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Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program

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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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Authors and Affiliations

  1. ProVal, INRIA Saclay – Île-de-France, Orsay cedex, 91893, France

    Sylvie Boldo & Guillaume Melquiond

  2. LRI, UMR 8623, Université Paris-Sud, CNRS, Orsay cedex, 91405, France

    Sylvie Boldo, Jean-Christophe Filliâtre & Guillaume Melquiond

  3. Pomdapi, INRIA Paris – Rocquencourt, Le Chesnay cedex, 78153, France

    François Clément & Pierre Weis

  4. LIPN, UMR 7030, Université de Paris-Nord, CNRS, Villetaneuse, 93430, France

    Micaela Mayero

  5. LIP, Arénaire (INRIA Grenoble - Rhône-Alpes, CNRS UMR 5668, UCBL, ENS Lyon), Lyon, 69364, France

    Micaela Mayero

Authors
  1. Sylvie Boldo
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  2. François Clément
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  3. Jean-Christophe Filliâtre
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  4. Micaela Mayero
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  5. Guillaume Melquiond
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  6. Pierre Weis
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Correspondence to Sylvie Boldo.

Additional information

This research was supported by the ANR projects CerPAN (ANR-05-BLAN-0281-04) and Fost (ANR-08-BLAN-0246-01).

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Boldo, S., Clément, F., Filliâtre, JC. et al. Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program. J Autom Reasoning 50, 423–456 (2013). https://doi.org/10.1007/s10817-012-9255-4

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