Calculating Certified Compilers for Non-Deterministic Languages?

Abstract. Reasoning about programming languages with non-deter-ministic semantics entails many difficulties. For instance, to prove cor-rectness of a compiler for such a language, one typically has to split the correctness property into a soundness and a completeness part, and then prove these two parts separately. In this paper, we present a set of proof rules to prove compiler correctness by a single proof in cal-culational style. The key observation that led to our proof rules is the fact that the soundness and completeness proof follow a similar pattern with only small differences. We condensed these differences into a single side condition for one of our proof rules. This side condition, however, is easily discharged automatically by a very simple form of proof search. We implemented this calculation framework in the Coq proof assistant. Apart from verifying a given compiler, our proof technique can also be used to formally derive – from the semantics of the source language – a compiler that is correct by construction. For such a derivation to succeed it is crucial that the underlying correctness argument proceeds as a sin-gle calculation, as opposed to separate calculations of the two directions of the correctness property. We demonstrate our technique by deriving a compiler for a simple language with interrupts.