## A direct algorithm for type inference in the rank-2 fragment of the second-order λ-calculus (1993)

Citations: | 78 - 14 self |

### BibTeX

@TECHREPORT{Kfoury93adirect,

author = {A. J. Kfoury and J. B. Wells},

title = {A direct algorithm for type inference in the rank-2 fragment of the second-order λ-calculus},

institution = {},

year = {1993}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 stratification 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 stratification. 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 howto use it to reduce the problem of typability at rank 2 to the problem of acyclic semi-unification. A by-product of our analysis is the publication of a simple solution procedure for acyclic semi-unification.