Object-Oriented Programming A Unified Foundation

371 Pages·1996·27.146 MB·English

by  Giuseppe Castagna (auth.)

Progress 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.
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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