Efficient inference of partial types

Partial types for the λ-calculus were introduced by Thatte (1988) as a means of typing objects that are not typable with simple types, such as heterogeneous lists and persistent data. He showed that type inference for partial types was semidecidable. Decidability remained open until O´Keefe and Wand gave an exponential time algorithm for type inference. The authors give an O(n³) algorithm. The 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