From meta level tactics to object level programs:
Abstract: "The paper describes a variant of Martin-Löf type theory extended by the principle of type induction, as introduced in the oyster-2 theorem proving system. The system has a procedural meta-language in which a variety of search strategies have been written. Theorem proving in the syste...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Edinburgh
1994
|
| Schriftenreihe: | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper
727 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "The paper describes a variant of Martin-Löf type theory extended by the principle of type induction, as introduced in the oyster-2 theorem proving system. The system has a procedural meta-language in which a variety of search strategies have been written. Theorem proving in the system yields object-level functional programs that implement procedures associated with the theorem that is proved. We demonstrate the application of type induction in proving the existence of a partial decision procedure for a fragment of type theory inside the theory itself. As a result of that proof, we obtain an object-level program that implements such a partial decision procedure, ie given a type theoretic formula x as input, it returns either a proof of x (formally, an element of the type x), or a refutation of x (formally, an element of the type x --> void) or a distinguished value indicating that no decision has been made. Initially an interactive proof of the existence of such a procedure is given, for the fragment of type theory representing classical propositional calculus. That proof turns out to have a very simple structure, the construction of which can easily be automated. Therefore we describe a tactical operator reflect(T) which takes an arbitrary terminating search strategy T as its argument and produces a proof of the existence of a partial decision procedure, the extract term of which simulates the strategy T. Effectively, we compile a meta-level search strategy into an object level functional program. Once we have the object- level procedure, it can be used to avoid execution of the meta-level program altogether where knowledge of its existence is sufficient, or executed in place of the meta-level program." |
| Beschreibung: | 23 S. |
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| 100 | 1 | |a Horn, Christian |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a From meta level tactics to object level programs |c Horn, C ; Smaill, A. |
| 264 | 1 | |a Edinburgh |c 1994 | |
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| 490 | 1 | |a University <Edinburgh> / Department of Artificial Intelligence: DAI research paper |v 727 | |
| 520 | 3 | |a Abstract: "The paper describes a variant of Martin-Löf type theory extended by the principle of type induction, as introduced in the oyster-2 theorem proving system. The system has a procedural meta-language in which a variety of search strategies have been written. Theorem proving in the system yields object-level functional programs that implement procedures associated with the theorem that is proved. We demonstrate the application of type induction in proving the existence of a partial decision procedure for a fragment of type theory inside the theory itself. As a result of that proof, we obtain an object-level program that implements such a partial decision procedure, ie given a type theoretic formula x as input, it returns either a proof of x (formally, an element of the type x), or a refutation of x (formally, an element of the type x --> void) or a distinguished value indicating that no decision has been made. Initially an interactive proof of the existence of such a procedure is given, for the fragment of type theory representing classical propositional calculus. That proof turns out to have a very simple structure, the construction of which can easily be automated. Therefore we describe a tactical operator reflect(T) which takes an arbitrary terminating search strategy T as its argument and produces a proof of the existence of a partial decision procedure, the extract term of which simulates the strategy T. Effectively, we compile a meta-level search strategy into an object level functional program. Once we have the object- level procedure, it can be used to avoid execution of the meta-level program altogether where knowledge of its existence is sufficient, or executed in place of the meta-level program." | |
| 650 | 7 | |a Bionics and artificial intelligence |2 sigle | |
| 650 | 7 | |a Computer software |2 sigle | |
| 650 | 4 | |a Automatic theorem proving | |
| 650 | 4 | |a Type theory | |
| 700 | 1 | |a Smaill, Alan |e Verfasser |4 aut | |
| 810 | 2 | |a Department of Artificial Intelligence: DAI research paper |t University <Edinburgh> |v 727 |w (DE-604)BV010450646 |9 727 | |
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Datensatz im Suchindex
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| author | Horn, Christian Smaill, Alan |
| author_facet | Horn, Christian Smaill, Alan |
| author_role | aut aut |
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| author_variant | c h ch a s as |
| building | Verbundindex |
| bvnumber | BV011043233 |
| ctrlnum | (OCoLC)34847595 (DE-599)BVBBV011043233 |
| format | Book |
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| id | DE-604.BV011043233 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:03Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007394569 |
| oclc_num | 34847595 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 23 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| record_format | marc |
| series2 | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper |
| spelling | Horn, Christian Verfasser aut From meta level tactics to object level programs Horn, C ; Smaill, A. Edinburgh 1994 23 S. txt rdacontent n rdamedia nc rdacarrier University <Edinburgh> / Department of Artificial Intelligence: DAI research paper 727 Abstract: "The paper describes a variant of Martin-Löf type theory extended by the principle of type induction, as introduced in the oyster-2 theorem proving system. The system has a procedural meta-language in which a variety of search strategies have been written. Theorem proving in the system yields object-level functional programs that implement procedures associated with the theorem that is proved. We demonstrate the application of type induction in proving the existence of a partial decision procedure for a fragment of type theory inside the theory itself. As a result of that proof, we obtain an object-level program that implements such a partial decision procedure, ie given a type theoretic formula x as input, it returns either a proof of x (formally, an element of the type x), or a refutation of x (formally, an element of the type x --> void) or a distinguished value indicating that no decision has been made. Initially an interactive proof of the existence of such a procedure is given, for the fragment of type theory representing classical propositional calculus. That proof turns out to have a very simple structure, the construction of which can easily be automated. Therefore we describe a tactical operator reflect(T) which takes an arbitrary terminating search strategy T as its argument and produces a proof of the existence of a partial decision procedure, the extract term of which simulates the strategy T. Effectively, we compile a meta-level search strategy into an object level functional program. Once we have the object- level procedure, it can be used to avoid execution of the meta-level program altogether where knowledge of its existence is sufficient, or executed in place of the meta-level program." Bionics and artificial intelligence sigle Computer software sigle Automatic theorem proving Type theory Smaill, Alan Verfasser aut Department of Artificial Intelligence: DAI research paper University <Edinburgh> 727 (DE-604)BV010450646 727 |
| spellingShingle | Horn, Christian Smaill, Alan From meta level tactics to object level programs Bionics and artificial intelligence sigle Computer software sigle Automatic theorem proving Type theory |
| title | From meta level tactics to object level programs |
| title_auth | From meta level tactics to object level programs |
| title_exact_search | From meta level tactics to object level programs |
| title_full | From meta level tactics to object level programs Horn, C ; Smaill, A. |
| title_fullStr | From meta level tactics to object level programs Horn, C ; Smaill, A. |
| title_full_unstemmed | From meta level tactics to object level programs Horn, C ; Smaill, A. |
| title_short | From meta level tactics to object level programs |
| title_sort | from meta level tactics to object level programs |
| topic | Bionics and artificial intelligence sigle Computer software sigle Automatic theorem proving Type theory |
| topic_facet | Bionics and artificial intelligence Computer software Automatic theorem proving Type theory |
| volume_link | (DE-604)BV010450646 |
| work_keys_str_mv | AT hornchristian frommetaleveltacticstoobjectlevelprograms AT smaillalan frommetaleveltacticstoobjectlevelprograms |