Proving Correctness of the Translation from Mini - ML to the CAM withthe Coq Proof Development

In this article we show how we proved correctness of the translation from a small applicative language with recursive deenitions (Mini-ML) to the Categorical abstract machine (CAM) using the Coq system. Our aim was to mechanise the proof of J. Despeyroux 10]. Like her, we use natural semantics to axiomatise the semantics of our languages. The axiomatisations of inferences systems and of the languages is nicely performed by the mechanism of inductive deenitions in the Coq system. Unfortunately both the source and the target semantics involve nested structures that cannot be formalised inductively. We have overcome this problem by making some slight modiications of both the source and target semantics and show how the changes in the source and target semantics are related. For the remaining tranlation we explain how we can use the Coq system to formalize non-terminating programs and incorrect programs, objects that are impossible to explain with only the formalism of natural semantics.