Specifying and implementing theorem provers in a higher-order logic programming language:
Abstract: "We argue that a logic programming language with a higher-order intuitionistic logic as its foundation can be used both to naturally specify and implement theorem provers. The language extends traditional logic programming languages by replacing first-order terms with simply-typed [la...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Dep. of Computer and Information Science, School of Engineering and Applied Science
1989
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| Schlagworte: | |
| Zusammenfassung: | Abstract: "We argue that a logic programming language with a higher-order intuitionistic logic as its foundation can be used both to naturally specify and implement theorem provers. The language extends traditional logic programming languages by replacing first-order terms with simply-typed [lambda]-terms, replacing first-order unification with higher-order unification, and allowing implication and universal quantification in queries and the bodies of clauses. Inference rules for a variety of proof systems can be naturally specified in this language The higher-order features of the language contribute to a concise specification of provisos concerning variable occurrences in formulas and the discharge of assumptions present in many proof systems. In addition, abstraction in meta-terms allows the construction of terms representing object level proofs which capture the notions of abstractions found in many proof systems. The operational interpretations of the connectives of the language provide a set of basic search operations which describe goal-directed search for proofs. To emphasize the generality of the meta-language, we compare it to another general specification language: the Logic Framework (LF) We describe a translation which compiles a specification of a logic in LF to a set of formulas of our meta-language, and prove this translation correct. A direct specification of inference rules provides a declarative account of a proof system and a specification of the process of searching for proofs, but generally does not implement a theorem prover that can be executed directly. We show that is sometimes possible to obtain a theorem prover that is complete under depth-first control by making only slight modifications to a specification. For the purpose of general theorem proving, we show how tactics and tacticals, which provide a framework for high-level control over search, can be directly implemented in our extended language |
| Beschreibung: | Zugl.: Philadelphia, Pa., Univ., Diss. |
| Beschreibung: | VIII, 190 S. |
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| 100 | 1 | |a Felty, Amy |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Specifying and implementing theorem provers in a higher-order logic programming language |
| 246 | 1 | 3 | |a MS CIS 89 53 |
| 264 | 1 | |a Philadelphia, Pa. |b Dep. of Computer and Information Science, School of Engineering and Applied Science |c 1989 | |
| 300 | |a VIII, 190 S. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Zugl.: Philadelphia, Pa., Univ., Diss. | ||
| 520 | 3 | |a Abstract: "We argue that a logic programming language with a higher-order intuitionistic logic as its foundation can be used both to naturally specify and implement theorem provers. The language extends traditional logic programming languages by replacing first-order terms with simply-typed [lambda]-terms, replacing first-order unification with higher-order unification, and allowing implication and universal quantification in queries and the bodies of clauses. Inference rules for a variety of proof systems can be naturally specified in this language | |
| 520 | 3 | |a The higher-order features of the language contribute to a concise specification of provisos concerning variable occurrences in formulas and the discharge of assumptions present in many proof systems. In addition, abstraction in meta-terms allows the construction of terms representing object level proofs which capture the notions of abstractions found in many proof systems. The operational interpretations of the connectives of the language provide a set of basic search operations which describe goal-directed search for proofs. To emphasize the generality of the meta-language, we compare it to another general specification language: the Logic Framework (LF) | |
| 520 | 3 | |a We describe a translation which compiles a specification of a logic in LF to a set of formulas of our meta-language, and prove this translation correct. A direct specification of inference rules provides a declarative account of a proof system and a specification of the process of searching for proofs, but generally does not implement a theorem prover that can be executed directly. We show that is sometimes possible to obtain a theorem prover that is complete under depth-first control by making only slight modifications to a specification. For the purpose of general theorem proving, we show how tactics and tacticals, which provide a framework for high-level control over search, can be directly implemented in our extended language | |
| 650 | 4 | |a Automatic theorem proving | |
| 650 | 4 | |a Logic programming | |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002737824 | ||
Datensatz im Suchindex
| _version_ | 1804118589296345088 |
|---|---|
| any_adam_object | |
| author | Felty, Amy |
| author_facet | Felty, Amy |
| author_role | aut |
| author_sort | Felty, Amy |
| author_variant | a f af |
| building | Verbundindex |
| bvnumber | BV004413002 |
| classification_tum | DAT 706d |
| ctrlnum | (OCoLC)23982464 (DE-599)BVBBV004413002 |
| discipline | Informatik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:12:42Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002737824 |
| oclc_num | 23982464 |
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| physical | VIII, 190 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Dep. of Computer and Information Science, School of Engineering and Applied Science |
| record_format | marc |
| spelling | Felty, Amy Verfasser aut Specifying and implementing theorem provers in a higher-order logic programming language MS CIS 89 53 Philadelphia, Pa. Dep. of Computer and Information Science, School of Engineering and Applied Science 1989 VIII, 190 S. txt rdacontent n rdamedia nc rdacarrier Zugl.: Philadelphia, Pa., Univ., Diss. Abstract: "We argue that a logic programming language with a higher-order intuitionistic logic as its foundation can be used both to naturally specify and implement theorem provers. The language extends traditional logic programming languages by replacing first-order terms with simply-typed [lambda]-terms, replacing first-order unification with higher-order unification, and allowing implication and universal quantification in queries and the bodies of clauses. Inference rules for a variety of proof systems can be naturally specified in this language The higher-order features of the language contribute to a concise specification of provisos concerning variable occurrences in formulas and the discharge of assumptions present in many proof systems. In addition, abstraction in meta-terms allows the construction of terms representing object level proofs which capture the notions of abstractions found in many proof systems. The operational interpretations of the connectives of the language provide a set of basic search operations which describe goal-directed search for proofs. To emphasize the generality of the meta-language, we compare it to another general specification language: the Logic Framework (LF) We describe a translation which compiles a specification of a logic in LF to a set of formulas of our meta-language, and prove this translation correct. A direct specification of inference rules provides a declarative account of a proof system and a specification of the process of searching for proofs, but generally does not implement a theorem prover that can be executed directly. We show that is sometimes possible to obtain a theorem prover that is complete under depth-first control by making only slight modifications to a specification. For the purpose of general theorem proving, we show how tactics and tacticals, which provide a framework for high-level control over search, can be directly implemented in our extended language Automatic theorem proving Logic programming (DE-588)4113937-9 Hochschulschrift gnd-content |
| spellingShingle | Felty, Amy Specifying and implementing theorem provers in a higher-order logic programming language Automatic theorem proving Logic programming |
| subject_GND | (DE-588)4113937-9 |
| title | Specifying and implementing theorem provers in a higher-order logic programming language |
| title_alt | MS CIS 89 53 |
| title_auth | Specifying and implementing theorem provers in a higher-order logic programming language |
| title_exact_search | Specifying and implementing theorem provers in a higher-order logic programming language |
| title_full | Specifying and implementing theorem provers in a higher-order logic programming language |
| title_fullStr | Specifying and implementing theorem provers in a higher-order logic programming language |
| title_full_unstemmed | Specifying and implementing theorem provers in a higher-order logic programming language |
| title_short | Specifying and implementing theorem provers in a higher-order logic programming language |
| title_sort | specifying and implementing theorem provers in a higher order logic programming language |
| topic | Automatic theorem proving Logic programming |
| topic_facet | Automatic theorem proving Logic programming Hochschulschrift |
| work_keys_str_mv | AT feltyamy specifyingandimplementingtheoremproversinahigherorderlogicprogramminglanguage AT feltyamy mscis8953 |