Verfügbarkeit: Program Proofs

Program Proofs:

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Hauptverfasser:	Leino, K. Rustan M. ca. 20./21. Jh (VerfasserIn), Leino, Kaleb ca. 20./21. Jh (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	MIT Press Ltd 2023
Schlagworte:	Softwaretest Programmverifikation COMPUTERS / Programming / Compilers COMPUTERS / Programming / Microsoft Computer programs - Testing Computer programs - Verification
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	20 line drawings, 30 figures
Beschreibung:	xxii, 474 Seiten Illustrationen, Diagramme 229 mm.
ISBN:	9780262546232

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Datensatz im Suchindex

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adam_text	Contents Preface Notes for Teachers 0. Introduction 0.0. Prerequisites............................................................................................ 0.1. Outline of Topics....................................................................................... 0.2. Dafny....................................................................................................... 0.3. Other Languages....................................................................................... ix xv 1 2 4 5 6 Part 0. Learning the Ropes 1. Basics 1.0. Methods.................................................................................................... 1.1. Assert Statements.................................................................................... 1.2. Working with the Verifier......................................................................... 1.3. Control Paths............................................................................................ 1.4. Method Contracts.................................................................................... 1.5. Functions................................................................................................. 1.6. Compiled versus Ghost............................................................................ 1.7. Summary.................................................................................................. 2. Making It Formal 2.0. Program State ......................................................................................... 2.1. Floyd Logic............................................................................................... 2.2. Hoare Triples............................................................................................ 2.3. Strongest Postconditions and Weakest Preconditions.............................. 2.4. WPandS?............................................................................................... 2.5. Conditional Control Flow......................................................................... 2.6. Sequential Composition............................................................................ 2.7. Method Calls and Postconditions............................................................ 2.8. Assert Statements.................................................................................... 2.9. Weakest Liberal Preconditions................................................................. 2.10. Method Calls with Preconditions............................................................ 2.11. Function Calls......................................................................................... 9 9 10 11 12 13 17 19 21 25 26 28 29 32 40 41 45 46 50 53 55 57 vi 2.12. Partial Expressions.......................................................................................... 58 2.13. Method Correctness....................................................................................... 60 2.14. Summary......................................................................................................... 60 3. Recursion and Termination 63 3.0. The Endless Problem....................................................................................... 64 3.1. Avoiding Infinite Recursion.............................................................................. 66 3.2. Well-Founded Relations.................................................................................... 70 3.3. Lexicographic Tuples....................................................................................... 72 3.4. Default decreases in Dafny ........................................................................... 79 3.5. Summary........................................................................................................... 80 4. Inductive Datatypes 83 4.0. Blue-Yellow Trees ............................................................................................. 84 4.1. Matching on Datatypes.................................................................................... 85 4.2. Discriminators and Destructors ..................................................................... 86 4.3. Structural Inclusion.......................................................................................... 88 4.4. Enumerations............................................................................................ 89 4.5. Type Parameters................................................................................................ 89 4.6. Abstract Syntax Trees for Expressions............................................................ 90 4.7. Summary........................................................................................................... 93 5. Lemmas and Proofs 95 5.0. Declaring a Lemma.......................................................................................... 96 5.1. Using a Lemma................................................................................................... 96 5.2. Proving a Lemma............................................................................................. 99 5.3. Back to Basics........................................................................................................ 102 5.4. Proof Calculations............................................................................................... 106 5.5. Example: Reduce.................................................................................................. 110 5.6. Example: Commutativity of Multiplication......................................................115 5.7. Example: Mirroring a Tree................................................................................ 118 5.8. Example: Working on Abstract Syntax Trees.................................................. 122 5.9. Summary.............................................................................................................. 130 Part 1. Functional Programs 6. Lists 137 6.0. List Definition..................................................................................................... 137 6.1. Length.................................................................................................................... 138 6.2. Intrinsic versus Extrinsic Specifications........................................................... 139 6.3. Take and Drop ..................................................................................................... 142 6.4. At .......................................................................................................................... 144 6.5. Find....................................................................................................................... 146 6.6. List Reversal........................................................................................................ 147 6.7. Lemmas in Expressions...................................................................................... 151 6.8. Eliding Type Arguments................................................................................... 157 6.9. Summary.............................................................................................................. 158 vii 7. Unary Numbers 161 7.0. Basic Definitions.................................................................................................. 162 7.1. Comparisons........................................................................................................ 162 7.2. Addition and Subtraction................................................................................... 165 7.3. Multiplication ..................................................................................................... 167 7.4. Division and Modulus......................................................................................... 167 7.5. Summary.............................................................................................................. 172 8. Sorting 175 8.0. Specification........................................................................................................ 175 8.1. InsertionSort........................................................................................................ 179 8.2. Merge Sort........................................................................................................... 181 8.3. Summary......................................................................................... 188 9. Abstraction 189 9.0. Grouping Declarations into Modules.............................................................. 190 9.1. Module Imports.................................................................................................. 190 9.2. ExportSets........................................................................................................... 191 9.3. Modular Specification of a Queue.................................................................... 194 9.4. Equality-Supporting Types................................................................................ 201 9.5. Summary..............................................................................................................204 10. Data-Structure Invariants 207 10.0. Priority-Queue Specification .......................................................................... 208 10.1. Designing the Data Structure.......................................................................... 210 10.2. Implementation..................................................................................................212 10.3. Making Intrinsic from Extrinsic....................................................................... 224 10.4. Summary........................................................................................................... 229 Part 2. Imperative Programs 11. Loops 235 11.0. Loop Specifications............................................................................................ 235 11.1. Loop Implementations...................................................................................... 241 11.2. Loop Termination............................................................................................... 247 11.3. Summarizing the Loop Rule............................................................................. 250 11.4. Integer Square Root............................................................................................ 252 11.5. Summary........................................................................................................... 255 12. Recursive Specifications, Iterative Programs 257 12.0. Iterative Fibonacci ............................................................................................ 257 12.1. Fibonacci Squared ............................................................................................ 260 12.2. Powers of 2 ........................................................................................................264 12.3. Sums....................................................................................................................267 12.4. Summary . . . .................................................................................................. 272 13. Arrays and Searching 275 13 .0. About Arrays................................................................................................. 275 13 .1. Linear Search................................................................................................. 280 viii 13.2. Binary Search..................................................................................................... 288 13.3. Minimum........................................................................................................... 292 13.4. Coincidence Count............................................................................................ 294 13.5. Slope Search........................................................................................................ 301 13.6. Canyon Search.................................................................................................. 304 13.7. Majority Vote..................................................................................................... 309 13.8. Summary........................................................................................................... 318 14. Modifying Arrays 321 14.0. Simple Frames..................................................................................................... 321 14.1. Basic Array Modification ................................................................................ 326 14.2. Summary........................................................................................................... 336 15. In-situ Sorting 337 15.0. Dutch National Flag......................................................................................... 337 15.1. Selection Sort..................................................................................................... 341 15.2. Quicksort........................................................................................................... 343 15.3. Summary........................................................................................................... 347 16. Objects 351 16.0. Checksums........................................................................................................ 352 16.1. Tokenizer ........................................................................................................... 359 16.2. Simple Aggregate Objects................................................................................ 364 16.3. Full Aggregate Objects...................................................................................... 374 16.4. Summary........................................................................................................... 382 17. Dynamic Heap Data Structures 387 17.0. Lazily Initialized Arrays................................................................................... 387 17.1. Extensible Array............................................................................................... 396 17.2. Binary Search Tree for a Map.......................................................................... 403 17.3. Iterator for the Map............................................................................................ 413 17.4. Summary........................................................................................................... 423 A. Dafny Syntax Cheat Sheet 427 B. Boolean Algebra 433 B.O. Boolean Values and Negation......................................................................... 433 B.l. Conjunction .......................................................................................................433 B.2. Predicates and Well-Definedness................................................................... 434 B.3. Disjunction and Proof Format......................................................................... 435 B.4. Implication..........................................................................................................437 B.5. Proving Implications........................................................................................ 438 B.6. Free Variables and Substitution...................................................................... 439 B.7. Universal Quantification..................................................................................441 B.8. Existential Quantification.................................................................................. 442 C. Answers to Select Exercises 445 References 459 Index 467
adam_txt	Contents Preface Notes for Teachers 0. Introduction 0.0. Prerequisites. 0.1. Outline of Topics. 0.2. Dafny. 0.3. Other Languages. ix xv 1 2 4 5 6 Part 0. Learning the Ropes 1. Basics 1.0. Methods. 1.1. Assert Statements. 1.2. Working with the Verifier. 1.3. Control Paths. 1.4. Method Contracts. 1.5. Functions. 1.6. Compiled versus Ghost. 1.7. Summary. 2. Making It Formal 2.0. Program State . 2.1. Floyd Logic. 2.2. Hoare Triples. 2.3. Strongest Postconditions and Weakest Preconditions. 2.4. WPandS?. 2.5. Conditional Control Flow. 2.6. Sequential Composition. 2.7. Method Calls and Postconditions. 2.8. Assert Statements. 2.9. Weakest Liberal Preconditions. 2.10. Method Calls with Preconditions. 2.11. Function Calls. 9 9 10 11 12 13 17 19 21 25 26 28 29 32 40 41 45 46 50 53 55 57 vi 2.12. Partial Expressions. 58 2.13. Method Correctness. 60 2.14. Summary. 60 3. Recursion and Termination 63 3.0. The Endless Problem. 64 3.1. Avoiding Infinite Recursion. 66 3.2. Well-Founded Relations. 70 3.3. Lexicographic Tuples. 72 3.4. Default decreases in Dafny . 79 3.5. Summary. 80 4. Inductive Datatypes 83 4.0. Blue-Yellow Trees . 84 4.1. Matching on Datatypes. 85 4.2. Discriminators and Destructors . 86 4.3. Structural Inclusion. 88 4.4. Enumerations. 89 4.5. Type Parameters. 89 4.6. Abstract Syntax Trees for Expressions. 90 4.7. Summary. 93 5. Lemmas and Proofs 95 5.0. Declaring a Lemma. 96 5.1. Using a Lemma. 96 5.2. Proving a Lemma. 99 5.3. Back to Basics. 102 5.4. Proof Calculations. 106 5.5. Example: Reduce. 110 5.6. Example: Commutativity of Multiplication.115 5.7. Example: Mirroring a Tree. 118 5.8. Example: Working on Abstract Syntax Trees. 122 5.9. Summary. 130 Part 1. Functional Programs 6. Lists 137 6.0. List Definition. 137 6.1. Length. 138 6.2. Intrinsic versus Extrinsic Specifications. 139 6.3. Take and Drop . 142 6.4. At . 144 6.5. Find. 146 6.6. List Reversal. 147 6.7. Lemmas in Expressions. 151 6.8. Eliding Type Arguments. 157 6.9. Summary. 158 vii 7. Unary Numbers 161 7.0. Basic Definitions. 162 7.1. Comparisons. 162 7.2. Addition and Subtraction. 165 7.3. Multiplication . 167 7.4. Division and Modulus. 167 7.5. Summary. 172 8. Sorting 175 8.0. Specification. 175 8.1. InsertionSort. 179 8.2. Merge Sort. 181 8.3. Summary. 188 9. Abstraction 189 9.0. Grouping Declarations into Modules. 190 9.1. Module Imports. 190 9.2. ExportSets. 191 9.3. Modular Specification of a Queue. 194 9.4. Equality-Supporting Types. 201 9.5. Summary.204 10. Data-Structure Invariants 207 10.0. Priority-Queue Specification . 208 10.1. Designing the Data Structure. 210 10.2. Implementation.212 10.3. Making Intrinsic from Extrinsic. 224 10.4. Summary. 229 Part 2. Imperative Programs 11. Loops 235 11.0. Loop Specifications. 235 11.1. Loop Implementations. 241 11.2. Loop Termination. 247 11.3. Summarizing the Loop Rule. 250 11.4. Integer Square Root. 252 11.5. Summary. 255 12. Recursive Specifications, Iterative Programs 257 12.0. Iterative Fibonacci . 257 12.1. Fibonacci Squared . 260 12.2. Powers of 2 .264 12.3. Sums.267 12.4. Summary . . . . 272 13. Arrays and Searching 275 13 .0. About Arrays. 275 13 .1. Linear Search. 280 viii 13.2. Binary Search. 288 13.3. Minimum. 292 13.4. Coincidence Count. 294 13.5. Slope Search. 301 13.6. Canyon Search. 304 13.7. Majority Vote. 309 13.8. Summary. 318 14. Modifying Arrays 321 14.0. Simple Frames. 321 14.1. Basic Array Modification . 326 14.2. Summary. 336 15. In-situ Sorting 337 15.0. Dutch National Flag. 337 15.1. Selection Sort. 341 15.2. Quicksort. 343 15.3. Summary. 347 16. Objects 351 16.0. Checksums. 352 16.1. Tokenizer . 359 16.2. Simple Aggregate Objects. 364 16.3. Full Aggregate Objects. 374 16.4. Summary. 382 17. Dynamic Heap Data Structures 387 17.0. Lazily Initialized Arrays. 387 17.1. Extensible Array. 396 17.2. Binary Search Tree for a Map. 403 17.3. Iterator for the Map. 413 17.4. Summary. 423 A. Dafny Syntax Cheat Sheet 427 B. Boolean Algebra 433 B.O. Boolean Values and Negation. 433 B.l. Conjunction .433 B.2. Predicates and Well-Definedness. 434 B.3. Disjunction and Proof Format. 435 B.4. Implication.437 B.5. Proving Implications. 438 B.6. Free Variables and Substitution. 439 B.7. Universal Quantification.441 B.8. Existential Quantification. 442 C. Answers to Select Exercises 445 References 459 Index 467
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title	Program Proofs
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