A Direct Algorithm for Type Inference in the Rank 2 Fragment of the Second-Order -Calculus

We study the problem of type inference for a family of polymorphic type disciplines containing the power of Core-ML. This family comprises all levels of the strati cation of the second-order lambda-calculus by \rank" of types. We show that typability is an undecidable problem at every rank k 3 of this strati cation. While it was already known that typability is decidable at rank 2, no direct and easy-to-implement algorithm was available. To design such an algorithm, we develop a new notion of reduction and show how to use it to reduce the problem of typability at rank 2 to the problem of acyclic semi-uni cation. A by-product of our analysis is the publication of a simple solution procedure for acyclic semi-uni cation. This work is partly supported by NSF grant CCR{9113196.

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