Canonized Rewriting and Ground AC Completion Modulo Shostak Theories

  • Sylvain Conchon
  • Evelyne Contejean
  • Mohamed Iguernelala
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6605)


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.


decision procedure associativity and commutativity rewriting AC-completion SMT solvers Shostak’s algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sylvain Conchon
    • 1
    • 2
  • Evelyne Contejean
    • 1
    • 2
  • Mohamed Iguernelala
    • 1
    • 2
  1. 1.LRIUniv Paris-Sud, CNRSOrsayFrance
  2. 2.INRIA Saclay – Ile-de-France, ProValOrsayFrance

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