We give a denotational semantics to a calculus λ[otimes ]
with overloading and subtyping. In λ[otimes ],
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 infinitely many others. Thus, we need to
consider infinitely
many domains, which are related by an infinite 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 λ[otimes ] is then
expressed in terms of the minimal solution of
this equation. We prove the adequacy theorem for λ[otimes ]
following the construction in
Pitts (1994) and use it to derive some syntactic properties.