HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Trusting computations: a mechanized proof from partial differential equations to actual program

Abstract : Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring specific accuracy issues due to their massive use of floating-point computations. Yet, it is uncommon to guarantee their correctness. Indeed, we had to extend existing methods and tools for proving the correct behavior of programs to verify an existing numerical analysis program. This C program implements the second-order centered finite difference explicit scheme for solving the 1D wave equation. In fact, we have gone much further as we have mechanically verified the convergence of the numerical scheme in order to get a complete formal proof covering all aspects from partial differential equations to actual numerical results. To the best of our knowledge, this is the first time such a comprehensive proof is achieved.
Complete list of metadata

Cited literature [36 references]  Display  Hide  Download

Contributor : Francois Clement Connect in order to contact the contributor
Submitted on : Monday, June 2, 2014 - 12:58:39 PM
Last modification on : Wednesday, February 9, 2022 - 5:26:06 PM
Long-term archiving on: : Tuesday, April 11, 2017 - 2:43:08 AM


Files produced by the author(s)



Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, et al.. Trusting computations: a mechanized proof from partial differential equations to actual program. Computers & Mathematics with Applications, Elsevier, 2014, 68 (3), pp.28. ⟨10.1016/j.camwa.2014.06.004⟩. ⟨hal-00769201v3⟩



Record views


Files downloads