Inferring program specifications in polynomial-time

Abstract

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∝ sufficiently expressive that the typing problem is effectively the checking of program specifications. We use familiar syntax-directed type inference rules to give a polynomialtime procedure for inferring type theorems in this rich type system. We discuss examples of simple functional programs and the specification information this procedure automatically infers. The enriched notion of type allows the definition 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.