Syntactic Type Polymorphism for Recursive Function De nitions

Higher-order programming languages, such as ML, permit a exible programming style by using compile-time type inference together with the concept of type polymorphism, which allows to specify the types of generic functions. In ML, however, recursive functions must always be given a unique (monomorphic) type inside their deenition. Giving polymorphic types to recursive functions is known as the problem of polymorphic recursion which has been shown equivalent to the problem of semi-uniication, known as undecidable. We show that the absence of a decidable speciication to give polymorphic types for recursive deeni-tions lies on the non-adequacy of representing type polymorphism by using type variables as primitive elements. We introduce the notion of syntactic type polymorphism to relate polymorphic types with syntactic information. We formulate a decidable calculus which gives polymorphic types to recursive functions in ML. We present an inference algorithm which we prove the termination and correctness.