Proof Search and Proof Check for Equational and Inductive Theorems

Eric Deplagne (1) , Claude Kirchner (1) , Hélène Kirchner (1) , Quang Huy Nguyen

1 PROTHEO - Constraints, automatic deduction and software properties proofs

This 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.

Mots clés: automated theorem proving; proof assistant; rewrite rules; proof terms

Mots clés: induction; preuve automatique; computation; assistant à la preuve; déduction; calcul; réécriture; terme de preuve; récurrence

Domaines: Autre [cs.OH]

Eric Deplagne, Claude Kirchner, Hélène Kirchner, Quang Huy Nguyen. Proof Search and Proof Check for Equational and Inductive Theorems. Conference on Automated Deduction - CADE-19, Jul 2003, Miami (FL), United States. 20 p, ⟨10.1007/978-3-540-45085-6_26⟩. ⟨inria-00099470⟩