In this thesis we have developed a general formulation of overloading based on the use of qualified types. Applications of qualified types can be described by choosing an appropriate system of predicates and we have illustrated this with particular examples including Haskell type classes, explicit subtyping and extensible records. We have shown how these ideas can be extended to construct a system that combines ML-style polymorphism and overloading in an implicitly typed programming language. Using the concept of evidence we have extended this work to describe the semantics of overloading in this language, establishing sufficient conditions to guarantee that the meaning of a given term is well-defined. Finally, we have described techniques that can be used to obtain efficient concrete implementations of systems based on this framework.

From a theoretical perspective, some of the main contributions of this thesis are:

• The formulation of a general purpose system that can be used to describe a number of different applications of overloading.

• The extension of standard results, for example the existence of principal types, to the type system of OML.

• A new approach to the proof of coherence, based on the use of conversions.

From a practical perspective, we mention:

• The implementation of overloading using the template-based approach, and the closely related implementation of type class overloading in Gofer.

• A new implementation for extensible records, based on the use of evidence.

• The use of information about satisfiability of predicate sets to obtain more informative inferred types.