In previous work, we presented rules for defining overloaded functions that
ensure type safety under symmetric multiple dispatch in an object-oriented
language with multiple inheritance, and we showed how to check these rules
without requiring the entire type hierarchy to be known, thus supporting
modularity and extensibility. In this work, we extend these rules to a
language that supports parametric polymorphism on both classes and functions.

In a multiple-inheritance language in which any type may be extended by types
in other modules, some overloaded functions that might seem valid are
correctly rejected by our rules. We explain how these functions can be
permitted in a language that additionally supports an exclusion relation among
types, allowing programmers to declare "nominal exclusions" and also
implicitly imposing exclusion among different instances of each polymorphic
type. We give rules for computing the exclusion relation, deriving many type
exclusions from declared and implicit ones.

We also show how to check our rules for ensuring the safety of overloaded
functions. In particular, we reduce the problem of handling parametric
polymorphism to one of determining subtyping relationships among universal and
existential types. Our system has been implemented as part of the open-source
Fortress compiler.