Subtyping recursive types in kernel Fun

Abstract

The problem of defining and checking a subtype relation between recursive types was studied in Armadio and Cardelli (1993) for a first order type system, but for second order systems, which combine subtyping and parametric polymorphism, only negative results are known. This paper studies the problem of subtype checking for recursive types in system kernel Fun, a typed /spl lambda/-calculus with subtyping and bounded second order polymorphism. Along the lines of Armadio and Cardelli (1993), we study the definition of a subtype relation over kernel Fun recursive types, and then we present a subtyping algorithm which is sound and complete with respect to this relation. We show that the natural extension of the techniques introduced in Armadio and Cardelli (1993) to compare first order recursive types gives a non complete algorithm. We prove the completeness and correctness of a different algorithm, which also admits an efficient implementation.