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SMT Solving Modulo Tableau and Rewriting Theories

Guillaume Bury 1 Simon Cruanes 2 David Delahaye 3 
2 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
3 MAREL - Models And Reuse Engineering, Languages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We propose an automated theorem prover that combines an SMT solver with tableau calculus and rewriting. Tableau inference rules are used to unfold propositional content into clauses while atomic formulas are handled using satisfiability decision procedures as in traditional SMT solvers. To deal with quantified first order formulas, we use metavariables and perform rigid unification modulo equalities and rewriting, for which we introduce an algorithm based on superposition, but where all clauses contain a single atomic formula. Rewriting is introduced along the lines of deduction modulo theory, where axioms are turned into rewrite rules over both terms and propositions. Finally, we assess our approach over a benchmark of problems in the set theory of the B method.
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Submitted on : Thursday, March 28, 2019 - 6:58:11 PM
Last modification on : Tuesday, October 25, 2022 - 4:23:57 PM
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  • HAL Id : hal-02083232, version 1


Guillaume Bury, Simon Cruanes, David Delahaye. SMT Solving Modulo Tableau and Rewriting Theories. SMT 2018 - 16th International Workshop on Satisfiability Modulo Theories, Jul 2018, Oxford, United Kingdom. ⟨hal-02083232⟩



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