Proofs you can believe in

Abstract

Basing program analyses on formal semantics has a long and successful tradition in the logic programming paradigm. These analyses rely on results about the relative correctness of mathematically sophisticated semantics, and authors of such analyses often invest considerable effort into establishing these results. The development of interactive theorem provers such as Coq and their recent successes both in the field of program verification as well as in mathematics, poses the question whether these tools can be usefully deployed in logic programming. This paper presents formalisations in Coq of several general results about the correctness of semantics in different styles; forward and backward, top-down and bottom-up. The results chosen are paradigmatic of the kind of correctness theorems that semantic analyses rely on and are therefore well-suited to explore the possibilities afforded by the application of interactive theorem provers to this task, as well as the difficulties likely to be encountered in the endeavour. It turns out that the advantages offered by moving to a functional setting, including the possibility to apply higher-order abstract syntax, are considerable.

Developing and certifying Datalog optimizations in coq/mathcomp

“…The DataCert project aims at building a fully and deeply verified environment for data intensive management tools, the same way [21,22] provide verified realistic C and ML compilers. Kriener et al used Coq in [20] to prove the equivalence of different Prolog semantics. However, as far as we know, our work is the first formally proved implementation of non-trivial optimizations for a declarative and popular language, Datalog.…”