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Refinement to Certify Abstract Interpretations, Illustrated on Linearization for Polyhedra

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01133865
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Submitted on : Thursday, November 15, 2018 - 3:44:08 PM
Last modification on : Tuesday, November 16, 2021 - 5:12:38 AM

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Sylvain Boulmé, Alexandre Maréchal. Refinement to Certify Abstract Interpretations, Illustrated on Linearization for Polyhedra. Journal of Automated Reasoning, 2018, ⟨10.1007/s10817-018-9492-2⟩. ⟨hal-01133865v4⟩

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