Table Of ContentUNDERGRADUATE TEXTS IN COMPUTER SCIENCE
Editors
David Gries
Fred B. Schneider
Springer Science+Business Media, LLC
UNDERGRADUATE TEXTS IN COMPUTER SCIENCE
Beidler, Data Structures and Algorithms
Brooks, Problem Solving with Fortran 90
Grillmeyer, Exploring Computer Science with Scheme
Jalote, An Integrated Approach to Software Engineering, Second Edition
Kizza, Ethical and Social Issues in the Information Age
Kozen, Automata and Computability
Merritt and Stix, Migrating from Pascal to C++
Pearce, Programming and Meta-Programming in Scheme
Zeigler, Objects and Systems
Jon Pearce
Programming and
Meta-Programming in
Scheme
, Springer
JonPearce
Department of Mathematics and Computer Science
San Jose University
San Jose, CA 95192-0103
USA
Series Editors:
David Gries
Fred B. Schneider
Department of Computer Science
Cornell University
Upson HalI
Ithaca, NY 14853-7501
USA
Library of Congress Cataloging-in-Publication Data
Pearce, Jon.
Programming and meta-programming in Scheme / Jon Pearce.
p. cm. - (Undergraduate texts in computer science)
Includes bibliographica1 references and index.
ISBN 978-1-4612-7243-4 ISBN 978-1-4612-1682-7 (eBook)
DOI 10.1007/978-1-4612-1682-7
1. Scheme (Computer program language) 1. Title. II. Series
QA76.73.s34P4 1997
005.13'~c21 97-28476
Prînted on acid-free paper.
© 1998 Springer Science+Business Media New York
Originally published by Springer-VerlagNew York,Inc. in 1998
Softcover reprint ofthe hardcover Ist edition 1998
AII rights reserved. This work may not be translated or copied in whole or in part without the written permis
sion of the publisher, Springer Science+Business Media, LLC, except for
brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information
storage and retrieval, electronic adaptation, computer software, or by similar or dissimiJar methodology now
known or hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are
not especialIy identified, is not to be taken as a sign that such names, as understood by the Trade Marks and
Merchandise Marks Act, may accordingly be used freely by anyone.
Production managed by Steven Pisano; manufacturing supervised by Johanna Tschebull.
Photocomposed pages prepared from the author's Microsoft Word files.
987654321
ISBN 978-1-4612-7243-4
To my parents
Preface
The current domination of computing by C and C++ is so complete that publishing a
book on Scheme almost seems subversive. My heresy goes beyond language. Infonned
by the anticorporate intellectual values of my computer gurus, I have come to possess the
unpopular notion that ideas are more important than technology, that principles like ab
straction and modularity take us further than gigabytes and megahertz. This is really a
book about those ideas disguised as a book about Scheme. Scheme was selected partly
for historical reasons, but mostly because it allows us to encounter ideas without first
mastering memory management, compilers, 110, and advanced idioms. I want to con
gratulate my co-conspirators at Springer for their courage in joining me.
For the last five years I have successfully used drafts of this book as a text in a junior
level declarative programming course taught at San Jose State University. The course is
modeled after Scheme-based freshman-level courses taught at other universities, hence
prerequisites are minimal. Motivated students with basic computer and mathematical lit
eracy will be able to read this book.
By confining lectures to the core sections of each chapter and a few critical appendi
ces, leaving the other appendices and problem sections as homework assignments, I typi
cally manage to cover all but the last chapter in a semester. Occasionally students read
and solve problems from the last chapter as special projects. Students who finish the
course know Scheme. They have been introduced to important principles, concepts,
paradigms, and techniques, and they have a functional perspective they confidently carry
into subsequent courses.
Jon Pearce
Contents
Preface vii
Introduction 1
1.1 LISP.............................................................................................................. 1
1.1.1. liSP Dialects ................................................................................. 2
1.2 Scheme ............................ ........ ......................... ........... .......................... ... .... 2
1.2.1. Scheme on the Web........................................................................ 3
1.3. Structure of the Text.................................................................................... 3
/.3.1. Themes ........................................................................................... 4
1. Expressions and Values 5
1.1. Values ..... ,.................................................................................................... 5
1.1.1. Numbers ...................................., .................................................... 6
1.1.2. Characters...................................................................................... 6
1.1.3. Booleans......................................................................................... 7
1./ .4. Symbols .......................................................................................... 7
1.1.5. Procedures ..................................................................................... 8
1.1.6. Strings ............................................................................................ 9
1.1.7. Lists ................................................................................................ 10
1.I.B. Vectors ........................................................................................... 10
1.1.9. Pairs............................................................................................... 10
1.1.10. Other Value Domains ................................................................... 11
1.2. Expressions ............................................. ... ... ....... ............. ....... .................... 11
1.2.1. Literals ........................................................................................... 12
1.2.2. Symbols and the Global Environment............................................ 12
1.2.3. Applications ................................................................................... 13
1.2.4. Structures ....................................................................................... 16
1.2.5. Literals Revisited............................................................................ 16
1.3. The Scheme Interpreter................................................................................ 17
1.3.1. The Expression Evaluator .............................................................. 17
1.3.2. The Control Loop ........................................................................... 18
1.4. Defmitions ................................................................................................... 18
Appendices. ...................... ...... ................ ... ............ .... ......... ..... .... .................. ..... 20
Appendix 1.1. Defining Domains ............................................................. 20
x Contents
Appendix 1.2. Sessions ............................................................................. 22
Appendix 1.3. Numbers ............................................................................ 24
Problems ..................•..................................................................•....................... 26
2. Procedures 31
2.1. Derming and Applying Procedures ............................................................. 31
2.1.1. The Environmental Influence ......................................................... 32
2.1.2. The Modularity Principle and Top-Down Design.......................... 34
2.2. Building Procedures Using Application ...................................................... 36
2.2.1. Example: Coercions ....................................................................... 36
2.2.2. Example: Palindromes ................................................................... 39
2.3. The Abstraction Principle ..........•...•.•.............••••...........•.....•...•.•.................. 40
2.3.1. Constructors................................................................................... 41
2.3.2. Selectors ......................................................................................... 43
2.3.3. Lists as Pairs .................................................................................. 44
2.3.4. Example: Association Lists as Records.......................................... 45
2.4. Polymorphic Procedures.............................................................................. 47
2.4.1. Equivalence Predicates .................................................................. 47
2.4.2. The not and null? Predicates ......................................................... 48
2.4.3. Recognition Predicates .................................................................. 49
2.4.4. Example: Searching Association Lists ........................................... 49
2.5. Meta-Procedures .......................................................................................... 51
Appendices ......................................................................................................... 53
Appendix 2.1. Mathematics in Scheme..................................................... 53
Appendix 2.2. Sequences ......................................................................... 63
Appendix 2.3. The Edit-Test-Debug Cycle .............................................. 71
Problems ............................................................................................................. 72
3. Evaluation Control and Recursion 78
3.1. Evaluation Control....................................................................................... 78
3.2. Short Circuit Evaluation .............................................................................. 79
3.3. Conditional Evaluation................................................................................ 81
3.3.1. The if-structure............................................................................... 81
3.3.2. The cond-structure ......................................................................... 84
3.3.3. Input Validation ............................................................................. 85
3.3.4. The case-structure.......................................................................... 85
3.4. Recursion..................................................................................................... 87
3.4.1. Example: Triangle Numbers .......................................................... 87
3.4.2. Tracing........................................................................................... 89
3.4.3. More on Input Validation............................................................... 90
3.4.4. Mathematical Induction ................................................................. 91
Contents xi
3.5. Thinking Recursively................................................................................... 93
3.5.1. Example: make-list......................................................................... 93
3.5.2. Example: nat-expt .......................................................................... 95
3.5.3. Example: evaluate.......................................................................... 96
Appendices ......................................................................................................... 97
Appendix 3.1. Sequential Evaluation ....................................................... 97
Appendix 3.2. Input and Output in Scheme.............................................. 98
Appendix 3.3. Defensive Programming .................................................... 104
Appendix 3.4. Debugging ......................................................................... 108
Problems ............................................................................................................. 111
4. Data Control 121
4.1. Procedure Blocks ......................................................................................... 121
4.1.1. The Nesting Instinct........................................................................ 122
4.2. The Environment Model of Eager Evaluation............................................. 126
4.2.1. Bindings ......................................................................................... 126
4.2.2. Environments ................................................................................. 127
4.2.3. Static Versus Dynamic Scope Rules ............................................... 129
4.3. Abstract Data Types .................................................................................... 132
4.3.1. Example: The CARD ADT. ............................................................ 132
4.3.2. Information Hiding and Data Abstraction ..................................... 135
4.3.3. Example: The POINT ADT ............................................................ 136
4.4. Overloading ................................................................................................. 137
4.5. Domains as Data .......................................................................................... 139
4.5.1. Programmer-Defined Types ........................................................... 140
4.5.2. Example: Complex Numbers .......................................................... 141
4.6. Data-Driven Programming .......................................................................... 145
Appendices ......................................................................................................... 147
. Appendix 4.1. Object-Oriented Programming ......................................... 147
Appendix 4.2. Expression Blocks ............................................................. 156
Problems ............................................................................................................. 159
s. Iteration 170
5.1. Modeling Systems ....................................................................................... 170
5.1.1. Iterative Evaluation ........................................................................ 171
5.1.2. Control Loops ................................................................................ 173
5.1.3. Example: A Digital Clock .............................................................. 175
5.1.4. Example: Compound Interest......................................................... 177
5.1.5. Example: A Simple Interactive System ........................................... 178
5.1.6. Example: Guess and Test ............................................................... 180
5.2. Computations as Data .................................................................................. 183
5.2.1. Predicting the Future ..................................................................... 184
xii Contents
5.2.2. Measuring Computations ............................................................... 185
5.2.3. Measuring Efficiency ..................................................................... 186
5.2.4. The Tyranny of Growth Rate .......................................................... 187
5.3. Finding Iterative Solutions .......................................................................... 187
5.4. Tail Recursion: Are do-loops Necessary? ................................................... 188
5.5. Finding Elementary Solutions ..................................................................... 190
Appendices ............. ............................................. ..... ......... ..... ............................ 191
Appendix 5.1. The Hyper-Exponential Hierarchy ................................... 191
Appendix 5.2. Undecidability .................................................................. 194
Appendix 5.3. Chaos ............................................................................... 196
Problems ............................................................................................................. 201
6. Recursive Domains 209
6.1. Recursive Domains as Hierarchies .................... .......................................... 210
6.1.1. Recursion over Hierarchies ........................................................... 211
6.2. List Recursion.. ................ ....... ....... .... ......... ......................... ........................ 211
6.2.1. Application: Are Lists Necessary? ................................................. 211
6.2.2. Application: Association Lists ........................................................ 213
6.3. The Signal Processing Paradigm ................................................................. 219
6.3.1. Filters ............................................................................................. 220
6.3.2, Amplifiers (Map) ............................................................................ 222
6.3.3. Receivers (Accumulators) .............................................................. 224
6.3.4. Transmitters (Generators) .............................................................. 226
6.3.5. Applications ................................................................................... 227
6.4. Trees and Tree Recursion ............................................................................ 228
6.4.1. Terminology ................................................................................... 229
6.4.2. The TREE Domain ......................................................................... 229
6.4.3. Tree Recursion ............................................................................... 230
6.4.4. Efficiency of Tree Recursions ......................................................... 236
Appendices ......... ....................................... ............................ ............................. 236
Appendix 6.1. Promises ........................................................................... 236
Appendix 6.2. Streams ............................................................................. 241
Problems ............................................................................................................. 246
7. Variables 257
7.1. Stores ........................................................................................................... 257
7.2. Variables and References ............................................................................. 259
7.3. Commands ................................................................................................... 261
7.4. L-Value versus R-Value ............................................................................... 263
7.5. Aliasing ........................................................................................................ 263
