Efficient inference of partial types

Partial types for the λ-calculus were introduced by >Thatte in 1988 as a means of typing objects that are not typable with simple types, such as heterogeneous lists and persistent data. In that paper he showed that type inference for partial types was semidecidable. Decidability remained open until quite recently, when O'Keefe and Wand gave an exponential time algorithm for type inference. In this paper we given an O(n3) algorithm. Our algorithm constructs a certain finite automaton that represents a canonical solution to a given set of type constraints. Moreover, the construction works equally well for recursive types; this sovles an open problem stated by O'Keefe and Wand (in “Proceedings, European Symposium on Programming,” Lect. Notes in Comput. Sci., Vol. 582, pp. 408–417, Springer-Verlag, New York/Berlin, 1992)