Journal of Functional Programming



FUNCTIONAL PEARL

Polytypic unification


PATRIK JANSSON a1 and JOHAN JEURING a2
a1 Computing Science, Chalmers University of Technology, S-412 96 Göteborg, Sweden
a2 Department of Computer Science, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands

Abstract

Unification, or two-way pattern matching, is the process of solving an equation involving two first-order terms with variables. Unification is used in type inference in many programming languages and in the execution of logic programs. This means that unification algorithms have to be written over and over again for different term types. Many other functions also make sense for a large class of datatypes; examples are pretty printers, equality checks, maps etc. They can be defined by induction on the structure of user-defined datatypes. Implementations of these functions for different datatypes are closely related to the structure of the datatypes. We call such functions polytypic. This paper describes a unification algorithm parametrised on the type of the terms, and shows how to use polytypism to obtain a unification algorithm that works for all regular term types.