Operational Refinement for Compiler Correctness
Compilers are an essential part of the software development process. Programmers all over the world rely on compilers every day to correctly translate their intentions, expressed as high-level source code, into executable low-level machine code. But what does it mean for a compiler to be correct?
This question is surprisingly difficult to answer. Despite the fact that various groups have made concerted efforts to prove the correctness of compilers since at least the early 1980?s, no clear consensus has arisen about what it means for a compiler to be correct. As a result, it seems that no two compiler verification efforts have stated their correctness theorems in the same way.
In this dissertation, I will advance a new approach to compiler correctness based on refinements of the operational semantics of programs. The cornerstones of this approach are behavioral refinement, which allows programs to improve by going wrong less often, and choice refinement, which allows compilers to reduce the amount of internal nondeterminism present in a program. I take particular care to explain why these notions of refinement are the correct formal interpretations of the informal ideas above.
In addition, I will show how these notions of refinement can be realistically applied to compiler verification efforts. First, I will present a toy language, WHILE-C, and show how choice and behavioral refinement can be used to verify the correctness of several interesting program transformations. The WHILE-C language and the transformations themselves are simple enough to be presented here in full detail. I will also show how the ideas of behavioral and choice refinement may be applied to the CompCert formally verified compiler, a realistic compiler for a significant subset of C.