Biorthogonality, Step-Indexing and Compiler Correctness

This paper defines logical relations between the denotational semantics of a simply typed functional language with recursion and the operational behaviour of low-level programs in a variant SECD machine. The relations, which are defined using biorthogonality and step-indexing, capture what it means for a piece of low-level code to implement a mathematical, domain-theoretic function and are used to prove correctness of a simple compiler. The results have been formalized in the Coq proof assistant.