I'd like to write an obviously correct implementation of a unifier, a program that when given two terms, finds a substitution that makes the two terms equal. The phrase "obviously correct" is meant to imply that the clarity of the code trumps efficiency. As near as I can tell, high performance unifiers are full of side-effects, and achieving the same performance without side-effects in Haskell is difficult or impossible. In contrast, it is easy to write obviously correct Hasklell implementations of unifiers for freely generated term algebras. One can use Lawrence Paulson's code in ML for the Working Programmer as a template or follow Martelli and Montanari's simple set of rules. My problem is one of my operators is multiplication, which is associative and commutative. These two properties make unification much more difficult. Mark Stickel described a complete unification algorithm for this problem, but the task of translating his description into an obviously correct Haskell program appears to be difficult. For example, the algorithm requires the generation of the basis of solutions to linear homogeneous diophantine equations. I haven't located an algorithm for this part yet. If you have experience implemented equational unification in Haskell, please share it. John