A proof theory for machine code

Abstract

This article develops a proof theory for low-level code languages. We first define a proof system, which we refer to as the sequential sequent calculus , and show that it enjoys the cut elimination property and that its expressive power is the same as that of the natural deduction proof system. We then establish the Curry-Howard isomorphism between this proof system and a low-level code language by showing the following properties: (1) the set of proofs and the set of typed codes is in one-to-one correspondence, (2) the operational semantics of the code language is directly derived from the cut elimination procedure of the proof system, and (3) compilation and decompilation algorithms between the code language and the typed lambda calculus are extracted from the proof transformations between the sequential sequent calculus and the natural deduction proof system. This logical framework serves as a basis for the development of type systems of various low-level code languages, type-preserving compilation, and static code analysis.