Type inference in context

Authors:
Adam Gundry;Conor McBride;James McKinna
Affiliations:
University of Strathclyde, Glasgow, United Kingdom;University of Strathclyde, Glasgow, United Kingdom;Radboud University, Nijmegen, Netherlands
Venue:
Proceedings of the third ACM SIGPLAN workshop on Mathematically structured functional programming
Year:
2010

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Abstract

We consider the problems of first-order unification and type inference from a general perspective on problem-solving, namely that of information increase in the problem context. This leads to a powerful technique for implementing type inference algorithms. We describe a unification algorithm and illustrate the technique for the familiar Hindley-Milner type system, but it can be applied to more advanced type systems. The algorithms depend on well-founded contexts: type variable bindings and type-schemes for terms may depend only on earlier bindings. We ensure that unification yields a most general unifier, and that type inference yields principal types, by advancing definitions earlier in the context only when necessary.