Automatic proofs and refutations for higher-order logic:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2012
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| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120628-1097834-1-6 Inhaltsverzeichnis |
| Beschreibung: | IX, 173 S. graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Automatic proofs and refutations for higher-order logic |c Jasmin Christian Blanchette |
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
CONTENTS
CONTENTS VII
1 INTRODUCTION 1
1.1 MOTIVATION 1
1.2 CONTRIBUTIONS 3
1.3 PUBLICATIONS 4
1.4 STRUCTURE OF THIS THESIS 5
1.5 A NOTE ON THE PROOFS 5
2 ISABELLE/HOL 7
2.1 THE METALOGIC 7
2.2 THE HOL OBJECT LOGIC 8
2.3 DEFINITIONAL PRINCIPLES 10
3 COUNTEREXAMPLE GENERATION USING A RELATIONAL MODEL FINDER 15
3.1 FIRST-ORDER RELATIONAL LOGIC 16
3.2 BASIC TRANSLATIONS 17
3.2.1 A SOUND AND COMPLETE TRANSLATION 18
3.2.2 APPROXIMATION OF INFINITE TYPES AND PARTIALITY 22
3.3 TRANSLATION OF DEFINITIONAL PRINCIPLES 26
3.3.1 SIMPLE DEFINITIONS 27
3.3.2 INDUCTIVE DATATYPES AND RECURSIVE FUNCTIONS 28
3.3.3 INDUCTIVE AND COINDUCTIVE PREDICATES 31
3.3.4 COINDUCTIVE DATATYPES AND CORECURSIVE FUNCTIONS 33
3.4 OPTIMIZATIONS 35
3.4.1 FUNCTION SPECIALIZATION 35
3.4.2 BOXING 35
3.4.3 QUANTIFIER MASSAGING 36
3.4.4 ALTERNATIVE DEFINITIONS 37
3.4.5 TABULATION 37
3.4.6 HEURISTIC CONSTANT UNFOLDING 37
3.4.7 NECESSARY DATATYPE VALUES 38
3.4.8 LIGHTWEIGHT TRANSLATION 38
3.5 EXAMPLES 39
3.5.1 A CONTEXT-FREE GRAMMAR 39
3.5.2 AA TREES 41
3.5.3 THE VOLPANO-SMITH-IRVINE SECURITY TYPE SYSTEM 43
3.5.4 A HOTEL KEY CARD SYSTEM 44
VII
HTTP://D-NB.INFO/1026452821
IMAGE 2
3.5.5 LAZY LISTS 45
3.6 EVALUATION 46
3.7 RELATED WORK 48
4 MONOTONICITY INFERENCE 51
4.1 MONOTONICITY 51
4.2 FIRST CALCULUS: TRACKING EQUALITY AND QUANTIFIERS 53
4.2.1 EXTENSION RELATION AND CONSTANCY 54
4.2.2 SYNTACTIC CRITERIA 56
4.3 SECOND CALCULUS: TRACKING SETS 57
4.3.1 EXTENSION RELATION 58
4.3.2 TYPE CHECKING 60
4.3.3 MONOTONICITY CHECKING 63
4.3.4 TYPE INFERENCE 65
4.4 THIRD CALCULUS: HANDLING SET COMPREHENSIONS 65
4.4.1 EXTENSION RELATION 66
4.4.2 TYPE CHECKING 67
4.4.3 MONOTONICITY CHECKING 71
4.4.4 TYPE INFERENCE 72
4.5 PRACTICAL CONSIDERATIONS 73
4.5.1 CONSTANT DEFINITIONS 73
4.5.2 INDUCTIVE DATATYPES 74
4.5.3 EVALUATION 76
4.6 RELATED WORK 76
5 CASE STUDY: NITPICKING C++ CONCURRENCY 79
5.1 BACKGROUND 79
5.2 THE C++ MEMORY MODEL 80
5.2.1 INTRODUCTORY EXAMPLE 81
5.2.2 MEMORY ACTIONS AND ORDERS 81
5.2.3 ORIGINAL FORMALIZATION 82
5.2.4 C P P M E M 8 3
5.2.5 FINE-TUNED FORMALIZATION 84
5.3 LITMUS TESTS 85
5.3.1 STORE BUFFERING 85
5.3.2 LOAD BUFFERING 87
5.3.3 INDEPENDENT READS OF INDEPENDENT WRITES 88
5.3.4 MESSAGE PASSING 89
5.3.5 WRITE-TO-READ CAUSALITY 90
5.3.6 SEQUENTIAL LOCK 90
5.3.7 GENERALIZED WRITE-TO-READ CAUSALITY 92
5.4 RELATED WORK 92
5.5 DISCUSSION 93
6 PROOF DISCOVERY USING AUTOMATIC THEOREM PROVERS 95
6.1 TPTP SYNTAX 95
6.2 SLEDGEHAMMER AND METIS 97
6.3 EXTENSION WITH SMT SOLVERS 99
6.3.1 THE S M T PROOF METHOD 100
VIII
IMAGE 3
6.3.2 SOLVER INVOCATION 101
6.3.3 PROOF RECONSTRUCTION 102
6.3.4 RELEVANCE FILTERING 103
6.3.5 EXAMPLE 103
6.4 ELIMINATION OF HIGHER-ORDER FEATURES 104
6.4.1 ARGUMENTS AND PREDICATES 105
6.4.2 TRANSLATION OF A-ABSTRACTIONS 107
6.4.3 HIGHER-ORDER REASONING 107
6.5 ENCODING OF POLYMORPHIC TYPES 109
6.5.1 TRADITIONAL TYPE ENCODINGS I L L
6.5.2 SOUND TYPE ERASURE VIA MONOTONICITY INFERENCE 114
6.5.3 MONOMORPHIZATION-BASED ENCODINGS 119
6.5.4 SOUNDNESS AND COMPLETENESS 123
6.6 FURTHER TECHNICAL IMPROVEMENTS 127
6.6.1 FULL FIRST-ORDER LOGIC OUTPUT 128
6.6.2 FINE-TUNED RELEVANCE FILTER 128
6.6.3 TIME SLICING 129
6.6.4 ADDITIONAL PROVERS 129
6.6.5 FAST MINIMIZATION 130
6.6.6 REVAMPED USER EXPERIENCE 131
6.6.7 SKOLEMIZATION WITHOUT CHOICE 132
6.7 EVALUATION 135
6.7.1 EXPERIMENTAL SETUP 136
6.7.2 TYPE ENCODINGS 137
6.7.3 TRANSLATION OF A-ABSTRACTIONS 138
6.7.4 COMBINATION OF AUTOMATIC PROVERS 139
6.8 STRUCTURED PROOF CONSTRUCTION 141
6.8.1 PROOF NOTATIONS 143
6.8.2 EXAMPLES OF PROOF REDIRECTION 145
6.8.3 THE REDIRECTION ALGORITHM 149
6.9 RELATED WORK 153
7 CONCLUSION 155
7.1 RESULTS 155
7.2 FUTURE WORK 157
7.2.1 COUNTEREXAMPLE GENERATION WITH NITPICK 157
7.2.2 PROOF DISCOVERY WITH SLEDGEHAMMER 158
BIBLIOGRAPHY 159
IX
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| spelling | Blanchette, Jasmin Christian Verfasser aut Automatic proofs and refutations for higher-order logic Jasmin Christian Blanchette 2012 IX, 173 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2012 Gegenbeispiel (DE-588)4214218-0 gnd rswk-swf Generierung (DE-588)4402224-4 gnd rswk-swf HOL (DE-588)4335765-9 gnd rswk-swf Isabelle Programm (DE-588)4353452-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Isabelle Programm (DE-588)4353452-1 s HOL (DE-588)4335765-9 s Gegenbeispiel (DE-588)4214218-0 s Generierung (DE-588)4402224-4 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20120628-1097834-1-6 http://mediatum.ub.tum.de/node?id=1097834 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120628-1097834-1-6 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025184337&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blanchette, Jasmin Christian Automatic proofs and refutations for higher-order logic Gegenbeispiel (DE-588)4214218-0 gnd Generierung (DE-588)4402224-4 gnd HOL (DE-588)4335765-9 gnd Isabelle Programm (DE-588)4353452-1 gnd |
| subject_GND | (DE-588)4214218-0 (DE-588)4402224-4 (DE-588)4335765-9 (DE-588)4353452-1 (DE-588)4113937-9 |
| title | Automatic proofs and refutations for higher-order logic |
| title_auth | Automatic proofs and refutations for higher-order logic |
| title_exact_search | Automatic proofs and refutations for higher-order logic |
| title_full | Automatic proofs and refutations for higher-order logic Jasmin Christian Blanchette |
| title_fullStr | Automatic proofs and refutations for higher-order logic Jasmin Christian Blanchette |
| title_full_unstemmed | Automatic proofs and refutations for higher-order logic Jasmin Christian Blanchette |
| title_short | Automatic proofs and refutations for higher-order logic |
| title_sort | automatic proofs and refutations for higher order logic |
| topic | Gegenbeispiel (DE-588)4214218-0 gnd Generierung (DE-588)4402224-4 gnd HOL (DE-588)4335765-9 gnd Isabelle Programm (DE-588)4353452-1 gnd |
| topic_facet | Gegenbeispiel Generierung HOL Isabelle Programm Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1097834 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20120628-1097834-1-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025184337&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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