Solving goals in equational languages
Identifieur interne : 003419 ( Istex/Corpus ); précédent : 003418; suivant : 003420Solving goals in equational languages
Auteurs : Nachum Dershowitz ; G. SivakumarSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Solving equations in equational Horn-clause theories is a programming paradigm that combines logic programming and functional programming in a clean manner. Languages like Eqlog, Slog and Rite, express programs as conditional rewrite rules and goals as equations to be solved. Procedures for completion of conditional equational theories, in a manner akin to that of Knuth and Bendix for unconditional theories, also require methods for solving equations appearing in conditions. Rewrite-based logic-programming uses (conditional) narrowing to solve equational goals. Recently a different, topdown equation solving procedure was proposed for unconditional rewrite systems. In this paper, we express equational goal solving using conditional rules. Some refinements are described: the notion of operator derivability is used to prune useless paths in the search tree and our use of oriented goals eliminates some redundant paths leading to non-normalized solutions. Our goal-directed method can also be extended to handle conditional systems.
Url:
DOI: 10.1007/3-540-19242-5_4
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ISTEX:DAFE3FFB5C021A43F7A79564074B2AB6FFF9AE65Le document en format XML
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Sivakumar</name><affiliation><mods:affiliation>Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, Urbana, Illinois, U.S.A.</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><title level="s" type="abbrev">Lect Notes Comput Sci</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Solving equations in equational Horn-clause theories is a programming paradigm that combines logic programming and functional programming in a clean manner. Languages like Eqlog, Slog and Rite, express programs as conditional rewrite rules and goals as equations to be solved. Procedures for completion of conditional equational theories, in a manner akin to that of Knuth and Bendix for unconditional theories, also require methods for solving equations appearing in conditions. Rewrite-based logic-programming uses (conditional) narrowing to solve equational goals. Recently a different, topdown equation solving procedure was proposed for unconditional rewrite systems. In this paper, we express equational goal solving using conditional rules. Some refinements are described: the notion of operator derivability is used to prune useless paths in the search tree and our use of oriented goals eliminates some redundant paths leading to non-normalized solutions. 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Languages like <hi rend="smallCaps">Eqlog, Slog</hi> and <hi rend="smallCaps">Rite</hi>, express programs as conditional rewrite rules and goals as equations to be solved. Procedures for completion of conditional equational theories, in a manner akin to that of Knuth and Bendix for unconditional theories, also require methods for solving equations appearing in conditions. Rewrite-based logic-programming uses (conditional) narrowing to solve equational goals. Recently a different, topdown equation solving procedure was proposed for unconditional rewrite systems. In this paper, we express equational goal solving using conditional rules. Some refinements are described: the notion of <hi rend="italic">operator derivability</hi> is used to prune useless paths in the search tree and our use of <hi rend="italic">oriented goals</hi> eliminates some redundant paths leading to non-normalized solutions. Our <hi rend="italic">goal-directed</hi> method can also be extended to handle conditional systems.</p></abstract><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></list></keywords></textClass><langUsage><language ident="EN"></language></langUsage></profileDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/ark:/67375/HCB-J8141ZJN-1/fulltext.txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus springer-ebooks not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" 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Articles</ChapterCategory><ChapterFirstPage>45</ChapterFirstPage><ChapterLastPage>55</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag</CopyrightHolderName><CopyrightYear>1988</CopyrightYear></ChapterCopyright><ChapterHistory><OnlineDate><Year>2005</Year><Month>5</Month><Day>27</Day></OnlineDate></ChapterHistory><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><BookID>3540192425</BookID><BookTitle>Conditional Term Rewriting Systems</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>Nachum</GivenName><FamilyName>Dershowitz</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff1"><AuthorName DisplayOrder="Western"><GivenName>G.</GivenName><FamilyName>Sivakumar</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>University of Illinois at Urbana-Champaign</OrgName><OrgAddress><Postcode>61801</Postcode><City>Urbana</City><State>Illinois</State><Country>U.S.A.</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>Solving equations in equational Horn-clause theories is a programming paradigm that combines logic programming and functional programming in a clean manner. Languages like <Emphasis Type="SmallCaps">Eqlog, Slog</Emphasis> and <Emphasis Type="SmallCaps">Rite</Emphasis>, express programs as conditional rewrite rules and goals as equations to be solved. Procedures for completion of conditional equational theories, in a manner akin to that of Knuth and Bendix for unconditional theories, also require methods for solving equations appearing in conditions. Rewrite-based logic-programming uses (conditional) narrowing to solve equational goals. Recently a different, topdown equation solving procedure was proposed for unconditional rewrite systems. In this paper, we express equational goal solving using conditional rules. Some refinements are described: the notion of <Emphasis Type="Italic">operator derivability</Emphasis> is used to prune useless paths in the search tree and our use of <Emphasis Type="Italic">oriented goals</Emphasis> eliminates some redundant paths leading to non-normalized solutions. Our <Emphasis Type="Italic">goal-directed</Emphasis> method can also be extended to handle conditional systems.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>This research was supported in part by the National Science Foundation under Grant DCR 85-13417.</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Solving goals in equational languages</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Solving goals in equational languages</title></titleInfo><name type="personal"><namePart type="given">Nachum</namePart><namePart type="family">Dershowitz</namePart><affiliation>Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, Urbana, Illinois, U.S.A.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">G.</namePart><namePart type="family">Sivakumar</namePart><affiliation>Department of Computer Science, University of Illinois at Urbana-Champaign, 61801, Urbana, Illinois, U.S.A.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="ReviewPaper" 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">1988</dateIssued><copyrightDate encoding="w3cdtf">1988</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: Solving equations in equational Horn-clause theories is a programming paradigm that combines logic programming and functional programming in a clean manner. Languages like Eqlog, Slog and Rite, express programs as conditional rewrite rules and goals as equations to be solved. Procedures for completion of conditional equational theories, in a manner akin to that of Knuth and Bendix for unconditional theories, also require methods for solving equations appearing in conditions. Rewrite-based logic-programming uses (conditional) narrowing to solve equational goals. Recently a different, topdown equation solving procedure was proposed for unconditional rewrite systems. In this paper, we express equational goal solving using conditional rules. Some refinements are described: the notion of operator derivability is used to prune useless paths in the search tree and our use of oriented goals eliminates some redundant paths leading to non-normalized solutions. 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encoding="w3cdtf">1988</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></subject><identifier type="DOI">10.1007/3-540-19242-5</identifier><identifier type="ISBN">978-3-540-19242-8</identifier><identifier type="eISBN">978-3-540-39166-1</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">21902</identifier><identifier type="BookID">3540192425</identifier><identifier type="BookChapterCount">24</identifier><identifier type="BookVolumeNumber">308</identifier><part><date>1988</date><detail 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type="given">P.</namePart><namePart type="family">Brinch Hansen</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Gries</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Luckham</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">C.</namePart><namePart type="family">Moler</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Pnueli</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">G.</namePart><namePart type="family">Seegmüller</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">J.</namePart><namePart type="family">Stoer</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">N.</namePart><namePart type="family">Wirth</namePart><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1988</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag, 1988</recordOrigin></recordInfo></relatedItem><identifier type="istex">DAFE3FFB5C021A43F7A79564074B2AB6FFF9AE65</identifier><identifier type="ark">ark:/67375/HCB-J8141ZJN-1</identifier><identifier type="DOI">10.1007/3-540-19242-5_4</identifier><identifier type="ChapterID">4</identifier><identifier type="ChapterID">Chap4</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag, 1988</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-RLRX46XW-4">springer</recordContentSource><recordOrigin>Springer-Verlag, 1988</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/ark:/67375/HCB-J8141ZJN-1/record.json</uri></json:item></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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