A Computationally Adequate Model for Overloading via Domain-Valued Functors

We give a denotational semantics to a calculus with overloading and subtyping. In , the interaction between overloading and subtyping causes self application, and non-normalizing terms exist for each type. Moreover, the semantics of a type depends not on that type alone, but also on in nitely many others. Thus, we need to consider in nitely many domains which are related by an in nite number of mutually recursive equations. We solve this by considering a functor category from the poset of types modulo equivalence to a category in which each type is interpreted. We introduce a categorical constructor corresponding to overloading, and formalize the equations as a single equation in the functor category. A semantics of is then expressed in terms of the minimal solution of this equation. We prove the adequacy theorem for following the construction in (Pitts 94) and use it to derive some syntactic properties.