Refinement to Certify Abstract Interpretations, Illustrated on Linearization for Polyhedra

Sylvain Boulmé (1) , Alexandre Maréchal (1)

1 VERIMAG - IMAG - VERIMAG

Our concern is the modular development of a certified static analyzer in Coq: we extend a certified abstract domain of convex polyhedra with a linearization procedure approximating polynomial expressions. In order to help such a development, we propose a proof framework, embedded in Coq, that implements a refinement calculus. It allows to hide for proofs several low-level aspects of the computations on abstract domains. Moreover, refinement proofs are naturally simplified thanks to computations of weakest preconditions.

Mots clés: Continuation-Passing Style; Linear arithmetic; Refinement calculus; Abstract Interpretation; The Coq proof assistant; Monad; Weakest precondition; Certified Software; Proof Assistants; Result Certification

Domaines: Informatique [cs]

Sylvain Boulmé, Alexandre Maréchal. Refinement to Certify Abstract Interpretations, Illustrated on Linearization for Polyhedra. Interactive Theorem Proving - 6th International Conference, 2015, Nanjing, China. ⟨hal-01133865v3⟩