Type Classes with Existential Types

We argue that the novel combination of type classes and existential types in a single language yields significant expressive power. We explore this combination in the context of higher-order functional languages with static typing, parametric polymorphism, algebraic data types, and Hindley-Milner type inference. Adding existential types to an existing functional language that already features type classes requires only a minor syntactic extension. We first demonstrate how to provide existential quantification over type classes by extending the syntax of algebraic data type definitions and give examples of possible uses. We then develop a type system and a type inference algorithm for the resulting language. Finally, we present a formal semantics by translation to an implicitly-typed second-order λ-calculus and show that the type system is semantically sound. Our extension has been implemented in the Chalmers Haskell B. system, and all examples from this paper have been developed using this system.