Proof Search and Proof Check for Equational and Inductive Theorems

Abstract

Colloque avec actes et comité de lecture. internationale.International audienceThis paper presents on-going researches on theoretical and practical issues of combining rewriting based automated theorem proving and user-guided proof development, with the strong constraint of safe cooperation of both. In practice, we instantiate the theoretical study on the coq proof assistant and the elan rewriting based system, focusing first on equational and then on inductive proofs. Different concepts, especially rewriting calculus and deduction modulo, contribute to define and to relate proof search, proof representation and proof check