Metamathematical extensibility in type theory:
An automated theorem prover is said to be metamathematically extensible if a metalanguage can be employed by the user to soundly extend the reasoning capabilities of the system. In this thesis, we present a framework for metamathematical extensibility for a system based upon a type-theoretic logic,...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Ithaca, NY
Cornell Univ., Dep. of Computer Science
1987
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| Schriftenreihe: | Technical report / Department of Computer Science, Cornell University, Ithaca, NY
892 |
| Schlagworte: | |
| Zusammenfassung: | An automated theorem prover is said to be metamathematically extensible if a metalanguage can be employed by the user to soundly extend the reasoning capabilities of the system. In this thesis, we present a framework for metamathematical extensibility for a system based upon a type-theoretic logic, the Nuprl system. Using this framework, the user can construct programs called proof tactics that may be used to provide new reasoning capabilities for the logic. These proof tactics can encode reasoning methods as simple asd a derived rule of inference or as ambitious as a theorem prover The design of the framework ensures that all proof tactics are correct. A formal metalanguage called Metaprl is defined that represents the proof theory of Nuprl in a natural and computationally-oriented fashion. The logic of Metaprl is an extension of the constructive type theory of Nuprl. Type theories like Nuprl and Metaprl are distinguished by the uniform treatment of computations (programs) and logical propositions and by rich languages for expressing computations. In Metaprl, formal specifications for tactics may be written and formally correct tactics extracted from the proofs of the specification Three classes of tactics are defined: complete tactics, partial tactics, and search tactics. Complete tactics are analogous to derived axioms for the Nuprl logic. Partial tactics are analogous to derived rules of inference. Search tactics are analogous to the procedural tactics of LCF and the current Nuprl system. Examples from each class of tactics are presented |
| Beschreibung: | Zugl.: Ithaca, NY, Cornell Univ., Diss. |
| Beschreibung: | VIII, 165 S. |
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| 245 | 1 | 0 | |a Metamathematical extensibility in type theory |
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| 490 | 0 | |a Technical report / Department of Computer Science, Cornell University, Ithaca, NY |v 892 | |
| 500 | |a Zugl.: Ithaca, NY, Cornell Univ., Diss. | ||
| 520 | 3 | |a An automated theorem prover is said to be metamathematically extensible if a metalanguage can be employed by the user to soundly extend the reasoning capabilities of the system. In this thesis, we present a framework for metamathematical extensibility for a system based upon a type-theoretic logic, the Nuprl system. Using this framework, the user can construct programs called proof tactics that may be used to provide new reasoning capabilities for the logic. These proof tactics can encode reasoning methods as simple asd a derived rule of inference or as ambitious as a theorem prover | |
| 520 | 3 | |a The design of the framework ensures that all proof tactics are correct. A formal metalanguage called Metaprl is defined that represents the proof theory of Nuprl in a natural and computationally-oriented fashion. The logic of Metaprl is an extension of the constructive type theory of Nuprl. Type theories like Nuprl and Metaprl are distinguished by the uniform treatment of computations (programs) and logical propositions and by rich languages for expressing computations. In Metaprl, formal specifications for tactics may be written and formally correct tactics extracted from the proofs of the specification | |
| 520 | 3 | |a Three classes of tactics are defined: complete tactics, partial tactics, and search tactics. Complete tactics are analogous to derived axioms for the Nuprl logic. Partial tactics are analogous to derived rules of inference. Search tactics are analogous to the procedural tactics of LCF and the current Nuprl system. Examples from each class of tactics are presented | |
| 650 | 4 | |a Automatic theorem proving | |
| 650 | 4 | |a Logic | |
| 650 | 4 | |a Type theory | |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
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Datensatz im Suchindex
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| author | Knoblock, Todd B. |
| author_facet | Knoblock, Todd B. |
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| author_sort | Knoblock, Todd B. |
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| building | Verbundindex |
| bvnumber | BV006618470 |
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| ctrlnum | (OCoLC)18206502 (DE-599)BVBBV006618470 |
| discipline | Informatik |
| format | Book |
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| indexdate | 2024-07-09T16:49:20Z |
| institution | BVB |
| language | English |
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| physical | VIII, 165 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Cornell Univ., Dep. of Computer Science |
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| series2 | Technical report / Department of Computer Science, Cornell University, Ithaca, NY |
| spelling | Knoblock, Todd B. Verfasser aut Metamathematical extensibility in type theory Ithaca, NY Cornell Univ., Dep. of Computer Science 1987 VIII, 165 S. txt rdacontent n rdamedia nc rdacarrier Technical report / Department of Computer Science, Cornell University, Ithaca, NY 892 Zugl.: Ithaca, NY, Cornell Univ., Diss. An automated theorem prover is said to be metamathematically extensible if a metalanguage can be employed by the user to soundly extend the reasoning capabilities of the system. In this thesis, we present a framework for metamathematical extensibility for a system based upon a type-theoretic logic, the Nuprl system. Using this framework, the user can construct programs called proof tactics that may be used to provide new reasoning capabilities for the logic. These proof tactics can encode reasoning methods as simple asd a derived rule of inference or as ambitious as a theorem prover The design of the framework ensures that all proof tactics are correct. A formal metalanguage called Metaprl is defined that represents the proof theory of Nuprl in a natural and computationally-oriented fashion. The logic of Metaprl is an extension of the constructive type theory of Nuprl. Type theories like Nuprl and Metaprl are distinguished by the uniform treatment of computations (programs) and logical propositions and by rich languages for expressing computations. In Metaprl, formal specifications for tactics may be written and formally correct tactics extracted from the proofs of the specification Three classes of tactics are defined: complete tactics, partial tactics, and search tactics. Complete tactics are analogous to derived axioms for the Nuprl logic. Partial tactics are analogous to derived rules of inference. Search tactics are analogous to the procedural tactics of LCF and the current Nuprl system. Examples from each class of tactics are presented Automatic theorem proving Logic Type theory (DE-588)4113937-9 Hochschulschrift gnd-content |
| spellingShingle | Knoblock, Todd B. Metamathematical extensibility in type theory Automatic theorem proving Logic Type theory |
| subject_GND | (DE-588)4113937-9 |
| title | Metamathematical extensibility in type theory |
| title_auth | Metamathematical extensibility in type theory |
| title_exact_search | Metamathematical extensibility in type theory |
| title_full | Metamathematical extensibility in type theory |
| title_fullStr | Metamathematical extensibility in type theory |
| title_full_unstemmed | Metamathematical extensibility in type theory |
| title_short | Metamathematical extensibility in type theory |
| title_sort | metamathematical extensibility in type theory |
| topic | Automatic theorem proving Logic Type theory |
| topic_facet | Automatic theorem proving Logic Type theory Hochschulschrift |
| work_keys_str_mv | AT knoblocktoddb metamathematicalextensibilityintypetheory |