Regular Patterns in Second-Order Unification
Résumé
The second-order unification problem is undecidable. While unification procedures, like Huet's pre-unification, terminate with success on unifiable problems, they might not terminate on non-unifiable ones. There are several results which decides the unification problem for monadic signatures. These results are based on the regular structure of the solutions of problems over monadic signatures. In this paper we describe an enhancement to Huet's pre-unification procedure for arbitrary second-order signatures which, in some cases, terminates on problem on which the original pre-unification procedure fails to terminate. This is obtained by identifying regular patterns in non-regular partial solutions.