Building Decision Procedures in the Calculus of Inductive Constructions
Identifieur interne : 002311 ( Istex/Corpus ); précédent : 002310; suivant : 002312Building Decision Procedures in the Calculus of Inductive Constructions
Auteurs : Frédéric Blanqui ; Jean-Pierre Jouannaud ; Pierre-Yves StrubSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent proposition P’ obtained from P thanks to possibly complex calculations. In this paper, we investigate a new version of the calculus of inductive constructions which incorporates arbitrary decision procedures into deduction via the conversion rule of the calculus. The novelty of the problem in the context of the calculus of inductive constructions lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved.
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DOI: 10.1007/978-3-540-74915-8_26
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ISTEX:963CD2E1E8BCAE9CDC43EDF70A100365DDC0DC20Le document en format XML
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Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved.</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>Frédéric Blanqui</name><affiliations><json:string>LORIA, Equipe Protheo, Campus Scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex,</json:string><json:string>E-mail: blanqui@loria.fr</json:string></affiliations></json:item><json:item><name>Jean-Pierre Jouannaud</name><affiliations><json:string>LogiCal LIX, UMR CNRS 7161, École Polytechnique, 91128 Plaiseau, France</json:string><json:string>E-mail: jouannaud@lix.polytechnique.fr</json:string></affiliations></json:item><json:item><name>Pierre-Yves Strub</name><affiliations><json:string>LogiCal LIX, UMR CNRS 7161, École Polytechnique, 91128 Plaiseau, France</json:string><json:string>E-mail: strub@lix.polytechnique.fr</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Calculus of Inductive Constructions</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Decision procedures</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Theorem provers</value></json:item></subject><arkIstex>ark:/67375/HCB-CNMDBBWJ-Q</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent proposition P’ obtained from P thanks to possibly complex calculations. 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The novelty of the problem in the context of the calculus of inductive constructions lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved.</p></abstract><textClass ana="keyword"><keywords xml:lang="en"><term>Calculus of Inductive Constructions</term><term>Decision procedures</term><term>Theorem provers</term></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject-collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject"><list><label>I</label><item><term type="Primary">Computer Science</term></item><label>I16048</label><item><term type="Secondary" subtype="priority-1">Mathematical Logic and Formal Languages</term></item><label>I21017</label><item><term type="Secondary" subtype="priority-2">Artificial Intelligence (incl. 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Robotics)</BookSubject><BookSubject Code="I1603X" Priority="3" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="M24005" Priority="4" Type="Secondary">Mathematical Logic and Foundations</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup></BookInfo><BookHeader><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>Jacques</GivenName><FamilyName>Duparc</FamilyName></EditorName><Contact><Email>jacques.duparc@unil.ch</Email></Contact></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Thomas</GivenName><GivenName>A.</GivenName><FamilyName>Henzinger</FamilyName></EditorName><Contact><Email>tah@epfl.ch</Email></Contact></Editor></EditorGroup></BookHeader><Part ID="Part7"><PartInfo TocLevels="0"><PartID>7</PartID><PartSequenceNumber>7</PartSequenceNumber><PartTitle>Lambda Calculus 2</PartTitle><PartChapterCount>3</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Computer Science Logic</BookTitle></PartContext></PartInfo><Chapter ID="Chap26" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>26</ChapterID><ChapterDOI>10.1007/978-3-540-74915-8_26</ChapterDOI><ChapterSequenceNumber>26</ChapterSequenceNumber><ChapterTitle Language="En">Building Decision Procedures in the Calculus of Inductive Constructions</ChapterTitle><ChapterFirstPage>328</ChapterFirstPage><ChapterLastPage>342</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2007</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><PartID>7</PartID><BookID>978-3-540-74915-8</BookID><BookTitle>Computer Science Logic</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Frédéric</GivenName><FamilyName>Blanqui</FamilyName></AuthorName><Contact><Email>blanqui@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Jean-Pierre</GivenName><FamilyName>Jouannaud</FamilyName></AuthorName><Contact><Email>jouannaud@lix.polytechnique.fr</Email></Contact></Author><Author AffiliationIDS="Aff2"><AuthorName DisplayOrder="Western"><GivenName>Pierre-Yves</GivenName><FamilyName>Strub</FamilyName></AuthorName><Contact><Email>strub@lix.polytechnique.fr</Email></Contact></Author><Affiliation ID="Aff1"><OrgName>LORIA, Equipe Protheo, Campus Scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex</OrgName><OrgAddress><Country> </Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>LogiCal LIX, UMR CNRS 7161, École Polytechnique, 91128 Plaiseau</OrgName><OrgAddress><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent proposition P’ obtained from P thanks to possibly complex calculations.</Para><Para>In this paper, we investigate a new version of the calculus of inductive constructions which incorporates arbitrary decision procedures into deduction via the conversion rule of the calculus. The novelty of the problem in the context of the calculus of inductive constructions lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>Calculus of Inductive Constructions</Keyword><Keyword>Decision procedures</Keyword><Keyword>Theorem provers</Keyword></KeywordGroup></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Building Decision Procedures in the Calculus of Inductive Constructions</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Building Decision Procedures in the Calculus of Inductive Constructions</title></titleInfo><name type="personal"><namePart type="given">Frédéric</namePart><namePart type="family">Blanqui</namePart><affiliation>LORIA, Equipe Protheo, Campus Scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex, </affiliation><affiliation>E-mail: blanqui@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Jean-Pierre</namePart><namePart type="family">Jouannaud</namePart><affiliation>LogiCal LIX, UMR CNRS 7161, École Polytechnique, 91128 Plaiseau, France</affiliation><affiliation>E-mail: jouannaud@lix.polytechnique.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Pierre-Yves</namePart><namePart type="family">Strub</namePart><affiliation>LogiCal LIX, UMR CNRS 7161, École Polytechnique, 91128 Plaiseau, France</affiliation><affiliation>E-mail: strub@lix.polytechnique.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2007</dateIssued><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent proposition P’ obtained from P thanks to possibly complex calculations. In this paper, we investigate a new version of the calculus of inductive constructions which incorporates arbitrary decision procedures into deduction via the conversion rule of the calculus. The novelty of the problem in the context of the calculus of inductive constructions lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved.</abstract><subject lang="en"><genre>Keywords</genre><topic>Calculus of Inductive Constructions</topic><topic>Decision procedures</topic><topic>Theorem provers</topic></subject><relatedItem type="host"><titleInfo><title>Computer Science Logic</title><subTitle>21st International Workshop, CSL 2007, 16th Annual Conference of the EACSL, Lausanne, Switzerland, September 11-15, 2007. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Jacques</namePart><namePart type="family">Duparc</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Thomas</namePart><namePart type="given">A.</namePart><namePart type="family">Henzinger</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2007</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I21017">Artificial Intelligence (incl. Robotics)</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="M24005">Mathematical Logic and Foundations</topic></subject><identifier type="DOI">10.1007/978-3-540-74915-8</identifier><identifier type="ISBN">978-3-540-74914-1</identifier><identifier type="eISBN">978-3-540-74915-8</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">152571</identifier><identifier type="BookID">978-3-540-74915-8</identifier><identifier type="BookChapterCount">43</identifier><identifier type="BookVolumeNumber">4646</identifier><identifier type="BookSequenceNumber">4646</identifier><identifier type="PartChapterCount">3</identifier><part><date>2007</date><detail type="part"><title>Lambda Calculus 2</title></detail><detail type="volume"><number>4646</number><caption>vol.</caption></detail><extent 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