Canonized rewriting and ground AC completion modulo shostak theories

Authors:
Sylvain Conchon;Evelyne Contejean;Mohamed Iguernelala
Affiliations:
LRI, Univ Paris-Sud, CNRS, Orsay and INRIA Saclay - Ile-de-France, ProVal, Orsay;LRI, Univ Paris-Sud, CNRS, Orsay and INRIA Saclay - Ile-de-France, ProVal, Orsay;LRI, Univ Paris-Sud, CNRS, Orsay and INRIA Saclay - Ile-de-France, ProVal, Orsay
Venue:
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
Year:
2011

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Abstract

AC-completion efficiently handles equality modulo associative and commutative function symbols. When the input is ground, the procedure terminates and provides a decision algorithm for the word problem. In this paper, we present a modular extension of ground ACcompletion for deciding formulas in the combination of the theory of equality with user-defined AC symbols, uninterpreted symbols and an arbitrary signature disjoint Shostak theory X. Our algorithm, called AC(X), is obtained by augmenting in a modular way ground AC-completion with the canonizer and solver present for the theory X. This integration rests on canonized rewriting, a new relation reminiscent to normalized rewriting, which integrates canonizers in rewriting steps. AC(X) is proved sound, complete and terminating, and is implemented to extend the core of the Alt-Ergo theorem prover.