A Matter of Trust: Skeptical Communication Between Coq and External Provers

Chantal Keller 1
1 TYPICAL - Types, Logic and computing
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : This thesis studies the cooperation between the Coq proof assistant and external provers through proof witnesses. We concentrate on two different kinds of provers that can return certicates: first, answers coming from SAT and SMT solvers can be checked in Coq to increase both the confidence in these solvers and Coq's automation; second, theorems established in interactive provers based on Higher-Order Logic can be exported to Coq and checked again, in order to offer the possibility to produce formal developments which mix these two dierent logical paradigms. It ended up in two software: SMTCoq, a bi-directional cooperation between Coq and SAT/SMT solvers, and HOLLIGHTCOQ, a tool importing HOL Light theorems into Coq. For both tools, we took great care to define a modular and efficient architecture, based on three clearly separated ingredients: an embedding of the formalism of the external tool inside Coq which is carefully translated into Coq terms, a certified checker to establish the proofs using the certicates, and an Ocaml preprocessor to transform proof witnesses coming from different provers into a generic certificate. This division allows that a change in the format of proof witnesses only affects the preprocessor, but no proved Coq code. Another fundamental component for efficiency and modularity is computational reflection, which exploits the computational power of Coq to establish generic and small proofs based on the certicates.
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Chantal Keller. A Matter of Trust: Skeptical Communication Between Coq and External Provers. Logic in Computer Science [cs.LO]. Ecole Polytechnique X, 2013. English. ⟨pastel-00838322⟩

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