Ad-hoc polymorphism allows the execution of programs to depend on type information. In modern systems, it is useful for implementing generic operations over data structures, such as equality, marshalling, or traversal. In the past, there have been two different forms of ad-hoc polymorphism. The nominal form dispatches on the name of the type argument, whereas the structural form operates by decomposing the structure of types. In languages with user-defined types, these two approaches are very different. Operations defined by the nominal approach are "open" — they must be extended with specialized branches for user-defined types. In contrast, structurally defined operations are closed to extension. They automatically apply to user-defined types by treating them as their underlying definitions. Both approaches have their benefits, so it important to provide both capabilities in a language. Therefore we present an expressive language that supports both forms of ad-hoc polymorphism in a single framework. Among the language's features are the ability to define both "open" and "closed" operations with a single mechanism, the ability to naturally restrict the domain of type-analyzing operations, and new mechanisms for defining higher-order polytypism and manipulating generative type definitions.

Joint work with Geoffrey Washburn at University of Pennsylvania.