Isabelle, Isar - a versatile environment for human readable formal proof documents:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
2002
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | München, Techn. Univ., Diss., 2002 |
| Physical Description: | XII, 317 S. |
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Record in the Search Index
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CONTENTS
1 INTRODUCTION 1
1.1 MOTIVATION . 1
1.2 RELATED WORK. 3
1.2.1 REAL THEOREM PROVING ENVIRONMENTS . 3
1.2.2 EXPERIMENTS ON HUMAN-READABLE PROOFS . 9
1.3 THE ISAR APPROACH TO FORMAL PROOF DOCUMENTS . 11
1.4 NOTIONS OF PROOF ACCORDING TO ISAR . 14
1.5 EXAMPLE: THE KNASTER-TARSKI THEOREM . 16
1.5.1 PRESENTATION FORMAT: TYPESET DOCUMENT OUTPUT. 16
1.5.2 PRIMARY PROOF: HUMAN-READABLE SOURCE . 17
1.5.3 PRIMITIVE FORMAT: INTERNAL PROOF TERMS. 20
1.6 OVERVIEW OF THE THESIS. 21
1.6.1 PART I: FOUNDATIONS . 21
1.6.2 PART II: TECHNIQUES. 21
1.6.3 PART III: APPLICATIONS. 22
1 FOUNDATIONS 23
2 PRELIMINARIES 25
2.1 BASIC MATHEMATICAL NOTIONS. 25
2.2 MINIMAL HIGHER-ORDER LOGIC . 27
2.2.1 TYPES AND TERMS. 28
2.2.2 PROPOSITIONS AND THEOREMS . 29
2.3 DEFINITIONAL THEORY EXTENSIONS . 31
2.3.1 SIMPLE DEFINITIONS . 32
2.3.2 WEAKENED DEFINITIONS. 32
2.3.3 OVERLOADED DEFINITIONS. 33
2.4 HIGHER-ORDER RESOLUTION . 33
2.4.1 HEREDITARY HARROP FORMULAS . 34
2.4.2 FUNDAMENTAL INFERENCE RULES . 35
2.5 THE ISABELLE/PURE FRAMEWORK. 37
V
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/964298074
VI
CONTENTS
3 THE ISAR PROOF LANGUAGE 41
3.1 INTRODUCTION. 41
3.2 SYNTAX AND SEMANTICS . 43
3.2.1 ISAR COMMANDS. 44
3.2.2 BASIC TYPES OF COMMANDS. 43
3.2.3 LSAR/VM TRANSITIONS. 47
3.2.4 RECOVERING STATIC SYNTAX . 30
3.3 GENERIC SUPPORT FOR NATURAL DEDUCTION. 37
3.3.1 CONTEXT ELEMENTS . 38
3.3.2 METHODS AND ATTRIBUTES. 39
3.3.3 DERIVED COMMANDS . 01
3.4 FURTHER CONCEPTS. 62
3.4.1 CASUAL TERM ABBREVIATIONS . 02
3.4.2 FORMAL COMMENTS AND ANTIQUOTATIONS . 04
3.4.3 TYPE INFERENCE AND POLYMORPHISM. 03
4 EXAMPLE: FIRST-ORDER LOGIC 69
4.1 FORMAL DEVELOPMENT. 09
4.1.1 SYNTAX. 09
4.1.2 PROPOSITIONAL LOGIC. 70
4.1.3 EQUALITY. 71
4.1.4 QUANTIFIERS. 71
4.2 DISCUSSION. 72
4.2.1 GENERIC PROOF SUPPORT FOR OBJECT-LOGICS. 72
4.2.2 NATURAL DEDUCTION SCHEMES . 74
4.2.3 DECLARATIVE VERSUS OPERATIONAL THEOREM PROVING . 76
4.2.4 FURTHER EXPRESSIONS OF NATURAL DEDUCTION . 82
II TECHNIQUES 93
5 ADVANCED NATURAL DEDUCTION 95
5.1 INTRODUCTION. 95
5.2 BASIC TECHNIQUES. 97
5.2.1 GENERAL CONTEXT ELEMENTS. 97
5.2.2 LOCAL FACTS AND GOALS .102
5.2.3 MIXED FORWARD AND BACKWARD REASONING.103
5.2.4 RAW PROOF BLOCKS .105
5.2.5 NON-ATOMIC STATEMENTS .108
5.3 GENERALIZED ELIMINATION.ILL
5.3.1 OBTAINING CONTEXTS .112
5.3.2 SUPPORTING REALISTIC SOUNDNESS PROOFS .113
5.3.3 COMMON PATTERNS OF GENERALIZED ELIMINATION .115
5.4 PROOF BY CASES AND INDUCTION.120
5.4.1 IMMEDIATE PATTERNS OF CASES AND INDUCTION .120
5.4.2 RULES AND CASES .123
\
CONTENTS
VII
5.4.3 PROOF METHODS.124
5.4.4 COMMON PATTERNS OF CASES AND INDUCTION .125
5.4.5 INDUCTION WITH NON-ATOMIC STATEMENTS.132
5.5 DISCUSSION.136
5.5.1 CONTEXT MANIPULATIONS IN MIZAR .136
5.5.2 SECOND-ORDER SCHEMES IN MIZAR AND DECLARE .138
5.5.3 GENERALIZED CASE-SPLITTING.141
6 CALCULATIONAL REASONING 145
6.1 INTRODUCTION.145
6.2 FOUNDATIONS OF CALCULATIONAL REASONING.147
6.2.1 CALCULATIONAL SEQUENCES.147
6.2.2 CALCULATIONAL ELEMENTS WITHIN THE PROOF LANGUAGE . 148
6.2.3 RULES AND PROOF SEARCH .151
6.3 COMMON PATTERNS OF CALCULATIONAL REASONING .152
6.3.1 VARIATION OF RULES .152
6.3.2 VARIATION OF CONCLUSIONS.155
6.3.3 VARIATION OF FACTS.156
6.3.4 VARIATION OF GENERAL STRUCTURE.158
6.4 DISCUSSION.158
6.4.1 ITERATED EQUALITIES IN MIZAR.158
6.4.2 DIJKSTRA'S UNIVERSAL CALCULATIONAL PROOF FORMAT .161
6.4.3 DEGENERATE CALCULATIONS AND BIG-STEP REASONING.165
III APPLICATIONS 173
7 THE ISABELLE/HOL APPLICATION ENVIRONMENT 175
7.1 THE HOL LOGIC.175
7.1.1 SIMPLY-TYPED SET THEORY.176
7.1.2 PRIMITIVE DEFINITIONS.177
7.2 ADVANCED DEFINITIONAL PACKAGES.180
7.2.1 INDUCTIVE SETS AND TYPES .181
7.2.2 RECURSIVE FUNCTION DEFINITIONS .186
7.2.3 EXTENSIBLE RECORDS.188
7.2.4 AXIOMATIC TYPE CLASSES .189
7.3 AUTOMATED PROOF METHODS .191
7.3.1 INCORPORATING ARBITRARY PROOF TOOLS.192
7.3.2 BASIC TYPES OF PROOF METHODS.193
7.4 THE MAIN ISABELLE/HOL LIBRARY.196
7.5 DISCUSSION.198
7.5.1 THEORY SPECIFICATIONS VERSUS PROOFS .198
7.5.2 PROOF METHODS AND RELEVANCE OF FACTS .203
VNI
CONTENTS
8 EXAMPLE: HIGHER-ORDER LOGIC 207
8.1 MINIMAL HIGHER-ORDER LOGIC.207
8.1.1 SIMPLY-TYPED LAMBDA-TERMS.207
8.1.2 BASIC LOGICAL CONNECTIVES .208
8.2 EXTENSIONAL EQUALITY.20!)
8.3 FURTHER CONNECTIVES.211
8.3.1 DEFINITIONS .211
8.3.2 DERIVED RULES.212
8.4 CLASSICAL LOGIC .210
8.5 HILBERT'S CHOICE OPERATOR .218
8.0 CONCRETE TYPES AND TYPE DEFINITIONS .21!)
8.0.1 BASIC CHARACTERIZATION OF TYPE DEFINITIONS .220
8.0.2 DERIVED RULES OF TYPE DEFINITIONS .222
8.7 DISCUSSION: ISAR TECHNIQUES .224
9 EXAMPLE: RATIONAL NUMBERS 229
9.1 MOTIVATION .229
9.2 QUOTIENT TYPES.232
9.2.1 EQUIVALENCE RELATIONS AND QUOTIENT TYPES.232
9.2.2 EQUALITY ON QUOTIENTS .233
9.2.3 PICKING REPRESENTING ELEMENTS .234
9.3 RATIONAL NUMBERS .235
9.3.1 FRACTIONS OVER INTEGERS .230
9.3.2 RATIONAL NUMBERS .240
9.4 DISCUSSION.245
9.4.1 ISAR TECHNIQUES.245
9.4.2 HOL TECHNIQUES .249
9.4.3 ARITHMETIC PROOF TOOLS.253
10 EXAMPLE: UNIX SECURITY 257
10.1 MOTIVATION .257
10.2 INTRODUCTION.260
10.2.1 THE UNIX PHILOSOPHY.260
10.2.2 UNIX SECURITY.261
10.2.3 ODD EFFECTS.262
10.3 UNIX FILE-SYSTEMS.263
10.3.1 NAMES.263
10.3.2 ATTRIBUTES.264
10.3.3 FILES.264
10.3.4 INITIAL FILE-SYSTEMS.266
10.3.5 ACCESSING FILE-SYSTEMS.266
10.4 FILE-SYSTEM TRANSITIONS .267
10.4.1 UNIX SYSTEM CALLS .267
10.4.2 BASIC PROPERTIES OF SINGLE TRANSITIONS.270
10.4.3 ITERATED TRANSITIONS.272
10.5 EXECUTABLE SEQUENCES.274
CONTENTS
IX
10.5.1 POSSIBLE TRANSITIONS.274
10.5.2 EXAMPLE EXECUTIONS.275
10.6 ODD EFFECTS TREATED FORMALLY.278
10.6.1 THE GENERAL PROCEDURE .278
10.G.2 THE PARTICULAR SETUP .279
10.6.3 INVARIANCE LEMMAS.280
10.6.4 PUTTING IT ALL TOGETHER.284
10.7 DISCUSSION.285
10.7.1 ISAR TECHNIQUES.285
10.7.2 EFFICIENCY OF ISABELLE/ISAR PROOF PROCESSING .291
11 CONCLUSION 297
11.1 STOCKTAKING.297
11.2 FUTURE WORK.299
BIBLIOGRAPHY 303
INDEX 315 |
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| spelling | Wenzel, Markus Michael 1969- Verfasser (DE-588)123579074 aut Isabelle, Isar - a versatile environment for human readable formal proof documents Markus Michael Wenzel Isabelle/Isar - a versatile environment for human-readable formal proof documents 2002 XII, 317 S. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2002 Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Automatisches Beweisverfahren (DE-588)4069034-9 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009791596&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wenzel, Markus Michael 1969- Isabelle, Isar - a versatile environment for human readable formal proof documents Automatisches Beweisverfahren (DE-588)4069034-9 gnd |
| subject_GND | (DE-588)4069034-9 (DE-588)4113937-9 |
| title | Isabelle, Isar - a versatile environment for human readable formal proof documents |
| title_alt | Isabelle/Isar - a versatile environment for human-readable formal proof documents |
| title_auth | Isabelle, Isar - a versatile environment for human readable formal proof documents |
| title_exact_search | Isabelle, Isar - a versatile environment for human readable formal proof documents |
| title_full | Isabelle, Isar - a versatile environment for human readable formal proof documents Markus Michael Wenzel |
| title_fullStr | Isabelle, Isar - a versatile environment for human readable formal proof documents Markus Michael Wenzel |
| title_full_unstemmed | Isabelle, Isar - a versatile environment for human readable formal proof documents Markus Michael Wenzel |
| title_short | Isabelle, Isar - a versatile environment for human readable formal proof documents |
| title_sort | isabelle isar a versatile environment for human readable formal proof documents |
| topic | Automatisches Beweisverfahren (DE-588)4069034-9 gnd |
| topic_facet | Automatisches Beweisverfahren Hochschulschrift |
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