Reasoning about programming languages with non-deterministic semantics entails many difficulties. For instance, to prove correctness 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 calculational 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 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 single 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.
|Titel||Mathematics of Program Construction|
|Redaktører||Ralf Hinze, Janis Voigtländer|
|Forlag||Springer International Publishing, Switzerland|
|Publikationsdato||1 jun. 2015|
|Status||Udgivet - 1 jun. 2015|
- compiler, verification,coq, program calculation