A kripke logical relation between ML and assembly

There has recently been great progress in proving the correctness of compilers for increasingly realistic languages with increasingly realistic runtime systems. Most work on this problem has focused on proving the correctness of a particular compiler, leaving open the question of how to verify the correctness of assembly code that is hand-optimized or linked together from the output of multiple compilers. This has led Benton and other researchers to propose more abstract, compositional notions of when a low-level program correctly realizes a high-level one. However, the state of the art in so-called "compositional compiler correctness" has only considered relatively simple high-level and low-level languages.

In this paper, we propose a novel, extensional, compiler-independent notion of equivalence between high-level programs in an expressive, impure ML-like λ-calculus and low-level programs in an (only slightly) idealized assembly language. We define this equivalence by means of a biorthogonal, step-indexed, Kripke logical relation, which enables us to reason quite flexibly about assembly code that uses local state in a different manner than the high-level code it implements (e.g. self-modifying code). In contrast to prior work, we factor our relation in a symmetric, language-generic fashion, which helps to simplify and clarify the formal presentation, and we also show how to account for the presence of a garbage collector. Our approach relies on recent developments in Kripke logical relations for ML-like languages, in particular the idea of possible worlds as state transition systems.