EFFICIENT INFERENCE OF PARTIAL TYPES

Partial types for the lambda-calculus were introduced by Thatte in 198 8 as a means of typing objects that are not typable with simple types, such as heterogeneous lists and persistent data. In that paper he sho wed that type inference for partial types was semidecidable. Decidabil ity remained open until quite recently, when O'Keefe and Wand gave an exponential time algorithm for type inference. In this paper we give a n O(n3) algorithm. Our algorithm constructs a certain finite automatio n that represents a canonical solution to a given set of type constrai nts. Moreover, the construction works equally well for recursive types ; this solves an open problem stated by O'Keefe and Wand (in ''Proceed ings, European Symposium on Programming,'' Lect. Notes in Comput. Sci. , Vol. 582, pp. 408-417, Springer-Verlag, New York/Berlin, 1992). (C) 1994 Academic Press, Inc.