Uniied Cardelli-mitchell's Polymorphic Calculus with Subtyping (preliminary Report) ?

We join Cardelli's and Mitchell's approaches to polymorphic subtyping by introducing a new uniied calculus G that subsumes both Cardelli-inspired systems with rigid subtyping on the one hand, and the more liberal Mitchell's containment calculus F Mit88] on the other. Up until now both approaches were considered incompatible, since F-provable containments between functional and universal types are unprovable in F and F-bounded, but F lacks the proper treatment of bounded quantiication. We give a logical motivation for the new subtyping system G by interpreting it in the second-order intuitionistic propositional logic. As our system turns out to be stronger (i.e., types more terms) than F , F , F-bounded, we prove the strong normalization theorem by applying the recent evaluation semantics techniques due to McAllester, Ku chan, and Otth MKO95].