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Communication Dans Un Congrès Année : 2011

Canonized Rewriting and Ground AC Completion Modulo Shostak Theories

Résumé

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.
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Dates et versions

hal-00777663 , version 1 (17-01-2013)

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  • HAL Id : hal-00777663 , version 1

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Sylvain Conchon, Evelyne Contejean, Mohamed Iguernelala. Canonized Rewriting and Ground AC Completion Modulo Shostak Theories. TACAS - Tools and Algorithms for the Construction and Analysis of Systems, 2011, Saarbrücken, Germany. ⟨hal-00777663⟩
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