Table Of ContentProgress in Theoretical Computer Science
Editor
Ronald V. Book, University of California
Editorial Board
Erwin Engeler, ETH Zentrum, Zurich, Switzerland
Jean-Pierre Jouannaud, Universite de Paris-Sud, Orsay, France
Robin Milner, Cambridge University, England
Martin Wirsing, UniversiHit Passau, Passau, Germany
Giuseppe Castagna
Object-Oriented Programming
A Unified Foundation
Birkhauser
Boston • Basel • Berlin
Giuseppe Castagna
CNRS
LIENS
Ecole Normale Superieure
75005 Paris
France
Library of Congress Cataioging-in-Publication Data
Castagna, Giuseppe, 1966-
Object-oriented programming: a unified foundation / Giuseppe
Castagna.
p. cm. -- (Progress in theoretical computer science)
Includes bibliographical references (p. 345-357)
ISBN-13: 978-1-4612-8670-7 e-ISBN-13: 978-1-4612-4138-6
DOl: 10.107/978-1-4612-4138-6
paper)
1. Object-oriented programming (Computer science) 2. Programming
languages (Electronic computers) I. Title. II. Series.
QA76.64.C372 1997
005.13--dc20 96-33163
CIP
Printed on acid-free paper ~
© 1997 Birkhauser Boston Birkhiiuser lL(J2)
Softcover reprint of the hardcover 1st edition 1997
Copyright is not claimed for works of U.S. Government employees.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system,
or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording,
or otherwise, without prior permission of the copyright owner.
Permission to photocopy for internal or personal use of specific clients is granted by
Birkhauser Boston for libraries and other users registered with the Copyright Clearance
Center (CCC), provided that the base fee of$6.00 per copy, plus $0.20 per page is paid directly
to CCC, 222 Rosewood Drive, Danvers, MA 01923, U.S.A. Special requests should be
addressed directly to Birkhauser Boston, 675 Massachusetts Avenue, Cambridge, MA 02139,
U.S.A.
Typeset by the author in LATEX.
9 8 7 6 5 4 3 2 1
Contents
Foreword (by Luca Cardelli) xiii
Presentation of the book xv
I Introduction 1
1 Background and notation 3
1.1 A-notation . . . . . . ....... 3
1.1.1 The origins of A-calculus . 7
1.1.2 Data types .... 8
1.2 Simply-typed A-calculus 9
1.2.1 Reduction. 10
1.2.2 Typing ..... 12
1.2.3 Properties . . . . 14
1.2.4 Fixed point operators . 17
1.3 Subtyping ........ 18
1.3.1 The ~-calculus 18
1.3.2 Records ...... 27
1.3.3 Cartesian products 28
1.3.4 Recursive types . 29
1.4 Further definitions. . . . . 30
1.4.1 Algebra ...... 30
1.4.2 Term rewriting systems . 31
1.4.3 Logic .......... 33
2 A quick overview 35
.........
2.1 Introduction . 35
2.2 Object-oriented programming 40
2.3 The A&-calculus ....... 44
2.4 Covariance and contravariance 51
2.5 Strong normalization ..... 54
vi CONTENTS
2.6 Three variations on the theme. . . . . . . . 55
2.7 Interpretation of object-oriented languages. 58
2.8 Imperative features 62
2.9 Semantics.......... 63
2.10 Second-order . . . . . . . . 66
2.11 Second order overloading . . 68
2.12 Ft- and object-oriented programming 71
2.13 Conclusion ....... . . . . . . . 75
II Simple typing 77
3 Object-oriented programming 79
3.1 A kernel object-oriented language 80
3.1.1 Objects.......... 80
3.1.2 Messages......... 80
3.1.3 Methods versus functions 81
3.1.4 Classes ...... . 83
3.1.5 Inheritance........ 85
3.1.6 Multiple inheritance .. . 88
3.1. 7 Implementation of message-passing 90
3.1.8 Extending classes. . . . . . . . . . 90
3.1.9 Self, super and the use of coercions 92
3.1.10 First-class messages: adding overloading 95
3.1.11 Multi-methods 97
3.2 Type checking . . . . . . . . 98
3.2.1 The types ..... . 98
3.2.2 Intuitive typing rules 99
3.3 Object-oriented programming ala CLOS . 102
3.3.1 Classes ...... . 102
3.3.2 Methods ..... . 103
3.3.3 Multiple dispatching 105
3.3.4 Super and coerce 105
3.3.5 Types 106
3.4 Comparison .... . 106
3.5 Conclusion .... . 108
3.6 Bibliographical notes 111
4 The It&-calculus 113
4.1 Informal presentation . . . . . . . . . . . . . . . . 113
4.1.1 Subtyping, run-time types and late binding 114
4.2 The syntax of It&-calculus 116
4.2.1 Subtyping system . . 117
4.2.2 Types........ 118
CONTENTS vii
4.2.3 Tenns...... 119
4.2.4 Type system .. 120
4.2.5 Reduction Rules 123
4.3 Soundness of the type system . 126
4.4 Church-Rosser 129
4.5 Basic encodings . . . . 132
4.5.1 Products ... 132
4.5.2 Simple records 132
4.5.3 Updatable records 133
4.6 A& and object-oriented programming 135
4.6.1 The "objects as records" analogy. 137
4.6.2 Inheritance . . . . . . . . . . . . 139
4.6.3 Binary methods and multiple dispatch 141
4.6.4 Covariance vs. contravariance 143
4.6.5 Class extension . . . 143
4.6.6 First class messages 144
4.6.7 Abstract classes. 144
4.7 Related work . . . . . . . . 147
5 Covariance and contravariance: conflict without a cause 153
5.1 Introduction ................ . 154
5.2 The controversy . . . . . . . . . . . . . . . 154
5.3 Covariance in the overloading-based model 157
5.4 Covariance in the record-based model 159
5.5 Practical aspects . 163
5.6 Conclusion .. . 165
6 Strong Normalization 167
6.1 The full calculus is not nonnalizing 167
6.2 Fixed point combinators ..... 168
6.3 The reasons for non nonnalization 169
6.4 Typed-inductive properties . . . . . 171
6.5 Strong Nonnalization is typed-inductive 175
7 Three variations on the theme 177
7.1 Adding explicit coercions . 177
7.1.1 Properties..... 179
7.1.2 More on updatable records 181
7.2 More freedom to the system: A&+ ..... 182
7.3 Unifying overloading and A-abstraction: A{ } 185
7.3.1 Subject Reduction 187
7.3.2 Church-Rosser 188
7.4 Reference to other work. . 191
viii CONTENTS
8 Interpretation of object-oriented languages 193
8.1 Formal presentation of KOOL ... 194
8.1.1 The terms of the language 195
8.1.2 The types of the language 197
8.2 It_object ........ . 204
8.2.1 The type system 209
8.2.2 Some results .. 211
8.3 Translation ...... . 213
8.3.1 Correctness of the type-checking. . 215
8.3.2 Some remarks. . . . . . . 215
8.4 It_object and It& ........ . 216
8.4.1 The encoding of the types 216
8.4.2 The encoding of the terms 219
9 Imperative features and other widgets 221
9.1 Imperative features ...... . 221
9.1.1 Imperative KOOL .. . 223
9.1.2 Imperative 1t&-ca1culus 224
9.1.3 Interpretation 226
9.2 Unique application 228
9.3 Signatures ..... . 229
10 Semantics 235
10.1 Introduction . 235
10.2 The completion of overloaded types 236
10.3 Early Binding ..... . 240
10.4 Semantics . . . . . . . . . . . . . . 242
10.4.1 PER as a model . . . . . . . 242
10.4.2 Overloaded types as Products 246
10.4.3 The semantics of terms . 250
10.5 Summary of the semantics 256
III Second order 259
11 Introduction to part III 261
11.1 Loss of information in the record-based model . 262
11.1.1 Implicit Polymorphism . 263
11.1.2 Explicit Polymorphism . . . . . . 263
11.2 F$. .................... . 265
11.2.1 Subtyping and typing algorithms . 267
11.3 Furtherfeatures . . . . . . . . . . . . . . 269
11.3.1 Records and update ....... . 269
11.3.2 Quantification over recursive types. 270
CONTENTS ix
11.3.3 F-bounded quantification . 271
11.3.4 Existential quantification . 272
12 Second order overloading 275
12.1 Loss of information in the overloading -based model . 275
12.1.1 Type dependency . . 277
12.2 Type system. . . . . . . . . . . 279
12.2.1 Some useful results. . . 281
12.2.2 Transitivity elimination . 282
12.2.3 Subtyping algorithm and coherence of the system . 288
12.3 Terms 291
12.4 Reduction . . . . . . . . . . . . . . . . . . . 293
12.4.1 Soundness of the type system 294
12.4.2 Church-Rosser . . . . . . . . . . . 308
13 Second order overloading and object-oriented programming 313
13.1 Object-oriented programming ......... 313
13.1.1 Extending classes. . . . . . . . . . . . 316
13.1.2 First class messages, super and coerce . 316
13.1.3 Typing rules for polymorphic KOOL 317
13.1.4 Multiple dispatch. 319
13.1.5 Advanced features 320
13.2 Conclusion ........ 322
14 Conclusion 323
14.1 Object-oriented programming 323
14.2 Proof Theory . . . . . . . . . 324
14.3 Beyond object-oriented programming 326
IV Appendixes 329
A Specification of KOOL 331
A.l Terms .. . 331
A.2 Pretypes ..... . 332
A.3 Subtyping . . . . . 332
A.4 Auxiliary Notation 333
A.5 Typing Rules ... 333
B Formal definition of the translation 335
B.l Without mutually recursive methods 336
B.2 With recursive methods . . . . . . 338
B.3 Overloaded functions ...... . 339
B.4 Correctness of the type-checking . 340
x CONTENTS
Bibliography 345
Index 358
