[10] Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, and Pierre Weis. Wave equation numerical resolution: Mathematics and program. Research Report 7826, INRIA, December 2011. [ bib | full text on HAL ]
We formally prove the C program that implements a simple 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 the floating-point computation leads to round-off errors. We formally specify in Coq the numerical scheme, prove both the method error and the round-off error of the program, and derive an upper bound for the total error. This proves the adequacy of the C program to the numerical scheme and the convergence of the effective computation. To our knowledge, this is the first time a numerical analysis program is fully machine-checked.

Keywords: Formal proof of numerical program; Convergence of numerical scheme; Proof of C program; Coq formal proof; Acoustic wave equation; Partial differential equation; Rounding error analysis
[9] François Bobot, Jean-Christophe Filliâtre, Claude Marché, and Andrei Paskevich. The Why3 platform, version 0.71. LRI, CNRS & Univ. Paris-Sud & INRIA Saclay, version 0.71 edition, October 2011. https://gforge.inria.fr/docman/view.php/2990/7635/manual.pdf. [ bib ]
Keywords: Why3
[8] Asma Tafat and Claude Marché. Binary heaps formally verified in Why3. Research Report 7780, INRIA, October 2011. http://hal.inria.fr/inria-00636083/en/. [ bib | full text on HAL ]
Keywords: Why3
[7] Krishnamani Kalyanasundaram and Claude Marché. Automated generation of loop invariants using predicate abstraction. Research Report 7714, INRIA, August 2011. http://hal.inria.fr/inria-00615623/en/. [ bib | full text on HAL ]
[6] François Bobot, Jean-Christophe Filliâtre, Claude Marché, Guillaume Melquiond, and Andrei Paskevich. The Why3 platform. LRI, CNRS & Univ. Paris-Sud & INRIA Saclay, version 0.64 edition, February 2011. http://why3.lri.fr/. [ bib ]
Keywords: Why3
[5] Yannick Moy and Claude Marché. The Jessie plugin for Deduction Verification in Frama-C --- Tutorial and Reference Manual. INRIA & LRI, 2011. http://krakatoa.lri.fr/. [ bib | PDF | http ]
[4] Évelyne Contejean, Pierre Courtieu, Julien Forest, Olivier Pons, and Xavier Urbain. Automated Certified Proofs with CiME3. Technical Report 2044, Cédric laboratory, CNAM Paris, France, 2011. [ bib | .pdf | Abstract ]
[3] Thi Minh Tuyen Nguyen and Claude Marché. Proving floating-point numerical programs by analysis of their assembly code. Research Report 7655, INRIA, 2011. http://hal.inria.fr/inria-00602266/en/. [ bib | full text on HAL ]
[2] Paolo Herms, Claude Marché, and Benjamin Monate. A certified multi-prover verification condition generator. Research Report 7793, INRIA, 2011. http://hal.inria.fr/hal-00639977/en/. [ bib | full text on HAL ]
[1] Catherine Lelay. étude de la différentiabilité et de l'intégrabilité en Coq : Application à la formule de d'Alembert pour l'équation des ondes. Master's thesis, Université Paris 7, 2011. http://www.lri.fr/~lelay/Rapport.pdf. [ bib ]