Type processing by constraint reasoning

Herbrand constraint solving or unification has long been understood as an efficient mechanism for type checking and inference for programs using Hindley/Milner types. If we step back from the particular solving mechanisms used for Hindley/Milner types, and understand type operations in terms of constraints we not only give a basis for handling Hindley/Milner extensions, but also gain insight into type reasoning even on pure Hindley/Milner types, particularly for type errors. In this paper we consider typing problems as constraint problems and show which constraint algorithms are required to support various typing questions. We use a light weight constraint reasoning formalism, Constraint Handling Rules, to generate suitable algorithms for many popular extensions to Hindley/Milner types. The algorithms we discuss are all implemented as part of the freely available Chameleon system.