An approach to the extension of a theorem prover by advanced structuring mechanisms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Logos
2010
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 229 S. graph. Darst. 24 cm |
| ISBN: | 9783832525026 3832525025 |
Internformat
MARC
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| 245 | 1 | 0 | |a An approach to the extension of a theorem prover by advanced structuring mechanisms |c Maksym Bortin |
| 264 | 1 | |a Berlin |b Logos |c 2010 | |
| 300 | |a 229 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 502 | |a Zugl.: Bremen, Univ., Diss., 2010 | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
CONTENTS
INTRODUCTION 11.1 THE THEOREM PROVER ISABELLE 21.2 CONSISTENCY AND
CORRECTNESS 31.3 SPECIFICATION, PARAMETRISATION AND STRUCTURING IN
ISABELLE 4 1.4 AXIOMATIC THEORIES AND MORPHISMS 71.5 RELATED WORK 101.6
THE STRUCTURE OF THE THESIS 18 1 EXTENDING A LOGICAL FRAMEWORK BY
MORPHISMS 21 2 FOUNDATIONS 23 2.1 THE SET OF THEORIES 232.2 CLASS
SIGNATURES 242.3 SORTS 252.4 TYPE SIGNATURES 282.5 TYPES 292.6 OPERATION
SIGNATURE 322.7 TERMS 332.8 PROPOSITIONS AND AXIOMS 392.9 DEFINITIONS,
LOGICAL AND DERIVED CONSTANTS 402.10 PROOF TERMS AND DERIVED
PROPOSITIONS 422.11 THEORY EXTENSIONS 472.12 OBJECT LOGICS 522.12.1
HIGHER ORDER LOGIC 532.13 CONCLUSION 56 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1003248020 DIGITALISIERT DURCH
IMAGE 2
CONTENTS
3 SIGNATURE MORPHISMS 59
3.1 RELATING CLASS SIGNATURES 60
3.1.1 CLASS MAP EXTENSION 61
3.2 RELATING TYPE SIGNATURES 62
3.2.1 TYPE MAP EXTENSION 66
3.2.2 EXAMPLE: SETS AS MONADS 69
3.3 RELATING OPERATION SIGNATURES 71
3.3.1 EXAMPLE: SETS AS MONADS 76
3.4 SIGNATURE MORPHISMS 77
3.4.1 EXAMPLE: SETS AS MONADS 78
3.4.2 BASE AND NORMALISABLE SIGNATURE MORPHISMS 79 3.5 NORMALISATION 80
3.5.1 MATCHING OF DEFINITIONS 84
3.6 COMPOSITION OF SIGNATURE MORPHISMS 85
3.6.1 COMPOSITION OF CLASS MAPS 85
3.6.2 COMPOSITION OF TYPE MAPS 86
3.6.3 COMPOSITION OF OPERATION MAPS 93
3.7 CONSTRUCTION OF SIGNATURE MORPHISMS IN ISABELLE 96
3.7.1 THE SIGMORPH COMMAND 96
3.7.2 CLASS MAP CONSTRUCTION 97
3.7.3 TYPE MAP CONSTRUCTION 100
3.7.4 OPERATION MAP CONSTRUCTION 102
3.7.5 EXAMPLE: SETS AS MONADS 102
3.8 CONCLUSION 103
4 THEORY MORPHISMS 105
4.1 THEORY MORPHISMS AND PROOF TERM TRANSLATION 106
4.1.1 EXAMPLE: SETS AS MONADS 108
4.1.2 PROOF TERM TRANSLATION 109
4.1.3 THEOREM TRANSLATION 112
4.2 COMPOSITION OF THEORY MORPHISMS 114
4.3 THEORY MORPHISMS IN ISABELLE 117
4.3.1 THE THYMORPH COMMAND 117
4.3.2 EXAMPLE: SETS AS MONADS 120
4.3.3 THE TRANSLATE_THM COMMAND 120
4.4 INCLUSIONS, IDENTITIES AND CATEGORIES 121
4.5 PARAMETERISED THEORIES AND INSTANTIATION 123
4.5.1 INSTANTIATION 124
4.5.2 INSTANTIATION OF PARAMETERISED THEORIES IN ISABELLE 142
IMAGE 3
CONTENTS
4.6 CONCLUSION 144
II STRUCTURED DEVELOPMENT IN ISABELLE 149
5 ALLEGORIES IN THE HIGHER ORDER LOGIC 151
5.1 INTRODUCTION 151
5.2 ALLEGORIES 152
5.3 PREDICATES ON ARROWS, RANGE OF AN ARROW 154
5.4 TWO EXAMPLE INSTANCES 158
5.4.1 A 4-ELEMENT ALLEGORY 158
5.4.2 BOUNDED SEMI-LATTICES 160
5.5 CONCLUSION 162
6 LOCALLY COMPLETE ALLEGORIES 163
6.1 FIXED POINTS AND KLEENE ALGEBRAS 166
6.1.1 KLEENE ALGEBRA 169
6.1.2 CHURCH-ROSSER PROPERTY AND CONFLUENCE 171
6.2 RELATORS AND HYLOMORPHISMS 175
6.3 REDUCTIVITY 178
6.4 THE DIVIDE-AND-CONQUER DESIGN TACTIC 180
6.5 CONSTRUCTION OF RELATORS 184
6.5.1 DERIVING NEW POLYNOMIAL RELATORS 187
6.6 CONCLUSION 189
7 RELATIONS 191
7.1 V-VALUED RELATIONS 191
7.2 THE ALLEGORY OF RELATIONS 195
7.2.1 THE DIVIDE-AND-CONQUER TACTIC FOR RELATIONS 196
7.2.2 DERIVING QUICKSORT 198
7.2.3 UPDATES ON BALANCED BINARY SEARCH TREES 202
7.3 CONCLUSION 207
8 CONCLUSION AND OUTLOOK 209
A STACK-EXAMPLE THEORY SOURCES OUTLINE 215
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| isbn | 9783832525026 3832525025 |
| language | English |
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| physical | 229 S. graph. Darst. 24 cm |
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| spelling | Bortin, Maksym Verfasser aut An approach to the extension of a theorem prover by advanced structuring mechanisms Maksym Bortin Berlin Logos 2010 229 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Bremen, Univ., Diss., 2010 Isabelle Programm (DE-588)4353452-1 gnd rswk-swf HOL (DE-588)4335765-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content HOL (DE-588)4335765-9 s Isabelle Programm (DE-588)4353452-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020773966&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bortin, Maksym An approach to the extension of a theorem prover by advanced structuring mechanisms Isabelle Programm (DE-588)4353452-1 gnd HOL (DE-588)4335765-9 gnd |
| subject_GND | (DE-588)4353452-1 (DE-588)4335765-9 (DE-588)4113937-9 |
| title | An approach to the extension of a theorem prover by advanced structuring mechanisms |
| title_auth | An approach to the extension of a theorem prover by advanced structuring mechanisms |
| title_exact_search | An approach to the extension of a theorem prover by advanced structuring mechanisms |
| title_full | An approach to the extension of a theorem prover by advanced structuring mechanisms Maksym Bortin |
| title_fullStr | An approach to the extension of a theorem prover by advanced structuring mechanisms Maksym Bortin |
| title_full_unstemmed | An approach to the extension of a theorem prover by advanced structuring mechanisms Maksym Bortin |
| title_short | An approach to the extension of a theorem prover by advanced structuring mechanisms |
| title_sort | an approach to the extension of a theorem prover by advanced structuring mechanisms |
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