The Haskell typechecker contains a nice example of a unifier for freely generated terms. My focus is on equational unification, but thanks anyway. John On Sun, Jul 6, 2008 at 10:38 PM, Don Stewart wrote:

ramsdell0:

...

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.

"Typing Haskell in Haskell" lives here,

http://hackage.haskell.org/cgi-bin/hackage-scripts/package/thih

"a Haskell program that implements a Haskell typechecker, thus providing a mathematically rigorous specification in a notation that is familiar to Haskell users. We expect this program to fill a serious gap in current descriptions of Haskell, both as a starting point for discussions about existing features of the type system, and as a platform from which to explore new proposals"

Might be useful as a starting point.

-- Don

Are you aware of "Term Rewriting and all That"? It describes how to do associative commutative unification; whether it satisfies your 'obviously correct' criterion I don't know.

Oh yes, I know about term rewriting. If your equations can be expressed as a set of confluent rewrite rules, one can use the Martelli and Montanari's formalization of unification to come up with an obviously correct equational unifier. Alas, that simple trick doesn't work for AC unification. Have you heard of Maude? I hear the next version will have support for AC unification. If I stay with Haskell, I'd have to use their support via interprocess communication. Yuck. http://maude.cs.uiuc.edu/ John

I think Edsko was more specifically referring to the book "Term Rewriting and all That" by Baader and Nipkow.

Thanks for pointing this out--I was confused. I notice the book has a chapter on equational unification that includes a section on AC unification. This book looks like a winner. Thank you. John

CIMe[1] might be useful to solve the generated diophantine equations.

It also has AC unification, and it probably wouldn't be all that hard to translate our code into OCaml. I think CiME isn't supported anymore. Still it's worth considering. It's quite large. The source distribution compiled effortlessly on Ubuntu. That's about all I know now.

I don't know what you are planning to do, but perhaps you'd be better served by Maude than by Haskell.

Switching to Maude is an option we're considering. John