Click'n'Prove: Interactive Proofs Within Set Theory
Identifieur interne : 001486 ( Hal/Curation ); précédent : 001485; suivant : 001487Click'n'Prove: Interactive Proofs Within Set Theory
Auteurs : Jean-Raymond Abrial ; Dominique Cansell [France]Source :
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Abstract
In this article, we first briefly present a proof assistant called the Predicate Prover, which essentially offers two functionalities: (1) an automatic semi-decision procedure for First Order Predicate Calculus, and (2) a systematic translation of statements written within Set Theory into equivalent ones in First Order Predicate Calculus. We then show that the automatic usage of this proof assistant is limited by several factors. We finally present (and this is the main part of this article) the principles that we have used in the construction of a {\em proactive} interface aiming at circumventing these limitations. Such principles are based on our practical experience in doing many interactive proofs (within Set Theory).
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scheme="mix" xml:lang="fr"><term>automatic prover</term><term>interactive prover</term><term>prouveur automatique</term><term>prouveur interactif</term><term>set theory</term><term>séquent</term><term>théorie des ensembles</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this article, we first briefly present a proof assistant called the Predicate Prover, which essentially offers two functionalities: (1) an automatic semi-decision procedure for First Order Predicate Calculus, and (2) a systematic translation of statements written within Set Theory into equivalent ones in First Order Predicate Calculus. 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Such principles are based on our practical experience in doing many interactive proofs (within Set Theory).</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Click'n'Prove: Interactive Proofs Within Set Theory</title><author role="aut"><persName><forename type="first">Jean-Raymond</forename><surname>Abrial</surname></persName><email></email><idno type="halauthor">131047</idno><orgName ref="#struct-364882"></orgName></author><author role="aut"><persName><forename type="first">Dominique</forename><surname>Cansell</surname></persName><email>Dominique.Cansell@loria.fr</email><idno type="halauthor">130116</idno><orgName ref="#struct-364584"></orgName><affiliation ref="#struct-2357"></affiliation></author><editor role="depositor"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2006-09-26 09:41:40</date><date type="whenModified">2016-05-19 01:09:34</date><date type="whenReleased">2006-09-28 15:22:46</date><date type="whenProduced">2003</date></edition><respStmt><resp>contributor</resp><name key="108626"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00099836</idno><idno type="halUri">https://hal.inria.fr/inria-00099836</idno><idno type="halBibtex">abrial:inria-00099836</idno><idno type="halRefHtml">David Basin et Burkhart Wolff. 16th International Conference on Theorem Proving in Higher Order Logics - TPHOLs'2003, 2003, Rome, Italy, Springer, 2758, pp.1-24, 2003, Lecture notes in Computer Science</idno><idno type="halRef">David Basin et Burkhart Wolff. 16th International Conference on Theorem Proving in Higher Order Logics - TPHOLs'2003, 2003, Rome, Italy, Springer, 2758, pp.1-24, 2003, Lecture notes in Computer Science</idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA-FM" p="LORIA">Méthodes formelles</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno></seriesStmt><notesStmt><note type="commentary">Colloque avec actes et comité de lecture. internationale.</note><note type="audience" n="2">International</note><note type="invited" n="0">No</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note><note type="proceedings" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Click'n'Prove: Interactive Proofs Within Set Theory</title><author role="aut"><persName><forename type="first">Jean-Raymond</forename><surname>Abrial</surname></persName><idno type="halAuthorId">131047</idno><orgName ref="#struct-364882"></orgName></author><author role="aut"><persName><forename type="first">Dominique</forename><surname>Cansell</surname></persName><email>Dominique.Cansell@loria.fr</email><idno type="halAuthorId">130116</idno><orgName ref="#struct-364584"></orgName><affiliation ref="#struct-2357"></affiliation></author></analytic><monogr><idno type="localRef">A03-R-137 || abrial03b</idno><meeting><title>16th International Conference on Theorem Proving in Higher Order Logics - TPHOLs'2003</title><date type="start">2003</date><settlement>Rome, Italy</settlement></meeting><editor>David Basin et Burkhart Wolff</editor><imprint><publisher>Springer</publisher><biblScope unit="serie">Lecture notes in Computer Science</biblScope><biblScope unit="volume">2758</biblScope><biblScope unit="pp">1-24</biblScope><date type="datePub">2003</date></imprint></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="fr">prouveur automatique</term><term xml:lang="fr">set theory</term><term xml:lang="fr">automatic prover</term><term xml:lang="fr">interactive prover</term><term xml:lang="fr">prouveur interactif</term><term xml:lang="fr">séquent</term><term xml:lang="fr">théorie des ensembles</term></keywords><classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode><classCode scheme="halTypology" n="COMM">Conference papers</classCode></textClass><abstract xml:lang="en">In this article, we first briefly present a proof assistant called the Predicate Prover, which essentially offers two functionalities: (1) an automatic semi-decision procedure for First Order Predicate Calculus, and (2) a systematic translation of statements written within Set Theory into equivalent ones in First Order Predicate Calculus. We then show that the automatic usage of this proof assistant is limited by several factors. We finally present (and this is the main part of this article) the principles that we have used in the construction of a {\em proactive} interface aiming at circumventing these limitations. Such principles are based on our practical experience in doing many interactive proofs (within Set Theory).</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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