Refinement calculus: a systematic introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
1998
|
| Ausgabe: | [Nachdr.] |
| Schriftenreihe: | Graduate texts in computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 501 - 508 |
| Beschreibung: | XV, 519 S. graph. Darst. |
| ISBN: | 0387984178 9780387984179 |
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Datensatz im Suchindex
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| adam_text | Ralph-Johan Back Joakim von Wright
REFINEMENT CALCULUS
A Systematic Introduction
With 27 Illustrations
Springer
Contents
Preface v
1 Introduction 1
1 1 Contracts 1
1 2 Using Contracts 6
1 3 Computers as Agents 9
1 4 Algebra of Contracts 10
1 5 Programming Constructs 12
1 6 Specification Constructs 15
1 7 Correctness 18
1 8 Refinement of Programs 20
1 9 Background 21
1 10 Overview of the Book 24
1 Foundations 27
2 Posets, Lattices, and Categories 29
2 1 Partially Ordered Sets 29
2 2 Lattices 36
2 3 Product and Function Spaces 40
2 4 Lattice Homomorphisms 43
2 5 Categories 49
2 6 Summary and Discussion 54
2 7 Exercises 54
3 Higher-Order Logic 57
3 1 Types and Terms 57
3 2 Semantics 62
3 3 Deductive Systems 63
3 4 Theories 65
3 5 Summary and Discussion 66
3 6 Exercises 67
Contents
4 Functions 69
4 1 Properties of Functions 69
4 2 Derivations 73
4 3 Definitions 77
4 4 ProductType 80
4 5 Summary and Discussion 82
4 6 Exercises 83
5 States and State Transformers 85
5 1 State Transformers 85
5 2 State Attributes and Program Variables 86
5 3 Reasoning with Program Variables 91
5 4 Straight-Line Programs 97
5 5 Procedures 98
5 6 Blocks and Value Parameters 101
5 7 Summary and Discussion 107
5 8 Exercises 108
6 Truth Values 109
6 1 Inference Rules for Boolean Lattices 109
6 2 Truth Values I l l
6 3 Derivations with Logical Connectives 112
6 4 Quantification 115
6 5 Assumptions 118
6 6 Derivations with Local Assumptions 120
6 7 Summary and Discussion 123
6 8 Exercises 124
7 Predicates and Sets 127
7 1 Predicates and Sets 127
7 2 Images and Indexed Sets 130
7 3 Inference Rules for Complete Lattices 131
7 4 Bounded Quantification 133
7 5 Selection and Individuals 135
7 6 Summary and Discussion 136
7 7 Exercises 137
8 Boolean Expressions and Conditionals 139
8 1 Boolean Expressions 139
8 2 Reasoning About Boolean Expressions 141
8 3 Conditional Expressions 143
8 4 Proving Properties About Conditional State Transformers 146
8 5 Summary and Discussion 148
8 6 Exercises 149
Contents xi
9 Relations 151
9 1 Relation Spaces 151
9 2 State Relation Category 153
9 3 Coercion Operators 154
9 4 Relational Assignment 155
9 5 Relations as Programs 159
9 6 Correctness and Refinement 161
9 7 Summary 164
9 8 Exercises 164
10 Types and Data Structures 167
10 1 Postulating a New Type 167
10 2 Constructing a New Type 170
10 3 RecordTypes 172
10 4 Array Types 175
10 5 Dynamic Data Structures 179
10 6 Summary and Discussion 181
10 7 Exercises 181
11 Statements 185
11 Predicate Transformers 187
11 1 Satisfying Contracts 187
11 2 Predicate Transformers 189
11 3 Basic Predicate Transformers 192
11 4 Relational Updates 195
11 5 Duality 198
11 6 Preconditions and Guards 199
11 7 Summary and Discussion 200
11 8 Exercises 202
12 The Refinement Calculus Hierarchy 203
12 1 State Categories 203
12 2 Homomorphisms 206
12 3 Summary and Discussion 211
12 4 Exercises 212
13 Statements 213
13 1 Subtyping, Sublattices and Subcategories 213
13 2 Monotonic Predicate Transformers 217
13 3 Statements and Monotonic Predicate Transformers 219
13 4 Derived Statements 223
13 5 Procedures 227
xii Contents
13 6 Summary and Discussion 228
13 7 Exercises 230
14 Statements as Games 233
14 1 Game Interpretation 233
14 2 Winning Strategies 239
14 3 Correctness and Refinement 244
14 4 Summary and Discussion 246
14 5 Exercises 246
15 Choice Semantics 249
15 1 Forward and Backward Semantics 249
15 2 Comparing Semantics for Contract Statements 252
15 3 Refinement in the Choice Semantics 254
15 4 Summary and Discussion 255
15 5 Exercises 256
16 Subclasses of Statements 259
16 1 Homomorphic Predicate Transformers 259
16 2 Subcategories of Statements 264
16 3 Summary and Discussion 266
16 4 Exercises 267
17 Correctness and Refinement of Statements 269
17 1 Correctness 269
17 2 Stepwise Refinement 273
17 3 Refinement Laws 280
17 4 Refinement in Context 287
17 5 Refinement with Procedures 291
17 6 Example: Data Refinement 292
17 7 Summary and Conclusions 295
17 8 Exercises 297
III Recursion and Iteration 299
18 Well-founded Sets and Ordinals 301
18 1 Weil-Founded Sets and Well-Orders 301
18 2 Constructing the Natural Numbers 303
18 3 Primitive Recursion 305
18 4 Ordinals 307
18 5 Ordinal Recursion 310
18 6 How Far Can We Go? 312
18 7 Summary and Discussion 314
18 8 Exercises 314
Contents xiii
19 Fixed Points 317
19 1 FixedPoints 317
19 2 Fixed points as Limits 320
19 3 Properties of Fixed Points 322
19 4 Summary and Discussion 326
19 5 Exercises 327
20 Recursion 329
20 1 Fixed Points and Predicate Transformers 329
20 2 Recursion Introduction and Elimination 334
20 3 Recursive Procedures 336
20 4 Example: Computing the Square Root 342
20 5 Summary and Discussion 343
20 6 Exercises 344
21 Iteration and Loops 347
21 1 Iteration 347
21 2 Properties of Iterations 350
21 3 Correctness of Iterations 352
21 4 Loops 353
21 5 Loop Correctness 356
21 6 Loop Introduction and Elimination 359
21 7 Summary and Discussion 361
21 8 Exercises 362
22 Continuity and Executable Statements , 365
22 1 Limits and Continuity 365
22 2 Continuity of Statements 367
22 3 Continuity of Derived Statements 371
22 4 Executable Statements 373
22 5 Interactive Guarded Commands 377
22 6 Summary and Discussion 380
22 7 Exercises 381
23 Working with Arrays 383
23 1 Resetting an Array 383
23 2 Linear Search 386
23 3 Selection Sort 388
23 4 Counting Sort 390
23 5 Summary and Discussion 402
23 6 Exercises 402
xiv Contents
24 The N-Queens Problem 403
24 1 Analyzing the Problem 403
24 2 First Step: The Terminating Case 406
24 3 Second Step: Extending a Partial Solution 407
24 4 Third Step: Completing for Recursion Introduction 409
24 5 Final Result 411
24 6 Summary and Discussion 411
24 7 Exercises 412
25 Loops and Two-Person Games 413
25 1 Modeling Two-Person Games 413
25 2 Winning Strategies 415
25 3 Extracting Winning Strategies 417
25 4 Strategy Improvement 421
25 5 Summary and Discussion 422
25 6 Exercises 422
IV Statement Subclasses 425
26 Statement Classes and Normal Forms 427
26 1 Universally Conjunctive Predicate Transformers 427
26 2 Conjunctive Predicate Transformers 429
26 3 Disjunctive Predicate Transformers 431
26 4 Functional Predicate Transformers 432
26 5 Continuous Predicate Transformers 435
26 6 Homomorphic Choice Semantics 437
26 7 Summary and Discussion 443
26 8 Exercises 444
27 Specification Statements 447
27 1 Specifications 448
27 2 Refining Specifications by Specifications 449
27 3 Combining Specifications 453
27 4 Refining Conjunctive Specifications 457
27 5 General Refinement of Specifications 458
27 6 Summary and Discussion 460
27 7 Exercises 461
28 Refinement in Context 463
28 1 Taking the Context into Account 463
28 2 Rules for Propagating Context Assertions 467
28 3 Propagation in Derived Statements 471
28 4 Context Assumptions 475
Contents xv
28 5 Summary and Discussion 477
28 6 Exercises 478
29 Iteration of Conjunctive Statements 479
29 1 Properties of Fixed Points 479
29 2 Relating the Iteration Statements 482
29 3 Iteration of Meets 484
29 4 Loop Decomposition 486
29 5 Other Loop Transformations 487
29 6 Example: Finding the Period 489
29 7 Summary and Discussion 494
29 8 Exercises 494
Appendix 497
References 501
Index 509
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| indexdate | 2024-07-09T18:21:07Z |
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| isbn | 0387984178 9780387984179 |
| language | German |
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| spelling | Back, Ralph-Johan Verfasser aut Refinement calculus a systematic introduction Ralph-Johan Back ; Joakim von Wright [Nachdr.] New York [u.a.] Springer 1998 XV, 519 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in computer science Literaturverz. S. 501 - 508 Analyse (wiskunde) gtt Mathematische programmering gtt Calculus Computer logic Computer programming HOL (DE-588)4335765-9 gnd rswk-swf Programm (DE-588)4047394-6 gnd rswk-swf Korrektheit (DE-588)4240223-2 gnd rswk-swf Verbandstheorie (DE-588)4127072-1 gnd rswk-swf Verfeinerung (DE-588)4267759-2 gnd rswk-swf Programm (DE-588)4047394-6 s Korrektheit (DE-588)4240223-2 s Verfeinerung (DE-588)4267759-2 s HOL (DE-588)4335765-9 s Verbandstheorie (DE-588)4127072-1 s DE-604 Wright, Joakim von 1955- Verfasser (DE-588)120261189 aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008169855&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Back, Ralph-Johan Wright, Joakim von 1955- Refinement calculus a systematic introduction Analyse (wiskunde) gtt Mathematische programmering gtt Calculus Computer logic Computer programming HOL (DE-588)4335765-9 gnd Programm (DE-588)4047394-6 gnd Korrektheit (DE-588)4240223-2 gnd Verbandstheorie (DE-588)4127072-1 gnd Verfeinerung (DE-588)4267759-2 gnd |
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| title | Refinement calculus a systematic introduction |
| title_auth | Refinement calculus a systematic introduction |
| title_exact_search | Refinement calculus a systematic introduction |
| title_full | Refinement calculus a systematic introduction Ralph-Johan Back ; Joakim von Wright |
| title_fullStr | Refinement calculus a systematic introduction Ralph-Johan Back ; Joakim von Wright |
| title_full_unstemmed | Refinement calculus a systematic introduction Ralph-Johan Back ; Joakim von Wright |
| title_short | Refinement calculus |
| title_sort | refinement calculus a systematic introduction |
| title_sub | a systematic introduction |
| topic | Analyse (wiskunde) gtt Mathematische programmering gtt Calculus Computer logic Computer programming HOL (DE-588)4335765-9 gnd Programm (DE-588)4047394-6 gnd Korrektheit (DE-588)4240223-2 gnd Verbandstheorie (DE-588)4127072-1 gnd Verfeinerung (DE-588)4267759-2 gnd |
| topic_facet | Analyse (wiskunde) Mathematische programmering Calculus Computer logic Computer programming HOL Programm Korrektheit Verbandstheorie Verfeinerung |
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