Inferring Program Specifications in Polynomial-Time

We consider the problem of automatically inferring properties of programs. Our approach is to explore the application of familiar type inference principles to a \type system" suuciently expressive that the typing problem is eeectively the checking of program speciications. We use familiar syntax-directed type inference rules to give a polynomial-time procedure for inferring type theorems in this rich type system. We discuss examples of simple functional programs and the speciication information this procedure automatically infers. The enriched notion of type allows the deenition of any recursively enumerable set as a type, and includes argument-dependent output types for functions. The inference procedure is capable for example of automatically inferring that an insertion sort program always returns a sorted permutation of its input.