A Semantic Approach to Order-sorted Rewriting
Identifieur interne : 00B403 ( Main/Exploration ); précédent : 00B402; suivant : 00B404A Semantic Approach to Order-sorted Rewriting
Auteurs : A. Werner [Allemagne]Source :
- Journal of Symbolic Computation [ 0747-7171 ] ; 1998.
English descriptors
- Teeft :
- Academic press, Algebra, Alse, Binary relation, Completeness, Completeness results, Completeness theorem, Critical pairs, Decidable, Disjoint, Equational, Fair derivation, Function declaration, Function declarations, Function symbol, Function symbols, Goguen, Ground term, Heidelberg, Homomorphism, Immediate consequence, Immediate consequences, Induction, Induction hypothesis, Inference rule, Inference rules, Least sort, Mod2, Natural number, Nite, Nite number, Noetherian, Normal form, Original signature, Other hand, Partial order, Proc, Quotient, Quotient algebra, Range sort, Range sorts, Second part, Second step, Semantic approach, Semantical, Semantical sorts, Semantics, Signature, Smolka, Sort constraints, Sort decreasingness, Soundness, Substitution, Subterm, Technical report, Term declarations, Term structure, Third case, Trivially, Undecidability results, Unique homomorphism, Unsorted, Unsorted lemma, Waldmann, Xint, Xint xint, Xnat, Yint, Yint yint, Ypos mod2.
Abstract
Abstract: Order-sorted rewriting builds a nice framework to handle partially defined functions and subtypes. To be able to prove a critical-pair lemma and Birkhoff's completeness theorem, order-sorted rewriting was restricted to sort decreasing term rewriting systems. However, natural examples show that this approach is too restrictive. To solve this problem, we generalize well-sorted terms to semantically well-sorted terms and well-sorted substitutions to a restricted form of semantically well-sorted substitutions. Semantically well-sorted terms with respect to a set of equationsEare terms that denote well-defined elements in every algebra satisfyingE. We prove a critical-pair lemma and Birkhoff's completeness theorem for so-called range-unique signatures and arbitrary order-sorted rewriting systems. A transformation is given which allows us to obtain an equivalent range-unique signature from each non-range-unique one. We also show decidability and undecidability results.
Url:
DOI: 10.1006/jsco.1997.0188
Affiliations:
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Werner</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:A63181D81CA9E63E0074CBF74254468D37E39542</idno><date when="1998" year="1998">1998</date><idno type="doi">10.1006/jsco.1997.0188</idno><idno type="url">https://api.istex.fr/ark:/67375/6H6-WFTLCQTQ-3/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">002733</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002733</idno><idno type="wicri:Area/Istex/Curation">002700</idno><idno type="wicri:Area/Istex/Checkpoint">002636</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">002636</idno><idno type="wicri:doubleKey">0747-7171:1998:Werner A:a:semantic:approach</idno><idno type="wicri:Area/Main/Merge">00BB26</idno><idno type="wicri:Area/Main/Curation">00B403</idno><idno type="wicri:Area/Main/Exploration">00B403</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">A Semantic Approach to Order-sorted Rewriting</title><author><name sortKey="Werner, A" sort="Werner, A" uniqKey="Werner A" first="A." last="Werner">A. Werner</name><affiliation wicri:level="3"><country xml:lang="fr">Allemagne</country><wicri:regionArea>ILKD, University of Karlsruhe, Karlsruhe, D-76128</wicri:regionArea><placeName><region type="land" nuts="1">Bade-Wurtemberg</region><region type="district" nuts="2">District de Karlsruhe</region><settlement type="city">Karlsruhe</settlement></placeName></affiliation></author></analytic><monogr></monogr><series><title level="j">Journal of Symbolic Computation</title><title level="j" type="abbrev">YJSCO</title><idno type="ISSN">0747-7171</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1998">1998</date><biblScope unit="volume">25</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="527">527</biblScope><biblScope unit="page" to="569">569</biblScope></imprint><idno type="ISSN">0747-7171</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0747-7171</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="Teeft" xml:lang="en"><term>Academic press</term><term>Algebra</term><term>Alse</term><term>Binary relation</term><term>Completeness</term><term>Completeness results</term><term>Completeness theorem</term><term>Critical pairs</term><term>Decidable</term><term>Disjoint</term><term>Equational</term><term>Fair derivation</term><term>Function declaration</term><term>Function declarations</term><term>Function symbol</term><term>Function symbols</term><term>Goguen</term><term>Ground term</term><term>Heidelberg</term><term>Homomorphism</term><term>Immediate consequence</term><term>Immediate consequences</term><term>Induction</term><term>Induction hypothesis</term><term>Inference rule</term><term>Inference rules</term><term>Least sort</term><term>Mod2</term><term>Natural number</term><term>Nite</term><term>Nite number</term><term>Noetherian</term><term>Normal form</term><term>Original signature</term><term>Other hand</term><term>Partial order</term><term>Proc</term><term>Quotient</term><term>Quotient algebra</term><term>Range sort</term><term>Range sorts</term><term>Second part</term><term>Second step</term><term>Semantic approach</term><term>Semantical</term><term>Semantical sorts</term><term>Semantics</term><term>Signature</term><term>Smolka</term><term>Sort constraints</term><term>Sort decreasingness</term><term>Soundness</term><term>Substitution</term><term>Subterm</term><term>Technical report</term><term>Term declarations</term><term>Term structure</term><term>Third case</term><term>Trivially</term><term>Undecidability results</term><term>Unique homomorphism</term><term>Unsorted</term><term>Unsorted lemma</term><term>Waldmann</term><term>Xint</term><term>Xint xint</term><term>Xnat</term><term>Yint</term><term>Yint yint</term><term>Ypos mod2</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Order-sorted rewriting builds a nice framework to handle partially defined functions and subtypes. To be able to prove a critical-pair lemma and Birkhoff's completeness theorem, order-sorted rewriting was restricted to sort decreasing term rewriting systems. However, natural examples show that this approach is too restrictive. To solve this problem, we generalize well-sorted terms to semantically well-sorted terms and well-sorted substitutions to a restricted form of semantically well-sorted substitutions. Semantically well-sorted terms with respect to a set of equationsEare terms that denote well-defined elements in every algebra satisfyingE. We prove a critical-pair lemma and Birkhoff's completeness theorem for so-called range-unique signatures and arbitrary order-sorted rewriting systems. A transformation is given which allows us to obtain an equivalent range-unique signature from each non-range-unique one. We also show decidability and undecidability results.</div></front></TEI><affiliations><list><country><li>Allemagne</li></country><region><li>Bade-Wurtemberg</li><li>District de Karlsruhe</li></region><settlement><li>Karlsruhe</li></settlement></list><tree><country name="Allemagne"><region name="Bade-Wurtemberg"><name sortKey="Werner, A" sort="Werner, A" uniqKey="Werner A" first="A." last="Werner">A. Werner</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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