Subtyping Recursive Types in Kernel Fun

The problem of defining and checking a subtype relation between recursive types was studied in [3] for a first order type system, but for second order systems, which combine subtyping and parametric polymorphism, only negative results are known [17]. This paper studies the problem of subtype checking for recursive types in system kernel Fun, a typed -calculus with subtyping and bounded second order polymorphism. Along the lines of [3], 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 [3] 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.