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We present a new approach to the polymorphic typing of data accepting in-place modification in ML-like languages. This approach is based on restrictions over type generalization, and a refined typing of functions. The type system given here leads to a better integration of imperative programming style with the purely applicative kernel of ML. In particular, generic functions that allocate mutable data can safely be given fully polymorphic types. We show the soundness of this type system, and give a type reconstruction algorithm.

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Abstract. Popular finite difference numerical schemes for the resolution of the one-dimensional acoustic wave equation are well-known to be convergent. We present a comprehensive formalization of the simplest scheme and formally prove its convergence in Coq. The main difficulties lie in the proper definition of asymptotic behaviors and the implicit way they are handled in the mathematical pen-and-paper proofs. To our knowledge, this is the first time this kind of mathematical proof is machine-checked.