Computability Closure: Ten Years Later
Identifieur interne : 001729 ( Hal/Curation ); précédent : 001728; suivant : 001730Computability Closure: Ten Years Later
Auteurs : Frédéric Blanqui [France]Source :
Abstract
The notion of computability closure has been introduced for proving the termination of higher-order rewriting with first-order matching by Jean-Pierre Jouannaud and Mitsuhiro Okada in a 1997 draft which later served as a basis for the author's PhD. In this paper, we show how this notion can also be used for dealing with beta-normalized rewriting with matching modulo beta-eta (on patterns à la Miller), rewriting with matching modulo some equational theory, and higher-order data types (types with constructors having functional recursive arguments). Finally, we show how the computability closure can easily be turned into a reduction ordering which, in the higher-order case, contains Jean-Pierre Jouannaud and Albert Rubio's higher-order recursive path ordering and, in the first-order case, is equal to the usual first-order recursive path ordering.
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DOI: 10.1007/978-3-540-73147-4_4
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Finally, we show how the computability closure can easily be turned into a reduction ordering which, in the higher-order case, contains Jean-Pierre Jouannaud and Albert Rubio's higher-order recursive path ordering and, in the first-order case, is equal to the usual first-order recursive path ordering.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Computability Closure: Ten Years Later</title><author role="aut"><persName><forename type="first">Frédéric</forename><surname>Blanqui</surname></persName><email>blanqui@loria.fr</email><idno type="halauthor">58558</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2360"></affiliation></author><editor role="depositor"><persName><forename>Frédéric</forename><surname>Blanqui</surname></persName><email>frederic.blanqui@inria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2007-07-09 17:35:57</date><date type="whenWritten">2007</date><date type="whenModified">2016-05-19 01:09:20</date><date type="whenReleased">2007-07-10 08:34:04</date><date type="whenProduced">2007-06-21</date><date type="whenEndEmbargoed">2007-07-09</date><ref type="file" target="https://hal.inria.fr/inria-00161092/document"><date notBefore="2007-07-09"></date></ref><ref type="file" subtype="author" n="1" target="https://hal.inria.fr/inria-00161092/file/main.pdf"><date notBefore="2007-07-09"></date></ref></edition><respStmt><resp>contributor</resp><name key="102606"><persName><forename>Frédéric</forename><surname>Blanqui</surname></persName><email>frederic.blanqui@inria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00161092</idno><idno type="halUri">https://hal.inria.fr/inria-00161092</idno><idno type="halBibtex">blanqui:inria-00161092</idno><idno type="halRefHtml">Colloquium in honor of Jean-Pierre Jouannaud, Jun 2007, Cachan, France. 4600 (4600), 2007, LNCS. <10.1007/978-3-540-73147-4_4></idno><idno type="halRef">Colloquium in honor of Jean-Pierre Jouannaud, Jun 2007, Cachan, France. 4600 (4600), 2007, LNCS. <10.1007/978-3-540-73147-4_4></idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</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="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">Computability Closure: Ten Years Later</title><author role="aut"><persName><forename type="first">Frédéric</forename><surname>Blanqui</surname></persName><email>blanqui@loria.fr</email><idno type="halAuthorId">58558</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2360"></affiliation></author></analytic><monogr><meeting><title>Colloquium in honor of Jean-Pierre Jouannaud</title><date type="start">2007-06-21</date><settlement>Cachan</settlement><country key="FR">France</country></meeting><imprint><biblScope unit="serie">LNCS</biblScope><biblScope unit="volume">4600</biblScope><biblScope unit="issue">4600</biblScope><date type="datePub">2007</date></imprint></monogr><idno type="arxiv">0707.1372</idno><idno type="doi">10.1007/978-3-540-73147-4_4</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="ro">lambda-calculus</term><term xml:lang="ro">termination</term><term xml:lang="ro">rewriting</term></keywords><classCode scheme="halDomain" n="info.info-lo">Computer Science [cs]/Logic in Computer Science [cs.LO]</classCode><classCode scheme="halTypology" n="COMM">Conference papers</classCode></textClass><abstract xml:lang="en">The notion of computability closure has been introduced for proving the termination of higher-order rewriting with first-order matching by Jean-Pierre Jouannaud and Mitsuhiro Okada in a 1997 draft which later served as a basis for the author's PhD. In this paper, we show how this notion can also be used for dealing with beta-normalized rewriting with matching modulo beta-eta (on patterns à la Miller), rewriting with matching modulo some equational theory, and higher-order data types (types with constructors having functional recursive arguments). Finally, we show how the computability closure can easily be turned into a reduction ordering which, in the higher-order case, contains Jean-Pierre Jouannaud and Albert Rubio's higher-order recursive path ordering and, in the first-order case, is equal to the usual first-order recursive path ordering.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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