C floating-point proofs layered with VST and Flocq

Abstract

We demonstrate tools and methods for proofs about the correctness and numerical accuracy of C programs. The tools are foundational, in that they are connected to formal semantic specifications of the C operational semantics and of the IEEE 754 floating-point format. The tools are modular, in that the reasoning about C programming can be done quite separately from the reasoning about numerical correctness and numerical accuracy. The tools are general, in that they accommodate almost the entire C language (with pointer data structures, function pointers, control flow, etc.) and applied mathematics (reasoned about in a general-purpose logic and proof assistant with substantial libraries for mathematical reasoning). We demonstrate on a simple Newton's-method square root function.