A semantic approach to order-sorted rewriting
Identifieur interne : 00D229 ( Main/Exploration ); précédent : 00D228; suivant : 00D230A semantic approach to order-sorted rewriting
Auteurs : Andreas Werner [Allemagne]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Order-sorted rewriting builds a nice framework to handle partially defined functions and subtypes (see [Smolka & al 87]). In the previous works about order-sorted rewriting the term rewriting system needs to be sort decreasing in order to be able to prove a critical pair lemma and Birkhoff's completeness theorem. However, this approach is too restrictive. Therefore, we generalize well-sorted terms to semantically well-sorted terms and well-sorted substitutions to some kind of semantically wellsorted substitutions. Semantically well-sorted terms with respect to a set of equations E are terms that denote well-defined elements in every algebra satisfying E. 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 to obtain an equivalent range unique signature from each non-range-unique one. We also show some decidability results.
Url:
DOI: 10.1007/3-540-56868-9_5
Affiliations:
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