Functional logic overloading is a novel approach to userdefined overloading that extends Haskell’s concept of type classes in significant ways. Whereas type classes are conceptually predicates on types in standard Haskell, they are type functions in our approach. Thus, we can base type inference on the evaluation of functional logic programs. Functional logic programming provides a solid theoretical foundation for type functions and, at the same time, allows for programmable overloading resolution strategies by choosing different evaluation strategies for functional logic programs. Type inference with type functions is an instance of type inference with constrained types, where the underlying constraint system is defined by a functional logic program. We have designed a variant of Haskell which supports our approach to overloading, and implemented a prototype frontend for the language.

The objective of this thesis is to demonstrate the feasibility of performing static analysis, specifically type checking, in a particularly modular way. We use a term space of fixpoints of sums of functors so that, by writing individual type checkers for each portion of the entire language, we can then combine those algebras into an algebra that functions over the entire target language. The overall computational style employed uses a sequenced paramorphism to reduce the terms to the value space of types. As a proof of concept, this thesis presents a nominal typechecker in Haskell for the language Rosetta. It relies heavily on InterpreterLib, a Haskell library for designing interpreters in exactly the style described.