Bounded Higher-order Unification using Regular Terms

We present a procedure for the bounded unication of higher-order terms [24]. The procedure extends G. P. Huet’s pre-unication procedure [11] with rules for the generation and folding of regular terms. The concise form of the procedure allows the reuse of the pre-unication correctness proof. Furthermore, the regular terms can be restricted in order to get a decidable uniability problem. Finally, the procedure avoids re-computation of terms in a non-deterministic search which leads to a better performance in practice when compared to other bounded unication algorithms.