Kinded Parameteric Overloading

The combination of overloading and parametric polymorphism has received some attention in the functional programming community. The main approach has been that of Haskell type classes. An approach to the type-checking and semantics of parametric overloading is presented, based on using structured kinds to constrain type variables. Open kinds constrain type variables by sets of operations and are useful for the incremental development of reusable procedures (in a similar manner to Haskell classes), while closed kinds constrain type variables by sets of types (essentially providing a type-safe form of dynamic typing). The type system includes a rule for “closing up” an open kind to a closed kind. Applications of these faciities include local overloading, the combination of parametric overloading with a Standard ML-like module system, and an optimization which replaces call-site closure construction with dynamic dispatching based on explicit type tags. A set difference operation for kinds allows the unambiguous typing of overlapping overload instances. The system of kinds is provided in some detail. A type system and type inference algorithm are sketched. An operational semantics is provided and used to verify semantic soundness. This operational semantics is also used to verify the correctness of the removal of call-site closure construction.