Mechanizing inductive theorem proving in conditional theories:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Düsseldorf
VDI-Verl.
1995
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| Ausgabe: | Als Ms. gedr. |
| Schriftenreihe: | Verein Deutscher Ingenieure: [Fortschrittberichte VDI / 10]
334 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Passau, Univ. Diss., 1994 |
| Beschreibung: | VI, 154 S. graph. Darst. |
| ISBN: | 3183334100 |
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Datensatz im Suchindex
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Titel: Mechanizing Inductive Theorem Proving in Conditional Theories
Autor: Fraus, Ulrich
Jahr: 1995
V Table of Contents Chapter 1: Introduction 1 1.1 Theorem Proving and Induction. 1 1.2 Example. 7 1.3 Motivation. 8 1.4 Outline of Contents. 13 Chapter 2: History of Logic and Theorem Proving 14 Chapter 3: Basic Notions 18 3.1 Syntax. 18 3.2 Rewriting. 20 3.3 Semantics. 21 Chapter 4: The Principle of Induction 24 4.1 Noetherian Induction. 24 4.2 Induction for Algebraic Specifications. 26 4.3 Components of Inductive Proofs. 27 Chapter 5: A Calculus for Conditional Theorem
Proving 31 5.1 Motivation. 31 5.2 Formal Notions for the Calculus. 32 5.2.1 Dealing With Sets of Induction Hypotheses. 32 5.2.2 Additional Notions. 35 5.3 The Conditional Calculus. 36 5.4 Derivations. 39 5.4.1 Example. 40 5.4.2 Disproving a Theorem. 42 5.4.3 Using Induction Hypotheses. 45 5.5 Semantics. 47 5.5.1 Unsatisfiability and Consistent Models. 47 5.5.2 Semantics of a Goal. 49 5.6 Correctness.
54 5.6.1 Correctness of the Rules . 54 5.6.2 Correctness of the Calculus. 60 5.7 Deductive Completeness. 62 Chapter 6: The Implemented Proof System 65 6.1 General. 65 6.2 Data Structures. 66 6.2.1 Internal Variables. 66 6.2.2 Goals. 67 6.2.3 Proof Tree. 67 6.2.4 Goal Queues. 69 6.3 Proof Steps. 69
vi Table of Contents 6.3.1 Simplification. 70 6.3.2 Complete Case Analysis. 73 6.3.3 Application of an Induction Hypothesis. 76 6.3.4 Application of a Lemma. 77 6.3.5 Generalization. 78 6.3.6 Inflation in Connection with Generalization (Twin Step). 78 6.3.7 Conditional Rewrite Steps. 79 6.4 Proof Algorithm. 80 6.5 System Parameters. 82 6.6 Example Session. 82 6.7 About the Current Implementation. 86 Chapter 7: Comparison of Calculus and Implementation 88 7.1 Implementation of the Calculus.
88 7.1.1 Goals. 88 7.1.2 Rules. 90 7.2 Extensions of the Proof Algorithm. 93 7.3 Strategies and Heuristics. 95 Chapter 8: Practical Applications of TIP 99 8.1 Compiler Verification. • . 99 8.2 Context Induction. 100 8.3 A Large Proof for a Technical Specification. 101 8.4 Use in Lectures. 102 8.5 Verification of PASCAL Code. 103 8.6 Induction for Attribute Grammars. 103 Chapter 9: Other Inductive Theorem Provers 105 9.1 Natural Induction Provers. 106 9.1.1 Boyer-Moore Prover.
106 9.1.2 Further Proof Systems. 112 9.1.3 Use of Tactics. 114 9.2 Completion Based Theorem Proving. 116 9.2.1 Proof Principle. 116 9.2.2 Implementations. 118 9.2.3 Relationship to Natural Inductive Proving. 119 Chapter 10: Conclusion 121 Appendix 123 Appendix A: The Natural Deduction Calculus. 123 Appendix B: Technical Data. 127 Appendix C: Basic Specifications. 128 Appendix D: Proof Listing of the Boyer-Moore prover. 130 Appendix E: List of Examples . 132 Appendix F: Proof Listings . 133 References 143 Index 151 |
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| id | DE-604.BV010064107 |
| illustrated | Illustrated |
| indexdate | 2024-11-13T11:03:28Z |
| institution | BVB |
| isbn | 3183334100 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006677796 |
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| physical | VI, 154 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| series2 | Verein Deutscher Ingenieure: [Fortschrittberichte VDI / 10] |
| spelling | Fraus, Ulrich Verfasser aut Mechanizing inductive theorem proving in conditional theories Ulrich Fraus Als Ms. gedr. Düsseldorf VDI-Verl. 1995 VI, 154 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Verein Deutscher Ingenieure: [Fortschrittberichte VDI / 10] 334 Zugl.: Passau, Univ. Diss., 1994 Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf Induktionsbeweis (DE-588)4222014-2 gnd rswk-swf Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf Induktion (DE-588)4026765-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Induktionsbeweis (DE-588)4222014-2 s Automatisches Beweisverfahren (DE-588)4069034-9 s Infinitesimalrechnung (DE-588)4072798-1 s DE-604 Induktion (DE-588)4026765-9 s 10] Verein Deutscher Ingenieure: [Fortschrittberichte VDI 334 (DE-604)BV000897204 334 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006677796&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fraus, Ulrich Mechanizing inductive theorem proving in conditional theories Infinitesimalrechnung (DE-588)4072798-1 gnd Induktionsbeweis (DE-588)4222014-2 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Induktion (DE-588)4026765-9 gnd |
| subject_GND | (DE-588)4072798-1 (DE-588)4222014-2 (DE-588)4069034-9 (DE-588)4026765-9 (DE-588)4113937-9 |
| title | Mechanizing inductive theorem proving in conditional theories |
| title_auth | Mechanizing inductive theorem proving in conditional theories |
| title_exact_search | Mechanizing inductive theorem proving in conditional theories |
| title_full | Mechanizing inductive theorem proving in conditional theories Ulrich Fraus |
| title_fullStr | Mechanizing inductive theorem proving in conditional theories Ulrich Fraus |
| title_full_unstemmed | Mechanizing inductive theorem proving in conditional theories Ulrich Fraus |
| title_short | Mechanizing inductive theorem proving in conditional theories |
| title_sort | mechanizing inductive theorem proving in conditional theories |
| topic | Infinitesimalrechnung (DE-588)4072798-1 gnd Induktionsbeweis (DE-588)4222014-2 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Induktion (DE-588)4026765-9 gnd |
| topic_facet | Infinitesimalrechnung Induktionsbeweis Automatisches Beweisverfahren Induktion Hochschulschrift |
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