Action Semantics

383 Pages·2005·6.027 MB·english

by  Peter D. Mosses

ACTION SEMANTICS
PETER D. MOSSES
Department of Computer Science
Aarhus University, Denmark
CAMBRIDGE
UNIVERSITY PRESS
http://www.cambridge.org
© Cambridge University Press 1992
First published 1992
First paperback edition 2005
ISBN 0 521 40347 2 hardback
ISBN 0 521 61933 5 paperback
Contents
I Introduction 1
1 Language Descriptions 3
1.1 Motivation 3
1.2 Requirements 4
1.3 Features 6
1.4 Syntax 8
1.4.1 Concrete Syntax 8
1.4.2 Abstract Syntax 10
1.4.3 Context-Sensitive Syntax 11
1.5 Semantics 13
1.5.1 Semantic Functions 13
1.5.2 Semantic Entities 15
1.6 Pragmatics 18
2 Action Semantic Descriptions 21
2.1 Abstract Syntax 24
2.2 Semantic Functions 27
2.3 Semantic Entities 31
3 Algebraic Specifications 36
3.1 A Natural Example 39
3.1.1 Symbols 41
3.1.2 Axioms 42
3.1.3 Models 47
3.2 Grammars 50
3.3 Semantic Equations 51
3.4 Structural Operational Semantics 52
VI
II Action Notation 57
4 Basic 59
4.1 Actions 62
4.2 /Action Notation/Facets 63
5 Data 67
5.1 /Data Notation 71
5.1.1 General 71
5.1.2 Instant 71
5.1.3 Tuples 72
5.1.4 Truth-Values 74
5.1.5 Numbers 75
5.1.6 Characters 78
5.1.7 Lists/Flat 79
5.1.8 Lists/Nested 80
5.1.9 Strings 81
5.1.10 Syntax 81
5.1.11 Sets 82
5.1.12 Maps 83
5.2 /Action Notation/Basic/Data 84
6 Functional 88
6.1 Actions 90
6.2 Yielders 92
6.3 /Action Notation/Basic/Yielders 93
6.4 /Action Notation/Facets 94
7 Declarative 98
7.1 Actions 102
7.2 Yielders 104
7.3 Data 105
7.4 /Action Notation/Facets 105
8 Imperative 108
8.1 Actions 110
8.2 Yielders 110
8.3 Data Ill
8.4 /Action Notation/Facets Ill
Vll
9 Reflective 114
9.1 Actions 116
9.2 Yielders 117
9.3 Data 117
10 Communicative 120
10.1 Actions 123
10.2 Yielders 125
10.3 Data 125
10.4 /Action Notation/Facets 126
III Semantic Descriptions 129
11 Statements 131
11.1 /Ad/Abstract Syntax 132
11.2 /Ad/Semantic Functions 133
11.2.1 Statements 133
11.3 /Ad/Semantic Entities 134
12 Literals 136
12.1 /Ad/Abstract Syntax 137
12.2 /Ad/Semantic Functions 138
12.2.1 Literals 138
12.3 /Ad/Semantic Entities 139
12.3.1 Sorts 139
12.3.2 Values 139
12.3.3 Numbers 139
12.3.4 Characters 140
12.3.5 Arrays 140
13 Expressions 142
13.1 /Ad/Abstract Syntax 144
13.2 /Ad/Semantic Functions 145
13.2.1 Expressions 145
13.2.2 Statements 148
13.3 /Ad/Semantic Entities 149
13.3.1 Values 149
13.3.2 Numbers 149
13.3.3 Arrays 150
vm
14 Declarations 152
14.1 /Ad/Abstract Syntax 154
14.2 /Ad/Semantic Functions 156
14.2.1 Declarations 156
14.2.2 Statements 157
14.2.3 Expressions 157
14.2.4 Identifiers 159
14.3 /Ad/Semantic Entities 159
14.3.1 Sorts 160
14.3.2 Values 160
14.3.3 Arrays 160
14.3.4 Records 160
14.3.5 Packages 160
15 Variables 163
15.1 /Ad/Abstract Syntax 167
15.2 /Ad/Semantic Functions 168
15.2.1 Declarations 168
15.2.2 Types 169
15.2.3 Statements 171
15.2.4 Expressions 171
15.3 /Ad/Semantic Entities 173
15.3.1 Sorts 173
15.3.2 Values 173
15.3.3 Variables 173
15.3.4 Types 173
15.3.5 Accesses 174
15.3.6 Arrays 174
15.3.7 Records 174
16 Subprograms 177
16.1 /Ad/Abstract Syntax 181
16.2 /Ad/Semantic Functions 182
16.2.1 Declarations 182
16.2.2 Statements 185
16.2.3 Expressions 187
16.3 /Ad/Semantic Entities 190
16.3.1 Sorts 190
16.3.2 Subprograms 191
16.3.3 Escapes 192
16.3.4 Errors 192
IX
17 Tasks 195
17.1 /Ad/Abstract Syntax 197
17.2 /Ad/Semantic Functions 198
17.2.1 Programs 198
17.2.2 Declarations 199
17.2.3 Statements 200
17.3 /Ad/Semantic Entities 202
17.3.1 Sorts 202
17.3.2 Tasks 203
17.3.3 Alternatives 203
17.3.4 Required Bindings 203
IV Conclusion 205
18 Other Frameworks 207
18.1 Denotational Semantics 208
18.2 VDM 211
18.3 Initial Algebra Semantics 212
18.4 Algebraic Semantics 212
18.5 Abstract Semantic Algebras 213
18.6 First-Order Identities 213
18.7 Evolving Algebras 214
18.8 Structural Operational Semantics 214
18.9 Hoare Logic 215
18.10Weakest Preconditions 216
19 Development 217
19.1 Origins 218
19.2 Current Status 225
19.3 Projects 228
19.4 Mailing List 228
Appendices 230
A AD Action Semantics 231
A.I Abstract Syntax 233
A.2 Semantic Functions 235
A.2.1 Identifiers 235
A.2.2 Literals 235
A.2.3 Expressions 235
A.2.4 Statements 241
A.2.5 Declarations 244
A.2.6 Types 248
A.2.7 Programs 249
A.3 Semantic Entities 250
A.3.1 Sorts 250
A.3.2 Values 250
A.3.3 Variables 250
A.3.4 Types 251
A.3.5 Numbers 251
A.3.6 Characters 252
A.3.7 Accesses 252
A.3.8 Arrays 253
A.3.9 Records 255
A.3.10 Packages 256
A.3.11 Subprograms 257
A.3.12 Tasks 259
A.3.13 Alternatives 260
A.3.14 Escapes 260
A.3.15 Errors 260
A.3.16 Required Bindings 260
B Action Notation 261
B.I Basic 263
B.2 Functional 264
B.3 Declarative 265
B.4 Imperative 266
B.5 Reflective 268
B.6 Communicative 268
B.7 Directive 270
B.8 Hybrid 271
B.9 Facets 272
XI
C Operational Semantics 278
C.I Abstract Syntax 280
C.I.I Actions 280
C.1.2 Yielders 280
C.1.3 Data 281
C.2 Semantic Entities 281
C.2.1 Acting 281
C.2.2 States 282
C.2.3 Commitments 282
C.2.4 Processing 283
C.3 Semantic Functions 284
C.3.1 Data 284
C.3.2 Yielders 284
C.3.3 Actions 285
C.3.4 Processes 291
C.4 Equivalence 293
C.4.1 Bisimulation 293
C.4.2 Testing Equivalence 295
D Informal Summary 296
D.I Basic Action Notation 299
D.2 Functional Action Notation 301
D.3 Declarative Action Notation 303
D.4 Imperative Action Notation 305
D.5 Reflective Action Notation 307
D.6 Communicative Action Notation 308
D.7 Directive Action Notation 311
D.8 Hybrid Action Notation 313
D.9 Facets 314
Xll
E Data Notation 316
E.I Instant 318
E.2 Tuples 319
E.3 Truth-Values 321
E.4 Numbers 322
E.4.1 Naturals 322
E.4.2 Integers 324
E.4.3 Rationals 325
E.4.4 Approximations 327
E.5 Characters 327
E.6 Lists 329
E.6.1 Flat 329
E.6.2 Nested 330
E.7 Strings 331
E.8 Syntax 332
E.9 Sets 332
E.10 Maps 334
F Meta-Notation 336
F.I Informal Summary 336
F.I.I Vocabulary 337
F.1.2 Sentences 338
F.1.3 Specifications 340
F.2 Formal Abbreviations 341
F.2.1 Specifications 341
F.2.2 Sentences 342
F.3 Abstract Syntax 345
F.4 Logic 346
G Assessment 347
G.I Modula-3 348
G.2 Ada 348
G.3 A Functional Programming Language 349
Bibliography 350
Symbol Index 357
Concept Index 365