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Preuve par induction dans le calcul des séquents modulo

Fabrice Nahon 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We are presenting an original narrowing-based proof search method for inductive theorems. It has the specificity to be grounded on deduction modulo and to rely on narrowing to provide both induction variables and instantiation schemes. It also yields a direct translation from a successful proof search derivation to a proof in the sequent calculus. The method is shown to be correct and refutationally complete in a proof theoretical way. We are extending this first approach to equational rewrite theories given by a rewrite system R and a set E of equalities. Whenever the equational rewrite system (R,E) has good properties of termination, sufficient completeness, and whenever E is constructor preserving, narrowing at defined-innermost positions is performed with unifiers which are constructor substitutions. This is especially interesting for associative and associative-commutative theories for which the general proof search system is refined.
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Submitted on : Friday, February 29, 2008 - 6:57:45 PM
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  • HAL Id : tel-01748243, version 3

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Fabrice Nahon. Preuve par induction dans le calcul des séquents modulo. Autre [cs.OH]. Université Henri Poincaré - Nancy 1, 2007. Français. ⟨tel-01748243v3⟩

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