collection have a guarantee that nobody can mutate the collection, whereas clients of a root collection only know that they can’t change the collection themselves. Even though the static type of such a collection provides no operations for modifying the collection, it might still be possible that the run-time type is a mutable collection that can be changed by other clients. By default, Scala always picks immutable collections. For instance, if you just write Set without any prefix or without having imported anything, you get an immutable set, and if you write Iterable you get an immutable Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.2 Chapter 24 · The Scala Collections API 535 iterable, because these are the default bindings imported from the scala package. To get the mutable default versions, you need to write explicitly collection.mutable.Set, or collection.mutable.Iterable. The last package in the collection hierarchy is collection.generic. This package contains building blocks for implementing collections. Typ- ically, collection classes defer the implementations of some of their opera- tions to classes in generic. Everyday users of the collection framework on the other hand should need to refer to classes in generic only in exceptional circumstances. 24.2 Collections consistency The most important collection classes are shown in Figure 24.1. There is quite a bit of commonality shared by all these classes. For instance, every kind of collection can be created by the same uniform syntax, writing the collection class name followed by its elements: Traversable(1, 2, 3) Iterable("x", "y", "z") Map("x" -> 24, "y" -> 25, "z" -> 26) Set(Color.Red, Color.Green, Color.Blue) SortedSet("hello", "world") Buffer(x, y, z) IndexedSeq(1.0, 2.0) LinearSeq(a, b, c) The same principle also applies for specific collection implementations: List(1, 2, 3) HashMap("x" -> 24, "y" -> 25, "z" -> 26) The toString methods for all collections produce output written as above, with a type name followed by the elements of the collection in parentheses. All collections support the API provided by Traversable, but their meth- ods all return their own class rather than the root class Traversable. For instance, the map method on List has a return type of List, whereas the map method on Set has a return type of Set. Thus the static return type of these methods is fairly precise: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.2 Chapter 24 · The Scala Collections API 536 Traversable Iterable Seq IndexedSeq Vector ResizableArray GenericArray LinearSeq MutableList List Stream Buffer ListBuffer ArrayBuffer Set SortedSet TreeSet HashSet (mutable) LinkedHashSet HashSet (immutable) BitSet EmptySet, Set1, Set2, Set3, Set4 Map SortedMap TreeMap HashMap (mutable) LinkedHashMap (mutable) HashMap (immutable) EmptyMap, Map1, Map2, Map3, Map4 Figure 24.1· Collection hierarchy. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.3 Chapter 24 · The Scala Collections API 537 scala> List(1, 2, 3) map (_ + 1) res0: List[Int] = List(2, 3, 4) scala> Set(1, 2, 3) map (_ * 2) res1: scala.collection.immutable.Set[Int] = Set(2, 4, 6) Equality is also organized uniformly for all collection classes; more on this in Section 24.14. Most of the classes in Figure 24.1 exist in three variants: root, mutable, and immutable. The only exception is the Buffer trait, which only exists as a mutable collection. In the remainder of this chapter, we will review these classes one by one. 24.3 Trait Traversable At the top of the collection hierarchy is trait Traversable. Its only abstract operation is foreach: def foreach[U](f: Elem => U) Collection classes implementing Traversable just need to define this method; all other methods can be inherited from Traversable. The foreach method is meant to traverse all elements of the collection, and apply the given operation, f, to each element. The type of the operation is Elem => U, where Elem is the type of the collection’s elements and U is an arbitrary result type. The invocation of f is done for its side effect only; in fact any function result of f is discarded by foreach. Traversable also defines many concrete methods, which are all listed in Table 24.1 on page 539. These methods fall into the following categories: Addition ++, which appends two traversables together, or appends all ele- ments of an iterator to a traversable. Map operations map, flatMap, and collect, which produce a new collec- tion by applying some function to collection elements. Conversions toIndexedSeq, toIterable, toStream, toArray, toList, toSeq, toSet, and toMap, which turn a Traversable collection into a more specific collection. All these conversions return the receiver ob- ject if it already matches the demanded collection type. For instance, applying toList to a list will yield the list itself. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.3 Chapter 24 · The Scala Collections API 538 Copying operations copyToBuffer and copyToArray. As their names im- ply, these copy collection elements to a buffer or array, respectively. Size operations isEmpty, nonEmpty, size, and hasDefiniteSize. Col- lections that are traversable can be finite or infinite. An example of an infinite traversable collection is the stream of natural numbers Stream.from(0). The method hasDefiniteSize indicates whether a collection is possibly infinite. If hasDefiniteSize returns true, the collection is certainly finite. If it returns false, the collection might be infinite, in which case size will emit an error or not return. Element retrieval operations head, last, headOption, lastOption, and find. These select the first or last element of a collection, or else the first element matching a condition. Note, however, that not all collec- tions have a well-defined meaning of what “first” and “last” means. For instance, a hash set might store elements according to their hash keys, which might change from run to run. In that case, the “first” element of a hash set could also be different for different runs of a program. A collection is ordered if it always yields its elements in the same order. Most collections are ordered, but some (such as hash sets) are not—dropping the ordering provides a little bit of extra efficiency. Ordering is often essential to give reproducible tests and help in de- bugging. That’s why Scala collections provide ordered alternatives for all collection types. For instance, the ordered alternative for HashSet is LinkedHashSet. Subcollection retrieval operations takeWhile, tail, init, slice, take, drop, filter, dropWhile, filterNot, and withFilter. These all return some subcollection identified by an index range or a predicate. Subdivision operations splitAt, span, partition, and groupBy, which split the elements of this collection into several subcollections. Element tests exists, forall, and count, which test collection elements with a given predicate. Folds foldLeft, foldRight, /:, :\, reduceLeft, reduceRight, which apply a binary operation to successive elements. Specific folds sum, product, min, and max, which work on collections of specific types (numeric or comparable). Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.3 Chapter 24 · The Scala Collections API 539 String operations mkString, addString, and stringPrefix, which pro- vide alternative ways of converting a collection to a string. View operations consisting of two overloaded variants of the view method. A view is a collection that’s evaluated lazily. You’ll learn more about views in Section 24.15. Table 24.1 · Operations in trait Traversable What it is What it does Abstract method: xs foreach f Executes function f for every element of xs. Addition: xs ++ ys A collection consisting of the elements of both xs and ys. ys is a TraversableOnce collection, i.e., either a Traversable or an Iterator. Maps: xs map f The collection obtained from applying the function f to every element in xs. xs flatMap f The collection obtained from applying the collection-valued function f to every element in xs and concatenating the results. xs collect f The collection obtained from applying the partial function f to every element in xs for which it is defined and collecting the results. Conversions: xs.toArray Converts the collection to an array. xs.toList Converts the collection to a list. xs.toIterable Converts the collection to an iterable. xs.toSeq Converts the collection to a sequence. xs.toIndexedSeq Converts the collection to an indexed sequence. xs.toStream Converts the collection to a stream (a lazily computed sequence). xs.toSet Converts the collection to a set. xs.toMap Converts a collection of key/value pairs to a map. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.3 Chapter 24 · The Scala Collections API 540 Table 24.1 · continued Copying: xs copyToBuffer buf Copies all elements of the collection to buffer buf. xs copyToArray(arr, s, len) Copies at most len elements of arr, starting at index s. The last two arguments are optional. Size info: xs.isEmpty Tests whether the collection is empty. xs.nonEmpty Tests whether the collection contains elements. xs.size The number of elements in the collection. xs.hasDefiniteSize True if xs is known to have finite size. Element retrieval: xs.head The first element of the collection (or, some element, if no order is defined). xs.headOption The first element of xs in an option value, or None if xs is empty. xs.last The last element of the collection (or, some element, if no order is defined). xs.lastOption The last element of xs in an option value, or None if xs is empty. xs find p An option containing the first element in xs that satisfies p, or None if no element qualifies. Subcollections: xs.tail The rest of the collection except xs.head. xs.init The rest of the collection except xs.last. xs slice (from, to) A collection consisting of elements in some index range of xs (from from, up to and excluding to). xs take n A collection consisting of the first n elements of xs (or, some arbitrary n elements, if no order is defined). xs drop n The rest of the collection except xs take n. xs takeWhile p The longest prefix of elements in the collection that all satisfy p. xs dropWhile p The collection without the longest prefix of elements that all satisfy p. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.3 Chapter 24 · The Scala Collections API 541 Table 24.1 · continued xs filter p The collection consisting of those elements of xs that satisfy the predicate p. xs withFilter p A non-strict filter of this collection. All operations on the resulting filter will only apply to those elements of xs for which the condition p is true. xs filterNot p The collection consisting of those elements of xs that do not satisfy the predicate p. Subdivisions: xs splitAt n Splits xs at a position, giving the pair of collections (xs take n, xs drop n). xs span p Splits xs according to a predicate, giving the pair of collections (xs takeWhile p, xs.dropWhile p). xs partition p Splits xs into a pair of collections; one with elements that satisfy the predicate p, the other with elements that do not, giving the pair of collections (xs filter p, xs.filterNot p). xs groupBy f Partitions xs into a map of collections according to a discriminator function f. Element conditions: xs forall p A boolean indicating whether the predicate p holds for all elements of xs. xs exists p A boolean indicating whether the predicate p holds for some element in xs. xs count p The number of elements in xs that satisfy the predicate p. Folds: (z /: xs)(op) Applies binary operation op between successive elements of xs, going left to right, starting with z. (xs :\ z)(op) Applies binary operation op between successive elements of xs, going right to left, starting with z. xs.foldLeft(z)(op) Same as (z /: xs)(op). xs.foldRight(z)(op) Same as (xs :\ z)(op). Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.4 Chapter 24 · The Scala Collections API 542 Table 24.1 · continued xs reduceLeft op Applies binary operation op between successive elements of non-empty collection xs, going left to right. xs reduceRight op Applies binary operation op between successive elements of non-empty collection xs, going right to left. Specific folds: xs.sum The sum of the numeric element values of collection xs. xs.product The product of the numeric element values of collection xs. xs.min The minimum of the ordered element values of collection xs. xs.max The maximum of the ordered element values of collection xs. Strings: xs addString (b, start, sep, end) Adds a string to StringBuilder b that shows all elements of xs between separators sep enclosed in strings start and end. start, sep, and end are all optional. xs mkString (start, sep, end) Converts the collection to a string that shows all elements of xs between separators sep enclosed in strings start and end. start, sep, and end are all optional. xs.stringPrefix The collection name at the beginning of the string returned from xs.toString. Views: xs.view Produces a view over xs. xs view (from, to) Produces a view that represents the elements in some index range of xs. 24.4 Trait Iterable The next trait from the top in Figure 24.1 is Iterable. All methods in this trait are defined in terms of an an abstract method, iterator, which Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.4 Chapter 24 · The Scala Collections API 543 yields the collection’s elements one by one. The foreach method from trait Traversable is implemented in Iterable in terms of iterator. Here is the actual implementation: def foreach[U](f: Elem => U): Unit = { val it = iterator while (it.hasNext) f(it.next()) } Quite a few subclasses of Iterable override this standard implementation of foreach in Iterable, because they can provide a more efficient imple- mentation. Remember that foreach is the basis of the implementation of all operations in Traversable, so its performance matters. Two more methods exist in Iterable that return iterators: grouped and sliding. These iterators, however, do not return single elements but whole subsequences of elements of the original collection. The maximal size of these subsequences is given as an argument to these methods. The grouped method chunks its elements into increments, whereas sliding yields a slid- ing window over the elements. The difference between the two should be- come clear by looking at the following interpreter interaction: scala> val xs = List(1, 2, 3, 4, 5) xs: List[Int] = List(1, 2, 3, 4, 5) scala> val git = xs grouped 3 git: Iterator[List[Int]] = non-empty iterator scala> git.next() res2: List[Int] = List(1, 2, 3) scala> git.next() res3: List[Int] = List(4, 5) scala> val sit = xs sliding 3 sit: Iterator[List[Int]] = non-empty iterator scala> sit.next() res4: List[Int] = List(1, 2, 3) scala> sit.next() res5: List[Int] = List(2, 3, 4) scala> sit.next() res6: List[Int] = List(3, 4, 5) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.4 Chapter 24 · The Scala Collections API 544 Trait Iterable also adds some other methods to Traversable that can be implemented efficiently only if an iterator is available. They are summarized in Table 24.2: Table 24.2 · Operations in trait Iterable What it is What it does Abstract method: xs.iterator An iterator that yields every element in xs, in the same order as foreach traverses elements Other iterators: xs grouped size An iterator that yields fixed-sized “chunks” of this collection xs sliding size An iterator that yields a sliding fixed-sized window of elements in this collection Subcollections: xs takeRight n A collection consisting of the last n elements of xs (or, some arbitrary n elements, if no order is defined) xs dropRight n The rest of the collection except xs takeRight n Zippers: xs zip ys An iterable of pairs of corresponding elements from xs and ys xs zipAll (ys, x, y) An iterable of pairs of corresponding elements from xs and ys, where the shorter sequence is extended to match the longer one by appending elements x or y xs.zipWithIndex An iterable of pairs of elements from xs with their indicies Comparison: xs sameElements ys Tests whether xs and ys contain the same elements in the same order Why have both Traversable and Iterable? You might wonder why the extra trait Traversable is above Iterable. Can we not do everything with an iterator? So what’s the point of having Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.4 Chapter 24 · The Scala Collections API 545 a more abstract trait that defines its methods in terms of foreach instead of iterator? One reason for having Traversable is that sometimes it is easier or more efficient to provide an implementation of foreach than to provide an implementation of iterator. Here’s a simple example. Let’s say you want a class hierarchy for binary trees that have integer elements at the leaves. You might design this hierarchy like this: sealed abstract class Tree case class Branch(left: Tree, right: Tree) extends Tree case class Node(elem: Int) extends Tree Now assume you want to make trees traversable. To do this, have Tree inherit from Traversable[Int] and define a foreach method like this: sealed abstract class Tree extends Traversable[Int] { def foreach[U](f: Int => U) = this match { case Node(elem) => f(elem) case Branch(l, r) => l foreach f; r foreach f } } That’s not too hard, and it is also very efficient—traversing a balanced tree takes time proportional to the number of elements in the tree. To see this, consider that for a balanced tree with N leaves you will have N - 1 interior nodes of class Branch. So the total number of steps to traverse the tree is N + N - 1. Now, compare this with making trees iterable. To do this, have Tree inherit from Iterable[Int] and define an iterator method like this: sealed abstract class Tree extends Iterable[Int] { def iterator: Iterator[Int] = this match { case Node(elem) => Iterator.single(elem) case Branch(l, r) => l.iterator ++ r.iterator } } At first glance, this looks no harder than the foreach solution. However, there’s an efficiency problem that has to do with the implementation of the iterator concatenation method, ++. Every time an element is produced by a Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.5 Chapter 24 · The Scala Collections API 546 concatenated iterator such as l.iterator ++ r.iterator, the computation needs to follow one indirection to get at the right iterator (either l.iterator, or r.iterator). Overall, that makes log(N) indirections to get at a leaf of a balanced tree with N leaves. So the cost of visiting all elements of a tree went up from about 2N for the foreach traversal method to N log(N) for the traversal with iterator. If the tree has a million elements that means about two million steps for foreach and about twenty million steps for iterator. So the foreach solution has a clear advantage. Subcategories of Iterable In the inheritance hierarchy below Iterable you find three traits: Seq, Set, and Map. A common aspect of these three traits is that they all implement the PartialFunction trait1 with its apply and isDefinedAt methods. How- ever, the way each trait implements PartialFunction differs. For sequences, apply is positional indexing, where elements are always numbered from 0. That is, Seq(1, 2, 3)(1) == 2. For sets, apply is a membership test. For instance, Set('a', 'b', 'c')('b') == true whereas Set()('a') == false. Finally for maps, apply is a selection. For instance, Map('a' -> 1, 'b' -> 10, 'c' -> 100)('b') == 10. In the following three sections, we will explain each of the three kinds of collections in more detail. 24.5 The sequence traits Seq, IndexedSeq, and LinearSeq The Seq trait represents sequences. A sequence is a kind of iterable that has a length and whose elements have fixed index positions, starting from 0. The operations on sequences, summarized in Figure 24.3, fall into the following categories: Indexing and length operations apply, isDefinedAt, length, indices, and lengthCompare. For a Seq, the apply operation means index- ing; hence a sequence of type Seq[T] is a partial function that takes an Int argument (an index) and yields a sequence element of type T. 1Partial functions were described in Section 15.7. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.5 Chapter 24 · The Scala Collections API 547 In other words Seq[T] extends PartialFunction[Int, T]. The el- ements of a sequence are indexed from zero up to the length of the sequence minus one. The length method on sequences is an alias of the size method of general collections. The lengthCompare method allows you to compare the lengths of two sequences even if one of the sequences has infinite length. Index search operations indexOf, lastIndexOf, indexOfSlice, lastIn- dexOfSlice, indexWhere, lastIndexWhere, segmentLength, and prefixLength, which return the index of an element equal to a given value or matching some predicate. Addition operations +:, :+, and padTo, which return new sequences ob- tained by adding elements at the front or the end of a sequence. Update operations updated and patch, which return a new sequence ob- tained by replacing some elements of the original sequence. Sorting operations sorted, sortWith, and sortBy, which sort sequence elements according to various criteria. Reversal operations reverse, reverseIterator, and reverseMap, which yield or process sequence elements in reverse order, from last to first. Comparison operations startsWith, endsWith, contains, corresponds, and containsSlice, which relate two sequences or search an element in a sequence. Multiset operations intersect, diff, union, and distinct, which per- form set-like operations on the elements of two sequences or remove duplicates. If a sequence is mutable, it offers in addition a side-effecting update method, which lets sequence elements be updated. Recall from Chapter 3 that syntax like seq(idx) = elem is just a shorthand for seq.update(idx, elem). Note the difference between update and updated. The update method changes a sequence element in place, and is only available for mutable sequences. The updated method is available for all sequences and always returns a new sequence instead of modifying the original. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.5 Chapter 24 · The Scala Collections API 548 Table 24.3 · Operations in trait Seq What it is What it does Indexing and length: xs(i) (or, written out, xs apply i) The element of xs at index i. xs isDefinedAt i Tests whether i is contained in xs.indices. xs.length The length of the sequence (same as size). xs.lengthCompare ys Returns -1 if xs is shorter than ys, +1 if it is longer, and 0 is they have the same length. Works even if one if the sequences is infinite. xs.indices The index range of xs, extending from 0 to xs.length - 1. Index search: xs indexOf x The index of the first element in xs equal to x (several variants exist). xs lastIndexOf x The index of the last element in xs equal to x (several variants exist). xs indexOfSlice ys The first index of xs such that successive elements starting from that index form the sequence ys. xs lastIndexOfSlice ys The last index of xs such that successive elements starting from that index form the sequence ys. xs indexWhere p The index of the first element in xs that satisfies p (several variants exist). xs segmentLength (p, i) The length of the longest uninterrupted segment of elements in xs, starting with xs(i), that all satisfy the predicate p. xs prefixLength p The length of the longest prefix of elements in xs that all satisfy the predicate p. Additions: x +: xs A new sequence consisting of x prepended to xs. xs :+ x A new sequence that consists of x append to xs. xs padTo (len, x) The sequence resulting from appending the value x to xs until length len is reached. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.5 Chapter 24 · The Scala Collections API 549 Table 24.3 · continued Updates: xs patch (i, ys, r) The sequence resulting from replacing r elements of xs starting with i by the patch ys. xs updated (i, x) A copy of xs with the element at index i replaced by x. xs(i) = x (or, written out, xs.update(i, x), only available for mutable.Seqs) Changes the element of xs at index i to y. Sorting: xs.sorted A new sequence obtained by sorting the elements of xs using the standard ordering of the element type of xs. xs sortWith lessThan A new sequence obtained by sorting the elements of xs, using lessThan as comparison operation. xs sortBy f A new sequence obtained by sorting the elements of xs. Comparison between two elements proceeds by mapping the function f over both and comparing the results. Reversals: xs.reverse A sequence with the elements of xs in reverse order. xs.reverseIterator An iterator yielding all the elements of xs in reverse order. xs reverseMap f A sequence obtained by mapping f over the elements of xs in reverse order. Comparisons: xs startsWith ys Tests whether xs starts with sequence ys (several variants exist). xs endsWith ys Tests whether xs ends with sequence ys (several variants exist). xs contains x Tests whether xs has an element equal to x. xs containsSlice ys Tests whether xs has a contiguous subsequence equal to ys. (xs corresponds ys)(p) Tests whether corresponding elements of xs and ys satisfy the binary predicate p. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.5 Chapter 24 · The Scala Collections API 550 Table 24.3 · continued Multiset operations: xs intersect ys The multi-set intersection of sequences xs and ys that preserves the order of elements in xs. xs diff ys The multi-set difference of sequences xs and ys that preserves the order of elements in xs. xs union ys Multiset union; same as xs ++ ys. xs.distinct A subsequence of xs that contains no duplicated element. Each Seq trait has two subtraits, LinearSeq and IndexedSeq. These do not add any new operations, but each offers different performance charac- teristics. A linear sequence has efficient head and tail operations, whereas an indexed sequence has efficient apply, length, and (if mutable) update operations. List is a frequently used linear sequence, as is Stream. Two fre- quently used indexed sequences are Array and ArrayBuffer. The Vector class provides an interesting compromise between indexed and linear access. It has both effectively constant time indexing overhead and constant time lin- ear access overhead. Because if this, vectors are a good foundation for mixed access patterns where both indexed and linear accesses are used. More on vectors in Section 24.9. Buffers An important sub-category of mutable sequences is buffers. Buffers allow not only updates of existing elements but also element insertions, element removals, and efficient additions of new elements at the end of the buffer. The principal new methods supported by a buffer are += and ++=, for element addition at the end, +=: and ++=: for addition at the front, insert and insertAll for element insertions, as well as remove and -= for element removal. These operations are summarized in Table 24.4. Two Buffer implementations that are commonly used are ListBuffer and ArrayBuffer. As the name implies, a ListBuffer is backed by a List and supports efficient conversion of its elements to a List, whereas an ArrayBuffer is backed by an array, and can be quickly converted into one. You saw a glimpse of the implementation of ListBuffer in Section 22.2. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.6 Chapter 24 · The Scala Collections API 551 Table 24.4 · Operations in trait Buffer What it is What it does Additions: buf += x Appends element x to buffer buf, and returns buf itself as result buf += (x, y, z) Appends given elements to buffer buf ++= xs Appends all elements in xs to buffer x +=: buf Prepends element x to buffer xs ++=: buf Prepends all elements in xs to buffer buf insert (i, x) Inserts element x at index i in buffer buf insertAll (i, xs) Inserts all elements in xs at index i in buffer Removals: buf -= x Removes element x from buffer buf remove i Removes element at index i from buffer buf remove (i, n) Removes n elements starting at index i from buffer buf trimStart n Removes first n elements from buffer buf trimEnd n Removes last n elements from buffer buf.clear() Removes all elements from buffer Cloning: buf.clone A new buffer with the same elements as buf 24.6 Sets Sets are Iterables that contain no duplicate elements. The operations on sets are summarized in Table 24.5 for general sets and Table 24.6 for mutable sets. They fall into the following categories: Tests contains, apply, and subsetOf. The contains method indicates whether a set contains a given element. The apply method for a set is the same as contains, so set(elem) is the same as set contains elem. That means sets can also be used as test functions that return true for the elements they contain. For example: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.6 Chapter 24 · The Scala Collections API 552 scala> val fruit = Set("apple", "orange", "peach", "banana") fruit: scala.collection.immutable.Set[java.lang.String] = Set(apple, orange, peach, banana) scala> fruit("peach") res7: Boolean = true scala> fruit("potato") res8: Boolean = false Additions + and ++, which add one or more elements to a set, yielding a new set as a result. Removals - and --, which remove one or more elements from a set, yielding a new set. Set operations for union, intersection, and set difference. These set oper- ations exist in two forms: alphabetic and symbolic. The alphabetic versions are intersect, union, and diff, whereas the symbolic ver- sions are &, |, and &~. The ++ that Set inherits from Traversable can be seen as yet another alias of union or |, except that ++ takes a Traversable argument whereas union and | take sets. Table 24.5 · Operations in trait Set What it is What it does Tests: xs contains x Tests whether x is an element of xs xs(x) Same as xs contains x xs subsetOf ys Tests whether xs is a subset of ys Additions: xs + x The set containing all elements of xs as well as x xs + (x, y, z) The set containing all elements of xs as well as the given additional elements xs ++ ys The set containing all elements of xs as well as all elements of ys Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.6 Chapter 24 · The Scala Collections API 553 Table 24.5 · continued Removals: xs - x The set containing all elements of xs except x xs - (x, y, z) The set containing all elements of xs except the given elements xs -- ys The set containing all elements of xs except the elements of ys xs.empty An empty set of the same class as xs Binary operations: xs & ys The set intersection of xs and ys xs intersect ys Same as xs & ys xs | ys The set union of xs and ys xs union ys Same as xs | ys xs &~ ys The set difference of xs and ys xs diff ys Same as xs &~ ys Mutable sets have methods that add, remove, or update elements, which are summarized in Table 24.6: Table 24.6 · Operations in trait mutable.Set What it is What it does Additions: xs += x Adds element x to set xs as a side effect and returns xs itself xs += (x, y, z) Adds the given elements to set xs as a side effect and returns xs itself xs ++= ys Adds all elements in ys to set xs as a side effect and returns xs itself xs add x Adds element x to xs and returns true if x was not previously contained in the set, false if it was previously contained Removals: xs -= x Removes element x from set xs as a side effect and returns xs itself Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.6 Chapter 24 · The Scala Collections API 554 Table 24.6 · continued xs -= (x, y, z) Removes the given elements from set xs as a side effect and returns xs itself xs --= ys Removes all elements in ys from set xs as a side effect and returns xs itself xs remove x Removes element x from xs and returns true if x was previously contained in the set, false if it was not previously contained xs retain p Keeps only those elements in xs that satisfy predicate p xs.clear() Removes all elements from xs Update: xs(x) = b (or, written out, xs.update(x, b)) If boolean argument b is true, adds x to xs, otherwise removes x from xs Cloning: xs.clone A new mutable set with the same elements as xs Just like an immutable set, a mutable set offers the + and ++ operations for element additions and the - and -- operations for element removals. But these are less often used for mutable sets since they involve copying the set. As a more efficient alternative, mutable sets offer the update methods += and -=. The operation s += elem adds elem to the set s as a side effect, and returns the mutated set as a result. Likewise, s -= elem removes elem from the set, and returns the mutated set as a result. Besides += and -= there are also the bulk operations ++= and --=, which add or remove all elements of a traversable or an iterator. The choice of the method names += and -= means that very similar code can work with either mutable or immutable sets. Consider first the following interpreter dialogue that uses an immutable set s: scala> var s = Set(1, 2, 3) s: scala.collection.immutable.Set[Int] = Set(1, 2, 3) scala> s += 4; s -= 2 scala> s res9: scala.collection.immutable.Set[Int] = Set(1, 3, 4) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.6 Chapter 24 · The Scala Collections API 555 In this example, we used += and -= on a var of type immutable.Set. As was explained in Step 10 in Chapter 3, a statement such as s += 4 is an abbreviation for s = s + 4. So this invokes the addition method + on the set s and then assigns the result back to the s variable. Consider now an analogous interaction with a mutable set: scala> val s = collection.mutable.Set(1, 2, 3) s: scala.collection.mutable.Set[Int] = Set(1, 2, 3) scala> s += 4 res10: s.type = Set(1, 4, 2, 3) scala> s -= 2 res11: s.type = Set(1, 4, 3) The end effect is very similar to the previous interaction; we start with a Set(1, 2, 3) and end up with a Set(1, 3, 4). However, even though the statements look the same as before, they do something different. The s += 4 statement now invokes the += method on the mutable set value s, changing the set in place. Likewise, the s -= 2 statement now invokes the -= method on the same set. Comparing the two interactions shows an important principle. You often can replace a mutable collection stored in a val by an immutable collection stored in a var, and vice versa. This works at least as long as there are no alias references to the collection through which you can observe whether it was updated in place or a new collection was created. Mutable sets also provide add and remove as variants of += and -=. The difference is that add and remove return a boolean result indicating whether the operation had an effect on the set. The current default implementation of a mutable set uses a hash table to store the set’s elements. The default implementation of an immutable set uses a representation that adapts to the number of elements of the set. An empty set is represented by just a singleton object. Sets of sizes up to four are represented by a single object that stores all elements as fields. Beyond that size, immutable sets are implemented as hash tries.2 A consequence of these representation choices is that for sets of small sizes, up to about four, immutable sets are more compact and more efficient 2Hash tries are described in Section 24.9. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.6 Chapter 24 · The Scala Collections API 556 than mutable sets. So if you expect the size of a set to be small, try to make it immutable. Two Set subtraits are SortedSet and BitSet. These are explained in the following subsections. Sorted sets A SortedSet is a set where, no matter what order elements were added to the set, the elements are traversed in sorted order. The default representation of a SortedSet is an ordered binary tree maintaining the invariant that all elements in the left subtree of a node are smaller than all elements in the right subtree. That way, a simple in-order traversal can return all tree elements in increasing order. Scala’s class immutable.TreeSet uses a red-black tree implementation to maintain this ordering invariant, and at the same time keep the tree balanced—meaning that all paths from the root of the tree to a leaf have about the same length. To create an empty tree set, you could first specify the desired ordering. For example, here is an ordering that puts strings in reverse order: scala> val myOrdering = Ordering.fromLessThan[String](_ > _) myOrdering: scala.math.Ordering[String] = ... Then, to create an empty tree set with that ordering, use: scala> import scala.collection.immutable.TreeSet import scala.collection.immutable.TreeSet scala> TreeSet.empty(myOrdering) res12: scala.collection.immutable.TreeSet[String] = TreeSet() Or you can leave out the ordering argument but give an element type or the empty set. In that case, the default ordering on the element type will be used: scala> val set = TreeSet.empty[String] set: scala.collection.immutable.TreeSet[String] = TreeSet() If you create new sets from a tree set (for instance by concatenation or filter- ing), they will keep the same ordering as the original set. For example: scala> val numbers = set + ("one", "two", "three", "four") numbers: scala.collection.immutable.TreeSet[String] = TreeSet(four, one, three, two) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.7 Chapter 24 · The Scala Collections API 557 Sorted sets also support ranges of elements. For instance, the range method returns all elements from a starting element up to, but excluding, an end element. Or, the from method returns all elements greater than or equal to a starting element in the set’s ordering. The result of calls to both methods is again a sorted set. Here are some examples: scala> numbers range ("one", "two") res13: scala.collection.immutable.TreeSet[String] = TreeSet(one, three) scala> numbers from "three" res14: scala.collection.immutable.TreeSet[String] = TreeSet(three, two) Bit sets Bit sets are sets of non-negative integer elements that are implemented in one or more words of packed bits. The internal representation of a bit set uses an array of Longs. The first Long covers elements from 0 to 63, the second from 64 to 127, and so on.3 For every Long, each of its 64 bits is set to 1 if the corresponding element is contained in the set, and is unset otherwise. It follows that the size of a bit set depends on the largest integer that’s stored in it. If N is that largest integer, then the size of the set is N/64 Long words, or N/8 bytes, plus a small number of extra bytes for status information. Bitsets are hence more compact than other sets if they contain many small elements. Another advantage of bit sets is that operations such as membership test with contains, or element addition and removal with += and -=, are all extremely efficient. 24.7 Maps Maps are Iterables of pairs of keys and values (also named mappings or as- sociations). As explained in Section 21.4, Scala’s Predef class offers an im- plicit conversion that lets you write key -> value as an alternate syntax for the pair (key, value). Therefore, Map("x" -> 24, "y" -> 25, "z" -> 26) 3Immutable bit sets of elements in the range of 0 to 127 optimize the array away and store the bits directly in a one or two Long fields. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.7 Chapter 24 · The Scala Collections API 558 means exactly the same as Map(("x", 24), ("y", 25), ("z", 26)), but reads better. The fundamental operations on maps, summarized in Table 24.7, are similar to those on sets. Mutable maps additionally support the operations shown in Table 24.8. Map operations fall into the following categories: Lookups apply, get, getOrElse, contains, and isDefinedAt. These op- erations turn maps into partial functions from keys to values. The fun- damental lookup method for a map is: def get(key): Option[Value] The operation “m get key” tests whether the map contains an associa- tion for the given key. If so, it returns the associated value in a Some. If no key is defined in the map, get returns None. Maps also define an apply method that returns the value associated with a given key directly, without wrapping it in an Option. If the key is not defined in the map, an exception is raised. Additions and updates +, ++, and updated, which let you add new bindings to a map or change existing bindings. Removals - and --, which remove bindings from a map. Subcollection producers keys, keySet, keysIterator, valuesIterator, and values, which return a map’s keys and values separately in vari- ous forms. Transformations filterKeys and mapValues, which produce a new map by filtering and transforming bindings of an existing map. Table 24.7 · Operations in trait Map What it is What it does Lookups: ms get k The value associated with key k in map ms as an option, or None if not found ms(k) (or, written out, ms apply k) The value associated with key k in map ms, or a thrown exception if not foundCover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.7 Chapter 24 · The Scala Collections API 559 Table 24.7 · continued ms getOrElse (k, d) The value associated with key k in map ms, or the default value d if not found ms contains k Tests whether ms contains a mapping for key k ms isDefinedAt k Same as contains Additions and updates: ms + (k -> v) The map containing all mappings of ms as well as the mapping k -> v from key k to value v ms + (k -> v, l -> w) The map containing all mappings of ms as well as the given key/value pairs ms ++ kvs The map containing all mappings of ms as well as all key/value pairs of kvs ms updated (k, v) Same as ms + (k -> v) Removals: ms - k The map containing all mappings of ms except for any mapping of key k ms - (k, l, m) The map containing all mappings of ms except for any mapping with the given keys ms -- ks The map containing all mappings of ms except for any mapping with a key in ks Subcollections: ms.keys An iterable containing each key in ms ms.keySet A set containing each key in ms ms.keysIterator An iterator yielding each key in ms ms.values An iterable containing each value associated with a key in ms ms.valuesIterator An iterator yielding each value associated with a key in ms Transformation: ms filterKeys p A map view containing only those mappings in ms where the key satisfies predicate p ms mapValues f A map view resulting from applying function f to each value associated with a key in ms Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.7 Chapter 24 · The Scala Collections API 560 Table 24.8 · Operations in trait mutable.Map What it is What it does Additions and updates: ms(k) = v (or, written out, ms.update(k, v)) Adds mapping from key k to value v to map ms as a side effect, overwriting any previous mapping of k ms += (k -> v) Adds mapping from key k to value v to map ms as a side effect and returns ms itself ms += (k -> v, l -> w) Adds the given mappings to ms as a side effect and returns ms itself ms ++= kvs Adds all mappings in kvs to ms as a side effect and returns ms itself ms put (k, v) Adds mapping from key k to value v to ms and returns any value previously associated with k as an option ms getOrElseUpdate (k, d) If key k is defined in map ms, returns its associated value. Otherwise, updates ms with the mapping k -> d and returns d Removals: ms -= k Removes mapping with key k from ms as a side effect and returns ms itself ms -= (k, l, m) Removes mappings with the given keys from ms as a side effect and returns ms itself ms --= ks Removes all keys in ks from ms as a side effect and returns ms itself ms remove k Removes any mapping with key k from ms and returns any value previously associated with k as an option ms retain p Keeps only those mappings in ms that have a key satisfying predicate p. ms.clear() Removes all mappings from ms Transformation and cloning: ms transform f Transforms all associated values in map ms with function f ms.clone Returns a new mutable map with the same mappings as ms Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.7 Chapter 24 · The Scala Collections API 561 The addition and removal operations for maps mirror those for sets. As for sets, mutable maps also support the non-destructive addition operations +, -, and updated, but they are used less frequently because they involve a copying of the mutable map. Instead, a mutable map m is usually updated “in place,” using the two variants m(key) = value or m += (key -> value). There is also the variant m put (key, value), which returns an Option value that contains the value previously associated with key, or None if the key did not exist in the map before. The getOrElseUpdate is useful for accessing maps that act as caches. Say you have an expensive computation triggered by invoking a function f: scala> def f(x: String) = { println("taking my time."); Thread.sleep(100) x.reverse } f: (x: String)String Assume further that f has no side-effects, so invoking it again with the same argument will always yield the same result. In that case you could save time by storing previously computed bindings of argument and results of f in a map, and only computing the result of f if a result of an argument was not found there. You could say the map is a cache for the computations of the function f. scala> val cache = collection.mutable.Map[String, String]() cache: scala.collection.mutable.Map[String,String] = Map() You can now create a more efficient caching version of the f function: scala> def cachedF(s: String) = cache.getOrElseUpdate(s, f(s)) cachedF: (s: String)String scala> cachedF("abc") taking my time. res15: String = cba scala> cachedF("abc") res16: String = cba Note that the second argument to getOrElseUpdate is “by-name,” so the computation of f("abc") above is only performed if getOrElseUpdate requires the value of its second argument, which is precisely if its first ar- gument is not found in the cache map. You could also have implemented Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.8 Chapter 24 · The Scala Collections API 562 cachedF directly, using just basic map operations, but it would have have taken more code to do so: def cachedF(arg: String) = cache get arg match { case Some(result) => result case None => val result = f(arg) cache(arg) = result result } 24.8 Synchronized sets and maps In Section 1.1, we mentioned that if you needed a thread-safe map, you could mix the SynchronizedMap trait into whatever particular map imple- mentation you desired. For example, you could mix SynchronizedMap into HashMap, as shown in Listing 24.1. This example begins with an import of two traits, Map and SynchronizedMap, and one class, HashMap, from pack- age scala.collection.mutable. The rest of the example is the definition of singleton object MapMaker, which declares one method, makeMap. The makeMap method declares its result type to be a mutable map of string keys to string values. The first statement inside the body of makeMap constructs a new mutable HashMap that mixes in the SynchronizedMap trait: new HashMap[String, String] with SynchronizedMap[String, String] Given this code, the Scala compiler will generate a synthetic subclass of HashMap that mixes in SynchronizedMap, and create (and return) an in- stance of it. This synthetic class will also override a method named default, because of this code: override def default(key: String) = "Why do you want to know?" If you ask a map to give you the value for a particular key, but it doesn’t have a mapping for that key, you’ll by default get a NoSuchElementException. If you define a new map class and override the default method, however, your Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.8 Chapter 24 · The Scala Collections API 563 import scala.collection.mutable.{Map, SynchronizedMap, HashMap} object MapMaker{ def makeMap: Map[String, String] = { new HashMap[String, String] with SynchronizedMap[String, String] { override def default(key: String) = "Why do you want to know?" } } } Listing 24.1· Mixing in the SynchronizedMap trait. new map will return the value returned by default when queried with a non- existent key. Thus, the synthetic HashMap subclass generated by the compiler from the code in Listing 24.1 will return the somewhat curt response string, "Why do you want to know?", when queried with a non-existent key. Because the mutable map returned by the makeMap method mixes in the SynchronizedMap trait, it can be used by multiple threads at once. Each access to the map will be synchronized. Here’s an example of the map being used, by one thread, in the interpreter: scala> val capital = MapMaker.makeMap capital: scala.collection.mutable.Map[String,String] = Map() scala> capital ++= List("US" -> "Washington", "France" -> "Paris", "Japan" -> "Tokyo") res17: scala.collection.mutable.Map[String,String] = Map((France,Paris), (US,Washington), (Japan,Tokyo)) scala> capital("Japan") res18: String = Tokyo scala> capital("New Zealand") res19: String = Why do you want to know? scala> capital += ("New Zealand" -> "Wellington") res20: capital.type = Map((New Zealand,Wellington),... Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.9 Chapter 24 · The Scala Collections API 564 scala> capital("New Zealand") res21: String = Wellington You can create synchronized sets similarly to the way you create syn- chronized maps. For example, you could create a synchronized HashSet by mixing in the SynchronizedSet trait, like this: import scala.collection.mutable val synchroSet = new mutable.HashSet[Int] with mutable.SynchronizedSet[Int] Finally, if you are thinking of using synchronized collections, you may also wish to consider the concurrent collections of java.util.concurrent instead. Alternatively, you may prefer to use unsynchronized collections with Scala actors. Actors will be covered in detail in Chapter 32. 24.9 Concrete immutable collection classes Scala provides many concrete immutable collection classes for you to choose from. They differ in the traits they implement (maps, sets, sequences), whether they can be infinite, and the speed of various operations. We’ll start by reviewing the most common immutable collection types. Lists Lists are finite immutable sequences. They provide constant-time access to their first element as well as the rest of the list, and they have a constant-time cons operation for adding a new element to the front of the list. Many other operations take linear time. See Chapters 16 and 22 for extensive discussions about lists. Streams A stream is like a list except that its elements are computed lazily. Because of this, a stream can be infinitely long. Only those elements requested will be computed. Otherwise, streams have the same performance characteristics as lists. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.9 Chapter 24 · The Scala Collections API 565 Whereas lists are constructed with the :: operator, streams are con- structed with the similar-looking #::. Here is a simple example of a stream containing the integers 1, 2, and 3: scala> val str = 1 #:: 2 #:: 3 #:: Stream.empty str: scala.collection.immutable.Stream[Int] = Stream(1, ?) The head of this stream is 1, and the tail of it has 2 and 3. The tail is not printed here, though, because it hasn’t been computed yet! Streams are re- quired to compute lazily, and the toString method of a stream is careful not to force any extra evaluation. Below is a more complex example. It computes a stream that contains a Fibonacci sequence starting with the given two numbers. A Fibonacci sequence is one where each element is the sum of the previous two elements in the series: scala> def fibFrom(a: Int, b: Int): Stream[Int] = a #:: fibFrom(b, a + b) fibFrom: (a: Int,b: Int)Stream[Int] This function is deceptively simple. The first element of the sequence is clearly a, and the rest of the sequence is the Fibonacci sequence starting with b followed by a + b. The tricky part is computing this sequence without causing an infinite recursion. If the function used :: instead of #::, then every call to the function would result in another call, thus causing an infinite recursion. Since it uses #::, though, the right-hand side is not evaluated until it is requested. Here are the first few elements of the Fibonacci sequence starting with two ones: scala> val fibs = fibFrom(1, 1).take(7) fibs: scala.collection.immutable.Stream[Int] = Stream(1, ?) scala> fibs.toList res22: List[Int] = List(1, 1, 2, 3, 5, 8, 13) Vectors Lists are very efficient when the algorithm processing them is careful to only process their heads. Accessing, adding, and removing the head of a list takes Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.9 Chapter 24 · The Scala Collections API 566 only constant time, whereas accessing or modifying elements later in the list takes time linear in the depth into the list. Vectors are a new collection type in Scala 2.8 that give efficient access to elements beyond the head. Access to any elements of a vector take only “effectively constant time,” as defined below. It’s a larger constant than for access to the head of a list or for reading an element of an array, but it’s a constant nonetheless. As a result, algorithms using vectors do not have to be careful about accessing just the head of the sequence. They can access and modify elements at arbitrary locations, and thus they can be much more convenient to write. Vectors are built and modified just like any other sequence: scala> val vec = scala.collection.immutable.Vector.empty vec: scala.collection.immutable.Vector[Nothing] = Vector() scala> val vec2 = vec :+ 1 :+ 2 vec2: scala.collection.immutable.Vector[Int] = Vector(1, 2) scala> val vec3 = 100 +: vec2 vec3: scala.collection.immutable.Vector[Int] = Vector(100, 1, 2) scala> vec3(0) res23: Int = 100 Vectors are represented as broad, shallow trees. Every tree node contains up to 32 elements of the vector or contains up to 32 other tree nodes. Vectors with up to 32 elements can be represented in a single node. Vectors with up to 32 * 32 = 1024 elements can be represented with a single indirection. Two hops from the root of the tree to the final element node are sufficient for vectors with up to 215 elements, three hops for vectors with 220, four hops for vectors with 225 elements and five hops for vectors with up to 230 elements. So for all vectors of reasonable size, an element selection involves up to five primitive array selections. This is what we meant when we wrote that element access is “effectively constant time.” Vectors are immutable, so you cannot change an element of a vector in place. However, with the updated method you can create a new vector that differs from a given vector only in a single element: scala> val vec = Vector(1, 2, 3) vec: scala.collection.immutable.Vector[Int] = Vector(1, 2, 3) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.9 Chapter 24 · The Scala Collections API 567 scala> vec updated (2, 4) res24: scala.collection.immutable.Vector[Int] = Vector(1, 2, 4) scala> vec res25: scala.collection.immutable.Vector[Int] = Vector(1, 2, 3) As the last line above shows, a call to updated has no effect on the original vector vec. Like selection, functional vector updates are also “effectively constant time.” Updating an element in the middle of a vector can be done by copying the node that contains the element, and every node that points to it, starting from the root of the tree. This means that a functional update creates between one and five nodes that each contain up to 32 elements or subtrees. This is certainly more expensive than an in-place update in a mutable array, but still a lot cheaper than copying the whole vector. Because vectors strike a good balance between fast random selections and fast random functional updates, they are currently the default implemen- tation of immutable indexed sequences: scala> collection.immutable.IndexedSeq(1, 2, 3) res26: scala.collection.immutable.IndexedSeq[Int] = Vector(1, 2, 3) Immutable stacks If you need a last-in-first-out sequence, you can use a Stack. You push an element onto a stack with push, pop an element with pop, and peek at the top of the stack without removing it with top. All of these operations are constant time. Here are some simple operations performed on a stack: scala> val stack = scala.collection.immutable.Stack.empty stack: scala.collection.immutable.Stack[Nothing] = Stack() scala> val hasOne = stack.push(1) hasOne: scala.collection.immutable.Stack[Int] = Stack(1) scala> stack res27: scala.collection.immutable.Stack[Nothing] = Stack() scala> hasOne.top res28: Int = 1 Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.9 Chapter 24 · The Scala Collections API 568 scala> hasOne.pop res29: scala.collection.immutable.Stack[Int] = Stack() Immutable stacks are used rarely in Scala programs because their func- tionality is subsumed by lists: A push on an immutable stack is the same as a :: on a list, and a pop on a stack is the same a tail on a list. Immutable queues A queue is just like a stack except that it is first-in-first-out rather than last-in- first-out. A simplified implementation of immutable queues was discussed in Chapter 19. Here’s how you can create an empty immutable queue: scala> val empty = scala.collection.immutable.Queue[Int]() empty: scala.collection.immutable.Queue[Int] = Queue() You can append an element to an immutable queue with enqueue: scala> val has1 = empty.enqueue(1) has1: scala.collection.immutable.Queue[Int] = Queue(1) To append multiple elements to a queue, call enqueue with a collection as its argument: scala> val has123 = has1.enqueue(List(2, 3)) has123: scala.collection.immutable.Queue[Int] = Queue(1, 2, 3) To remove an element from the head of the queue, use dequeue: scala> val (element, has23) = has123.dequeue element: Int = 1 has23: scala.collection.immutable.Queue[Int] = Queue(2, 3) Note that dequeue returns a pair consisting of the element removed and the rest of the queue. Ranges A range is an ordered sequence of integers that are equally spaced apart. For example, “1, 2, 3” is a range, as is “5, 8, 11, 14.” To create a range in Scala, use the predefined methods to and by. Here are some examples: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.9 Chapter 24 · The Scala Collections API 569 scala> 1 to 3 res30: scala.collection.immutable.Range.Inclusive with scala.collection.immutable.Range.ByOne = Range(1, 2, 3) scala> 5 to 14 by 3 res31: scala.collection.immutable.Range = Range(5, 8, 11, 14) If you want to create a range that is exclusive of its upper limit, use the convenience method until instead of to: scala> 1 until 3 res32: scala.collection.immutable.Range with scala.collection.immutable.Range.ByOne = Range(1, 2) Ranges are represented in constant space, because they can be defined by just three numbers: their start, their end, and the stepping value. Because of this representation, most operations on ranges are extremely fast. Hash tries Hash tries4 are a standard way to implement immutable sets and maps effi- ciently. Their representation is similar to vectors in that they are also trees where every node has 32 elements or 32 subtrees, but selection is done based on a hash code. For instance, to find a given key in a map, you use the lowest five bits of the hash code of the key to select the first subtree, the next five bits the next subtree, and so on. Selection stops once all elements stored in a node have hash codes that differ from each other in the bits that are selected so far. Thus, not all the bits of the hash code are necessarily used. Hash tries strike a nice balance between reasonably fast lookups and reasonably efficient functional insertions (+) and deletions (-). That’s why they underlie Scala’s default implementations of immutable maps and sets. In fact, Scala has a further optimization for immutable sets and maps that contain less than five elements. Sets and maps with one to four elements are stored as single objects that just contain the elements (or key/value pairs in the case of a map) as fields. The empty immutable set and empty immutable map is in each case a singleton object—there’s no need to duplicate storage for those because an empty immutable set or map will always stay empty. 4“Trie” comes from the word "retrieval" and is pronounced tree or try. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.9 Chapter 24 · The Scala Collections API 570 Red-black trees Red-black trees are a form of balanced binary trees where some nodes are designated “red” and others “black.” Like any balanced binary tree, opera- tions on them reliably complete in time logarithmic to the size of the tree. Scala provides implementations of sets and maps that use a red-black tree internally. You access them under the names TreeSet and TreeMap: scala> val set = collection.immutable.TreeSet.empty[Int] set: scala.collection.immutable.TreeSet[Int] = TreeSet() scala> set + 1 + 3 + 3 res33: scala.collection.immutable.TreeSet[Int] = TreeSet(1, 3) Red-black trees are also the standard implementation of SortedSet in Scala, because they provide an efficient iterator that returns all elements of the set in sorted order. Immutable bit sets A bit set represents a collection of small integers as the bits of a larger integer. For example, the bit set containing 3, 2, and 0 would be represented as the integer 1101 in binary, which is 13 in decimal. Internally, bit sets use an array of 64-bit Longs. The first Long in the array is for integers 0 through 63, the second is for 64 through 127, and so on. Thus, bit sets are very compact so long as the largest integer in the set is less than a few hundred or so. Operations on bit sets are very fast. Testing for inclusion takes constant time. Adding an item to the set takes time proportional to the number of Longs in the bit set’s array, which is typically a small number. Here are some simple examples of the use of a bit set: scala> val bits = scala.collection.immutable.BitSet.empty bits: scala.collection.immutable.BitSet = BitSet() scala> val moreBits = bits + 3 + 4 + 4 moreBits: scala.collection.immutable.BitSet = BitSet(3, 4) scala> moreBits(3) res34: Boolean = true Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.10 Chapter 24 · The Scala Collections API 571 scala> moreBits(0) res35: Boolean = false List maps A list map represents a map as a linked list of key-value pairs. In general, operations on a list map might have to iterate through the entire list. Thus, operations on a list map take time linear in the size of the map. In fact there is little usage for list maps in Scala because standard immutable maps are almost always faster. The only possible difference is if the map is for some reason constructed in such a way that the first elements in the list are selected much more often than the other elements. scala> val map = collection.immutable.ListMap( 1 -> "one", 2 -> "two") map: scala.collection.immutable.ListMap[Int,java.lang.String] = Map((1,one), (2,two)) scala> map(2) res36: java.lang.String = two 24.10 Concrete mutable collection classes Now that you’ve seen the most commonly used immutable collection classes that Scala provides in its standard library, take a look at the mutable collec- tion classes. Array buffers You’ve already seen array buffers in Section 17.1. An array buffer holds an array and a size. Most operations on an array buffer have the same speed as an array, because the operations simply access and modify the underlying array. Additionally, array buffers can have data efficiently added to the end. Appending an item to an array buffer takes amortized constant time. Thus, array buffers are useful for efficiently building up a large collection whenever the new items are always added to the end. Here are some examples: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.10 Chapter 24 · The Scala Collections API 572 scala> val buf = collection.mutable.ArrayBuffer.empty[Int] buf: scala.collection.mutable.ArrayBuffer[Int] = ArrayBuffer() scala> buf += 1 res37: buf.type = ArrayBuffer(1) scala> buf += 10 res38: buf.type = ArrayBuffer(1, 10) scala> buf.toArray res39: Array[Int] = Array(1, 10) List buffers You’ve also already seen list buffers in Section 17.1. A list buffer is like an array buffer except that it uses a linked list internally instead of an array. If you plan to convert the buffer to a list once it is built up, use a list buffer instead of an array buffer. Here’s an example:5 scala> val buf = collection.mutable.ListBuffer.empty[Int] buf: scala.collection.mutable.ListBuffer[Int] = ListBuffer() scala> buf += 1 res40: buf.type = ListBuffer(1) scala> buf += 10 res41: buf.type = ListBuffer(1, 10) scala> buf.toList res42: List[Int] = List(1, 10) String builders Just like an array buffer is useful for building arrays, and a list buffer is useful for building lists, a string builder is useful for building strings. String builders are so commonly used that they are already imported into the default namespace. Create them with a simple new StringBuilder, like this: 5The “buf.type” that appears in the interpreter responses in this and several other ex- amples in this section is a singleton type. As will be explained in Section 29.6, buf.type means the variable holds exactly the object referred to by buf. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.10 Chapter 24 · The Scala Collections API 573 scala> val buf = new StringBuilder buf: StringBuilder = StringBuilder() scala> buf += 'a' res43: buf.type = StringBuilder(a) scala> buf ++= "bcdef" res44: buf.type = StringBuilder(a, b, c, d, e, f) scala> buf.toString res45: String = abcdef Linked lists Linked lists are mutable sequences that consist of nodes that are linked with next pointers. In most languages null would be picked as the empty linked list. That does not work for Scala collections, because even empty sequences must support all sequence methods. LinkedList.empty.isEmpty, in par- ticular, should return true and not throw a NullPointerException. Empty linked lists are encoded instead in a special way: Their next field points back to the node itself. Like their immutable cousins, linked lists are best operated on sequen- tially. In addition, linked lists make it easy to insert an element or linked list into another linked list. Double linked lists DoubleLinkedLists are like the single linked lists described in the previous subsection, except besides next, they have another mutable field, prev, that points to the element preceding the current node. The main benefit of that additional link is that it makes element removal very fast. Mutable lists A MutableList consists of a single linked list together with a pointer that refers to the terminal empty node of that list. This makes list append a con- stant time operation because it avoids having to traverse the list in search for its terminal node. MutableList is currently the standard implementation of mutable.LinearSeq in Scala. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.10 Chapter 24 · The Scala Collections API 574 Queues Scala provides mutable queues in addition to immutable ones. You use a mutable queue similarly to the way you use an immutable one, but instead of enqueue, you use the += and ++= operators to append. Also, on a muta- ble queue, the dequeue method will just remove the head element from the queue and return it. Here’s an example: scala> val queue = new scala.collection.mutable.Queue[String] queue: scala.collection.mutable.Queue[String] = Queue() scala> queue += "a" res46: queue.type = Queue(a) scala> queue ++= List("b", "c") res47: queue.type = Queue(a, b, c) scala> queue res48: scala.collection.mutable.Queue[String] = Queue(a, b, c) scala> queue.dequeue res49: String = a scala> queue res50: scala.collection.mutable.Queue[String] = Queue(b, c) Array sequences Array sequences are mutable sequences of fixed size that store their elements internally in an Array[AnyRef]. They are implemented in Scala by class ArraySeq. You would typically use an ArraySeq if you want an array for its per- formance characteristics, but you also want to create generic instances of the sequence where you do not know the type of the elements and do not have a ClassManifest to provide it at run-time. You will find out about these issues with arrays shortly, in Section 24.11. Stacks You saw immutable stacks earlier. There is also a mutable version. It works exactly the same as the immutable version except that modifications happen in place. Here’s an example: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.10 Chapter 24 · The Scala Collections API 575 scala> val stack = new scala.collection.mutable.Stack[Int] stack: scala.collection.mutable.Stack[Int] = Stack() scala> stack.push(1) res51: stack.type = Stack(1) scala> stack res52: scala.collection.mutable.Stack[Int] = Stack(1) scala> stack.push(2) res53: stack.type = Stack(2, 1) scala> stack res54: scala.collection.mutable.Stack[Int] = Stack(2, 1) scala> stack.top res55: Int = 2 scala> stack res56: scala.collection.mutable.Stack[Int] = Stack(2, 1) scala> stack.pop res57: Int = 2 scala> stack res58: scala.collection.mutable.Stack[Int] = Stack(1) Array stacks ArrayStack is an alternative implementation of a mutable stack, which is backed by an Array that gets resized as needed. It provides fast indexing and is generally slightly more efficient for most operations than a normal mutable stack. Hash tables A hash table stores its elements in an underlying array, placing each item at a position in the array determined by the hash code of that item. Adding an element to a hash table takes only constant time, so long as there isn’t already another element in the array that has the same hash code. Hash tables are thus very fast so long as the objects placed in them have a good distribution of hash codes. As a result, the default mutable map and set types in Scala are based on hash tables. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.10 Chapter 24 · The Scala Collections API 576 Hash sets and maps are used just like any other set or map. Here are some simple examples: scala> val map = collection.mutable.HashMap.empty[Int,String] map: scala.collection.mutable.HashMap[Int,String] = Map() scala> map += (1 -> "make a web site") res59: map.type = Map((1,make a web site)) scala> map += (3 -> "profit!") res60: map.type = Map((1,make a web site), (3,profit!)) scala> map(1) res61: String = make a web site scala> map contains 2 res62: Boolean = false Iteration over a hash table is not guaranteed to occur in any particular order. Iteration simply proceeds through the underlying array in whichever order it happens to be. To get a guaranteed iteration order, use a linked hash map or set instead of a regular one. A linked hash map or set is just like a regular hash map or set except that it also includes a linked list of the elements in the order they were added. Iteration over such a collection is always in the same order that the elements were initially added. Weak hash maps A weak hash map is a special kind of hash map in which the garbage collector does not follow links from the map to the keys stored in it. This means that a key and its associated value will disappear from the map if there is no other reference to that key. Weak hash maps are useful for tasks such as caching, where you want to re-use an expensive function’s result if the function is called again on the same key. If keys and function results are stored in a regular hash map, the map could grow without bounds, and no key would ever become garbage. Using a weak hash map avoids this problem. As soon as a key object becomes unreachable, it’s entry is removed from the weak hash map. Weak hash maps in Scala are implemented as a wrapper of an underlying Java implementation, java.util.WeakHashMap. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.10 Chapter 24 · The Scala Collections API 577 Concurrent Maps A concurrent map can be accessed by several threads at once. In addition to the usual Map operations, it provides the following atomic operations: Table 24.9 · Operations in trait ConcurrentMap What it is What it does m putIfAbsent(k, v) Adds key/value binding k -> m unless k is already defined in m m remove (k, v) Removes entry for k if it is currently mapped to v m replace (k, old, new) Replaces value associated with key k to new, if it was previously bound to old m replace (k, v) Replaces value associated with key k to v, if it was previously bound to some value ConcurrentMap is a trait in the Scala collections library. Currently, its only implementation is Java’s java.util.concurrent.ConcurrentMap, which can be converted automatically into a Scala map using the standard Java/Scala collection conversions, which will be described in Section 24.18. Mutable bit sets A mutable bit set is just like an immutable one, except that it can be mod- ified in place. Mutable bit sets are slightly more efficient at updating than immutable ones, because they don’t have to copy around Longs that haven’t changed. Here is an example: scala> val bits = scala.collection.mutable.BitSet.empty bits: scala.collection.mutable.BitSet = BitSet() scala> bits += 1 res63: bits.type = BitSet(1) scala> bits += 3 res64: bits.type = BitSet(1, 3) scala> bits res65: scala.collection.mutable.BitSet = BitSet(1, 3) Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.11 Chapter 24 · The Scala Collections API 578 24.11 Arrays Arrays are a special kind of collection in Scala. One the one hand, Scala ar- rays correspond one-to-one to Java arrays. That is, a Scala array Array[Int] is represented as a Java int[], an Array[Double] is represented as a Java double[] and an Array[String] is represented as a Java String[]. But at the same time, Scala arrays offer much more their Java analogues. First, Scala arrays can be generic. That is, you can have an Array[T], where T is a type parameter or abstract type. Second, Scala arrays are compatible with Scala sequences—you can pass an Array[T] where a Seq[T] is required. Finally, Scala arrays also support all sequence operations. Here’s an exam- ple of this in action: scala> val a1 = Array(1, 2, 3) a1: Array[Int] = Array(1, 2, 3) scala> val a2 = a1 map (_ * 3) a2: Array[Int] = Array(3, 6, 9) scala> val a3 = a2 filter (_ % 2 != 0) a3: Array[Int] = Array(3, 9) scala> a3.reverse res1: Array[Int] = Array(9, 3) Given that Scala arrays are represented just like Java arrays, how can these additional features be supported in Scala? In fact, the answer to this question differs between Scala 2.8 and earlier versions. Previously, the Scala com- piler somewhat “magically” wrapped and unwrapped arrays to and from Seq objects, when required, in a process called boxing and unboxing. The details of this were quite complicated, in particular when you created a new array of generic type Array[T]. There were some puzzling corner cases and the performance of array operations was not all that predictable. The Scala 2.8 design is much simpler. Almost all compiler magic is gone. Instead the Scala 2.8 array implementation makes systematic use of implicit conversions. In Scala 2.8 an array does not pretend to be a sequence. It can’t really be that because the data type representation of a native array is not a subtype of Seq. Instead there is an implicit “wrapping” conversion between arrays and instances of class scala.collection.mutable.WrappedArray, which is a subclass of Seq. Here you see it in action: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.11 Chapter 24 · The Scala Collections API 579 scala> val seq: Seq[Int] = a1 seq: Seq[Int] = WrappedArray(1, 2, 3) scala> val a4: Array[Int] = seq.toArray a4: Array[Int] = Array(1, 2, 3) scala> a1 eq a4 res2: Boolean = true This interaction demonstrates that arrays are compatible with sequences, be- cause there’s an implicit conversion from Array to WrappedArray. To go the other way, from a WrappedArray to an Array, you can use the toArray method defined in Traversable. The last interpreter line above shows that wrapping then unwrapping with toArray gives you back the same array you started with. There is yet another implicit conversion that gets applied to arrays. This conversion simply “adds” all sequence methods to arrays but does not turn the array itself into a sequence. “Adding” means that the array is wrapped in another object of type ArrayOps, which supports all sequence methods. Typically, this ArrayOps object is short-lived; it will usually be inaccessible after the call to the sequence method and its storage can be recycled. Modern VMs often avoid creating this object entirely. The difference between the two implicit conversions on arrays is demon- strated here: scala> val seq: Seq[Int] = a1 seq: Seq[Int] = WrappedArray(1, 2, 3) scala> seq.reverse res2: Seq[Int] = WrappedArray(3, 2, 1) scala> val ops: collection.mutable.ArrayOps[Int] = a1 ops: scala.collection.mutable.ArrayOps[Int] = [I(1, 2, 3) scala> ops.reverse res3: Array[Int] = Array(3, 2, 1) You see that calling reverse on seq, which is a WrappedArray, will give again a WrappedArray. That’s logical, because wrapped arrays are Seqs, and calling reverse on any Seq will give again a Seq. On the other hand, calling reverse on the ops value of class ArrayOps will result in an Array, not a Seq. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.11 Chapter 24 · The Scala Collections API 580 The ArrayOps example above was quite artificial, intended only to show the difference to WrappedArray. Normally, you’d never define a value of class ArrayOps. You’d just call a Seq method on an array: scala> a1.reverse res4: Array[Int] = Array(3, 2, 1) The ArrayOps object gets inserted automatically by the implicit conversion. So the line above is equivalent to the following line, where intArrayOps was the conversion that was implicitly inserted previously: scala> intArrayOps(a1).reverse res5: Array[Int] = Array(3, 2, 1) This raises the question how the compiler picked intArrayOps over the other implicit conversion to WrappedArray in the line above. After all, both conversions map an array to a type that supports a reverse method, which is what the input specified. The answer to that question is that the two implicit conversions are prioritized. The ArrayOps conversion has a higher priority than the WrappedArray conversion. The first is defined in the Predef object whereas the second is defined in a class scala.LowPriorityImplicits, which is a superclass of Predef. Implicits in subclasses and subobjects take precedence over implicits in base classes. So if both conversions are ap- plicable, the one in Predef is chosen. A very similar scheme, which was described in Section 21.7, works for strings. So now you know how arrays can be compatible with sequences and how they can support all sequence operations. What about genericity? In Java you cannot write a T[] where T is a type parameter. How then is Scala’s Array[T] represented? In fact a generic array like Array[T] could be at run-time any of Java’s eight primitive array types byte[], short[], char[], int[], long[], float[], double[], boolean[], or it could be an array of objects. The only common run-time type encompassing all of these types is AnyRef (or, equivalently java.lang.Object), so that’s the type to which the Scala compiler maps Array[T]. At run-time, when an element of an ar- ray of type Array[T] is accessed or updated there is a sequence of type tests that determine the actual array type, followed by the correct array operation on the Java array. These type tests slow down array operations somewhat. You can expect accesses to generic arrays to be three to four times slower than accesses to primitive or object arrays. This means that if you need max- imal performance, you should prefer concrete over generic arrays. Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.11 Chapter 24 · The Scala Collections API 581 Representing the generic array type is not enough, however, There must also be a way to create generic arrays. This is an even harder problem, which requires a little bit of help from you. To illustrate the problem, consider the following attempt to write a generic method that creates an array: // This is wrong! def evenElems[T](xs: Vector[T]): Array[T] = { val arr = new Array[T]((xs.length + 1)/ 2) for (i <- 0 until xs.length by 2) arr(i / 2) = xs(i) arr } The evenElems method returns a new array that consists of all elements of the argument vector xs that are at even positions in the vector. The first line of the body of evenElems creates the result array, which has the same element type as the argument. So depending on the actual type parameter for T, this could be an Array[Int], or an Array[Boolean], or an array of some of the other primitive types in Java, or an array of some reference type. But these types all have different runtime representations, so how is the Scala runtime going to pick the correct one? In fact, it can’t do that based on the information it is given, because the actual type that corresponds to the type parameter T is erased at runtime. That’s why you will get the following error message if you attempt to compile the code above: error: cannot find class manifest for element type T val arr = new Array[T]((arr.length + 1)/ 2) ˆ What’s required here is that you help the compiler by providing a runtime hint of what the actual type parameter of evenElems is. This runtime hint takes the form of a class manifest of type scala.reflect.ClassManifest. A class manifest is a type descriptor object that describes what the top-level class of a type is. Alternatively to class manifests there are also full manifests of type scala.reflect.Manifest, which describe all aspects of a type. But for array creation, only class manifests are needed. The Scala compiler will generate code to construct and pass class man- ifests automatically if you instruct it to do so. “Instructing” means that you demand a class manifest as an implicit parameter, like this: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.11 Chapter 24 · The Scala Collections API 582 def evenElems[T](xs: Vector[T]) (implicit m: ClassManifest[T]): Array[T] = ... Using an alternative and shorter syntax, you can also demand that the type comes with a class manifest by using a context bound. This means following the type with a colon and the class name ClassManifest, like this: // This works def evenElems[T: ClassManifest](xs: Vector[T]): Array[T] = { val arr = new Array[T]((xs.length + 1)/ 2) for (i <- 0 until xs.length by 2) arr(i / 2) = xs(i) arr } The two revised versions of evenElems mean exactly the same. What hap- pens in either case is that when the Array[T] is constructed, the compiler will look for a class manifest for the type parameter T, that is, it will look for an implicit value of type ClassManifest[T]. If such a value is found, the manifest is used to construct the right kind of array. Otherwise, you’ll see an error message like the one shown previously. Here is an interpreter interaction that uses the evenElems method: scala> evenElems(Vector(1, 2, 3, 4, 5)) res6: Array[Int] = Array(1, 3, 5) scala> evenElems(Vector("this", "is", "a", "test", "run")) res7: Array[java.lang.String] = Array(this, a, run) In both cases, the Scala compiler automatically constructed a class manifest for the element type (first Int, then String) and passed it to the implicit parameter of the evenElems method. The compiler can do that for all con- crete types, but not if the argument is itself another type parameter without its class manifest. For instance, the following fails: scala> def wrap[U](xs: Vector[U]) = evenElems(xs) :6: error: could not find implicit value for evidence parameter of type ClassManifest[U] def wrap[U](xs: Vector[U]) = evenElems(xs) ˆ Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.12 Chapter 24 · The Scala Collections API 583 What happened here is that the evenElems demands a class manifest for the type parameter U, but none was found. The solution in this case is, of course, to demand another implicit class manifest for U. So the following works: scala> def wrap[U: ClassManifest](xs: Vector[U]) = evenElems(xs) wrap: [U](xs: Vector[U])(implicit evidence$1: ClassManifest[U])Array[U] This example also shows that the context bound in the definition of U is just a shorthand for an implicit parameter named here evidence$1 of type ClassManifest[U]. In summary, generic array creation demands class manifests. Whenever you create an array of a type parameter T, you also need to provide an implicit class manifest for T. The easiest way to do this is to declare the type param- eter with a ClassManifest context bound, as in [T: ClassManifest]. 24.12 Strings Like arrays, strings are not directly sequences, but they can be converted to them, and they also support all sequence operations. Here are some examples of operations you can invoke on strings: scala> val str = "hello" str: java.lang.String = hello scala> str.reverse res6: String = olleh scala> str.map(_.toUpper) res7: String = HELLO scala> str drop 3 res8: String = lo scala> str slice (1, 4) res9: String = ell scala> val s: Seq[Char] = str s: Seq[Char] = WrappedString(h, e, l, l, o) These operations are supported by two implicit conversions, which were ex- plained in Section 21.7. The first, low-priority conversion maps a String Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.13 Chapter 24 · The Scala Collections API 584 to a WrappedString, which is a subclass of immutable.IndexedSeq. This conversion was applied in the last line of the previous example in which a string was converted into a Seq. The other, high-priority conversion maps a string to a StringOps object, which adds all methods on immutable se- quences to strings. This conversion was implicitly inserted in the method calls of reverse, map, drop, and slice in the previous example. 24.13 Performance characteristics As the previous explanations have shown, different collection types have different performance characteristics. That’s often the primary reason for picking one collection type over another. You can see the performance char- acteristics of some common operations on collections summarized in two tables, Table 24.10 and Table 24.11. The entries in these two tables are explained as follows: C The operation takes (fast) constant time. eC The operation takes effectively constant time, but this might depend on some assumptions such as the maximum length of a vector or the distribution of hash keys. aC The operation takes amortized constant time. Some invocations of the operation might take longer, but if many operations are performed on average only constant time per operation is taken. Log The operation takes time proportional to the loga- rithm of the collection size. L The operation is linear, that is it takes time propor- tional to the collection size. - The operation is not supported. Table 24.10 treats sequence types—both immutable and mutable—with the following operations: Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.14 Chapter 24 · The Scala Collections API 585 head Selecting the first element of the sequence. tail Producing a new sequence that consists of all ele- ments except the first one. apply Indexing. update Functional update (with updated) for immutable sequences, side-effecting update (with update) for mutable sequences. prepend Adding an element to the front of the sequence. For immutable sequences, this produces a new se- quence. For mutable sequences it modifies the exist- ing sequence. append Adding an element at the end of the sequence. For immutable sequences, this produces a new se- quence. For mutable sequences it modifies the exist- ing sequence. insert Inserting an element at an arbitrary position in the sequence. This is only supported directly for muta- ble sequences. Table 24.11 treats mutable and immutable sets and maps with the follow- ing operations: lookup Testing whether an element is contained in set, or selecting a value associated with a key. add Adding a new element to a set or a new key/value pair to a map. remove Removing an element from a set or a key from a map. min The smallest element of the set, or the smallest key of a map. 24.14 Equality The collection libraries have a uniform approach to equality and hashing. The idea is, first, to divide collections into sets, maps, and sequences. Collec- tions in different categories are always unequal. For instance, Set(1, 2, 3) is unequal to List(1, 2, 3) even though they contain the same elements. On the other hand, within the same category, collections are equal if and Cover · Overview · Contents · Discuss · Suggest · Glossary · Index Section 24.14 Chapter 24 · The Scala Collections API 586 head tail apply update prepend append insert immutable List C C L L C L - Stream C C L L C L - Vector eC eC eC eC eC eC - Stack C C L L C L - Queue aC aC L L L C - Range C C C - - - - String C L C L L L - mutable ArrayBuffer C L C C L aC L ListBuffer C L L L C C L StringBuilder C L C C L aC L MutableList C L L L C C L Queue C L L L C C L ArraySeq C L C C - - - Stack C L L L C L L ArrayStack C L C C aC L L Array C L C C - - - Table 24.10· Performance characteristics of sequence types lookup add remove min immutable HashSet/HashMap eC eC eC L TreeSet/TreeMap Log Log Log Log BitSet C L L eCa ListMap L L L L mutable HashSet/HashMap eC