Certification of a Type Inference Tool for ML: Damas–Milner within Coq

We develop a formal proof of the ML type inference algorithm, within the Coq proof assistant. We are much concerned with methodology and reusability of such a mechanization. This proof is an essential step toward the certification of a complete ML compiler.In this paper we present the Coq formalization of the typing system and its inference algorithm. We establish formally the correctness and the completeness of the type inference algorithm with respect to the typing rules of the language. We describe and comment on the mechanized proofs.

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