Unification in Extensions of Shallow Equational Theories
Identifieur interne : 005047 ( Hal/Curation ); précédent : 005046; suivant : 005048Unification in Extensions of Shallow Equational Theories
Auteurs : Florent Jacquemard [France] ; Christoph Meyer ; Christoph WeidenbachSource :
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Abstract
We show that unification in certain extensions of shallow equational theories is decidable. Our extensions generalize the known classes of shallow or standard equational theories. In order to prove decidability of unification in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natural extension of tree automata with equality constraints between brother subterms as well as shallow sort theories. We show that saturation under sorted superposition is effective on sorted shallow equational theories. So called semi-linear equational theories can be effectively transformed into equivalent sorted shallow equational theories and generalize the classes of shallow and standard equational theories.
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Our extensions generalize the known classes of shallow or standard equational theories. In order to prove decidability of unification in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natural extension of tree automata with equality constraints between brother subterms as well as shallow sort theories. We show that saturation under sorted superposition is effective on sorted shallow equational theories. 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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">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="LORIA-FM" p="LORIA">Méthodes formelles</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">Rapport interne.</note><note type="audience" n="0">Not set</note><note type="report" n="3">Intern report</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Unification in Extensions of Shallow Equational Theories</title><author role="aut"><persName><forename type="first">Florent</forename><surname>Jacquemard</surname></persName><email>Florent.Jacquemard@loria.fr</email><idno type="idHal">florentjacquemard</idno><idno type="halAuthorId">129854</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2360"></affiliation></author><author role="aut"><persName><forename type="first">Christoph</forename><surname>Meyer</surname></persName><idno type="halAuthorId">129855</idno><orgName ref="#struct-364522"></orgName></author><author role="aut"><persName><forename type="first">Christoph</forename><surname>Weidenbach</surname></persName><idno type="halAuthorId">129856</idno><orgName ref="#struct-364522"></orgName></author></analytic><monogr><idno type="reportNumber">98-R-387 || jacquemard98a</idno><imprint><biblScope unit="pp">33 p</biblScope><date type="datePub">1998</date></imprint></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="fr">decidability.</term><term xml:lang="fr">e-unification</term><term xml:lang="fr">tree automata</term><term xml:lang="fr">monadic theories</term><term xml:lang="fr">superposition</term><term xml:lang="fr">automates d'arbres</term><term xml:lang="fr">théories monadiques</term><term xml:lang="fr">décidabilité.</term><term xml:lang="it">décidabilité</term></keywords><classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode><classCode scheme="halTypology" n="REPORT">Reports</classCode></textClass><abstract xml:lang="en">We show that unification in certain extensions of shallow equational theories is decidable. Our extensions generalize the known classes of shallow or standard equational theories. In order to prove decidability of unification in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natural extension of tree automata with equality constraints between brother subterms as well as shallow sort theories. We show that saturation under sorted superposition is effective on sorted shallow equational theories. So called semi-linear equational theories can be effectively transformed into equivalent sorted shallow equational theories and generalize the classes of shallow and standard equational theories.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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