Subtyping recursion and parametric polymorphism in kernel fun

We study subtype checking for recursive types in system kernel Fun, a typed λ-calculus with subtyping and bounded second-order polymorphism. Along the lines of [ACM Transactions on Programming Languages and Systems, 15(4), (1993) 575], we define a subtype relation over kernel Fun recursive types, and prove it to be transitive. We then show that the natural extension of the algorithm introduced in [loc.cit] to compare first-order recursive types yields a non complete algorithm. Finally, we prove the completeness and correctness of a different algorithm, which lends itself to efficient implementations.