TitleAn Efficient Nominal Unification Algorithm
Publication TypeConference Paper
Year of Publication2010
AuthorsLevy J, Villaret M
Conference NameProceedings of the 21st International Conference on Rewriting Techniques and Applications, RTA 2010
Conference LocationEdinburgh, Scottland, UK
ISBN Number978-3-939897-18-7
KeywordsHigher-Order Unification, Nominal Unification

Nominal Unification is an extension of first-order unification where terms can contain binders and unification is performed modulo alpha-equivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearly-reduce nominal unification problems to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for first-order unification. Second, we prove that solvability of these reduced problems may be checked in quadratic time. Finally, we point out how using ideas of Brown and Tarjan for unbalanced merging, we could solve these reduced problems more efficiently.