We have just submitted the final version of two papers, presenting the state of our recent research.
- A Formally-Verified C Static Analyzer, by Jacques-Henri Jourdan, Vincent Laporte, Sandrine Blazy, Xavier Leroy, and David Pichardie
- Verified compilation of floating-point computations, by Sylvie Boldo, Jacques-Henri Jourdan, Xavier Leroy, and Guillaume Melquiond
Jacques-Henri Jourdan, Vincent Laporte, Sandrine Blazy, Xavier Leroy, and David Pichardie, at POPL'15
This paper reports on the design and soundness proof, using the Coq proof assistant, of Verasco, a static analyzer based on abstract interpretation for most of the ISO C 1999 language (excluding recursion and dynamic allocation). Verasco establishes the absence of run-time errors in the analyzed programs. It enjoys a modular architecture that supports the extensible combination of multiple abstract domains, both relational and non-relational. Verasco integrates with the CompCert formally-verified C compiler so that not only the soundness of the analysis results is guaranteed with mathematical certitude, but also the fact that these guarantees carry over to the compiled code.
This work lead to the first release of Verasco, which is slowly (but surely) taking shape !
Sylvie Boldo, Jacques-Henri Jourdan, Xavier Leroy, and Guillaume Melquiond, in the Journal of Automated Reasoning
Floating-point arithmetic is known to be tricky: roundings, formats, exceptional values. The IEEE-754 standard was a push towards straightening the field and made formal reasoning about floating-point computations easier and flourishing. Unfortunately, this is not sufficient to guarantee the final result of a program, as several other actors are involved: programming language, compiler, and architecture. The CompCert formally-verified compiler provides a solution to this problem: this compiler comes with a mathematical specification of the semantics of its source language (a large subset of ISO C99) and target platforms (ARM, PowerPC, x86-SSE2), and with a proof that compilation preserves semantics. In this paper, we report on our recent success in formally specifying and proving correct CompCert’s compilation of floating-point arithmetic. Since CompCert is verified using the Coq proof assistant, this effort required a suitable Coq formalization of the IEEE-754 standard; we extended the Flocq library for this purpose. As a result, we obtain the first formally verified compiler that provably preserves the semantics of floating-point programs.
This may be of interest if you want to understand the problems (and their solutions) one faces when making a compiler support floating-points operations (correctly, if possible).