Wave equation numerical resolution: a comprehensive mechanized proof of a C program
Se ha publicado un nuevo artículo de formalización en Coq: Wave equation numerical resolution: a comprehensive mechanized proof of a C program.
Sus autores son Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond y Pierre Weis.
El resumen del artículo es
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.
El código correspondiente se encuentra en http://fost.saclay.inria.fr/wave_total_error.html