A Certified Type-Preserving Compiler from Lambda Calculus to Assembly Language ∗

We present a certified compiler from the simply-typed lambda calculus to assembly language. The compiler is certified in the sense that it comes with a machine-checked proof of semantics preservation, performed with the Coq proof assistant. The compiler and the terms of its several intermediate languages are given dependent types that guarantee that only well-typed programs are representable. Thus, type preservation for each compiler pass follows without any significant “proofs ” of the usual kind. Semantics preservation is proved based on denotational semantics assigned to the intermediate languages. We demonstrate how working with a type-preserving compiler enables type-directed proof search to discharge large parts of our proof obligations automatically. Categories and Subject Descriptors F.3.1 [Logics and meaning