Formal verification of numerical programs: from C annotated programs to Coq proofs

International audienceNumerical programs may require a high level of guarantee. This can be achieved by applying formal methods, such as machine-checked proofs. But these tools handle mathematical theorems while we are interested in C code. To achieve this high level of confidence on C programs, we use a chain of tools: Frama-C, its Jessie plugin, Why and Coq. This requires the C program to be annotated: this means that each function must be precisely specified, and we will prove the correctness of the program by proving both that it meets its specifications and that it does not fail. Examples will be given to illustrate the features of this approach