Termination Modulo Combinations of Equational Theories
Identifieur interne : 003889 ( Main/Exploration ); précédent : 003888; suivant : 003890Termination Modulo Combinations of Equational Theories
Auteurs : Francisco Durán [Espagne] ; Salvador Lucas [Espagne] ; José Meseguer [États-Unis]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Rewriting with rules R modulo axioms E is a widely used technique in both rule-based programming languages and in automated deduction. Termination methods for rewriting systems modulo specific axioms E (e.g., associativity-commutativity) are known. However, much less seems to be known about termination methods that can be modular in the set E of axioms. In fact, current termination tools and proof methods cannot be applied to commonly occurring combinations of axioms that fall outside their scope. This work proposes a modular termination proof method based on semantics- and termination-preserving transformations that can reduce the proof of termination of rules R modulo E to an equivalent proof of termination of the transformed rules modulo a typically much simpler set B of axioms. Our method is based on the notion of variants of a term recently proposed by Comon and Delaune. We illustrate its practical usefulness by considering the very common case in which E is an arbitrary combination of associativity, commutativity, left- and right-identity axioms for various function symbols.
Url:
DOI: 10.1007/978-3-642-04222-5_15
Affiliations:
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Termination methods for rewriting systems modulo specific axioms E (e.g., associativity-commutativity) are known. However, much less seems to be known about termination methods that can be modular in the set E of axioms. In fact, current termination tools and proof methods cannot be applied to commonly occurring combinations of axioms that fall outside their scope. This work proposes a modular termination proof method based on semantics- and termination-preserving transformations that can reduce the proof of termination of rules R modulo E to an equivalent proof of termination of the transformed rules modulo a typically much simpler set B of axioms. Our method is based on the notion of variants of a term recently proposed by Comon and Delaune. We illustrate its practical usefulness by considering the very common case in which E is an arbitrary combination of associativity, commutativity, left- and right-identity axioms for various function symbols.</div></front></TEI><affiliations><list><country><li>Espagne</li><li>États-Unis</li></country><region><li>Andalousie</li><li>Illinois</li></region><settlement><li>Malaga</li></settlement><orgName><li>Université de Malaga</li></orgName></list><tree><country name="Espagne"><region name="Andalousie"><name sortKey="Duran, Francisco" sort="Duran, Francisco" uniqKey="Duran F" first="Francisco" last="Durán">Francisco Durán</name></region><name sortKey="Lucas, Salvador" sort="Lucas, Salvador" uniqKey="Lucas S" first="Salvador" last="Lucas">Salvador Lucas</name></country><country name="États-Unis"><region name="Illinois"><name sortKey="Meseguer, Jose" sort="Meseguer, Jose" uniqKey="Meseguer J" first="José" last="Meseguer">José Meseguer</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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