Completeness and confluence of order-sorted term rewriting
Identifieur interne : 00D213 ( Main/Exploration ); précédent : 00D212; suivant : 00D214Completeness and confluence of order-sorted term rewriting
Auteurs : Lars With [Allemagne]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: We show various results for order-sorted term rewriting. We extend the result that order-sorted rewriting is complete if the rewrite system is compatible and confluent [17] by proving that order-sorted rewriting is complete if we consider the semantical sorts of the terms, i.e., we have confidence in the rewrite steps because they replace equals by equals. In the order-sorted case the critical pair theorem [13] holds only if the rewrite system is weakly sort decreasing [16]. We show that every rewrite system can be made weakly sort decreasing by extending the expressibility of the signature by adding term declarations. Unification with term declarations is undecidable in general [16]. We give a condition for the decidability of unification with term declarations that is considerably more general than the conditions given in [16]. We furthermore solve two open problems stated in [16]: unification in linear signatures is decidable and thus regularity of linear signatures, too.
Url:
DOI: 10.1007/3-540-56393-8_30
Affiliations:
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<front><div type="abstract" xml:lang="en">Abstract: We show various results for order-sorted term rewriting. We extend the result that order-sorted rewriting is complete if the rewrite system is compatible and confluent [17] by proving that order-sorted rewriting is complete if we consider the semantical sorts of the terms, i.e., we have confidence in the rewrite steps because they replace equals by equals. In the order-sorted case the critical pair theorem [13] holds only if the rewrite system is weakly sort decreasing [16]. We show that every rewrite system can be made weakly sort decreasing by extending the expressibility of the signature by adding term declarations. Unification with term declarations is undecidable in general [16]. We give a condition for the decidability of unification with term declarations that is considerably more general than the conditions given in [16]. We furthermore solve two open problems stated in [16]: unification in linear signatures is decidable and thus regularity of linear signatures, too.</div>
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