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Wave equation numerical resolution: a comprehensive mechanized proof of a C program

Abstract : We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.
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https://hal.inria.fr/hal-00649240
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Submitted on : Thursday, July 12, 2012 - 10:41:13 AM
Last modification on : Wednesday, February 9, 2022 - 5:26:06 PM
Long-term archiving on: : Thursday, December 15, 2016 - 10:36:35 PM

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Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, et al.. Wave equation numerical resolution: a comprehensive mechanized proof of a C program. Journal of Automated Reasoning, Springer Verlag, 2013, 50 (4), pp.423-456. ⟨10.1007/s10817-012-9255-4⟩. ⟨hal-00649240v3⟩

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