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Matching in a Class of Combined Non-Disjoint Theories

Christophe Ringeissen 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Solving equational problems is an ubiquitous process in automated deduction, where one needs for instance unification in completion procedures to compute critical pairs, and matching to apply rewrite rules. We present new equational matching and unification results in some combinations of non-disjoint equational theories. Some results are already known for theories sharing an appropriate notion of constructors. We investigate the idea of considering theories that are not explicitly based on the notion of constructors. In this direction, a new class of theories is presented, where a theory is defined as a union of two subtheories, one such that shared symbols do not affect the behavior of the theory, and another one given by a term rewrite system on shared symbols. Matching and unification problems are studied for this class of theories, and for unions of theories in this class. Results obtained for the matching problem are particularly relevant.
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https://hal.inria.fr/inria-00099610
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Submitted on : Tuesday, September 26, 2006 - 9:39:21 AM
Last modification on : Friday, February 26, 2021 - 3:28:06 PM

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  • HAL Id : inria-00099610, version 1

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Christophe Ringeissen. Matching in a Class of Combined Non-Disjoint Theories. 19th International Conference on Automated Deduction - CADE'2003, Geoff Sutcliffe, Aug 2003, Miami, Floride, USA, pp.212-227. ⟨inria-00099610⟩

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