Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of   a C Program
  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. 
Sylvie Boldo (INRIA Saclay - Ile de France, LRI), Francois Clement   (INRIA Rocquencourt), Jean-Christophe Filli\^atre (INRI...
cs.LO math.NA