Polytypic unification

Paper, abstract and implementation.
See also JFP 8 (5), September 1998.


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.


The core of the unification algorithm is written in Haskell (using the interpreter Hugs) and the polytypic part is written in the Haskell extension PolyP. The full code is available as .tar.gz and in unpacked form.
Last modified: Thu Feb 18 17:22:24 MET 1999 by
Patrik Jansson / NOpatrikjSP@AMchalmers.se