Sequence Unification Through Currying

Sequence variables play an interesting role in unification and matching when dealing with terms in an unranked signature. Sequence Unification generalizes Word Unification and seems to be appealing for information extraction in XML documents, program transformation, and rule-based programming. In this work we study a relation between Sequence Unification and another generalization of Word Unification: Context Unification. We introduce a variant of Context Unification, called Left-Hole Context Unification that serves us to reduce Sequence Unification to it: We define a partial currying procedure to translate sequence unification problems into left-hole context unification problems, and prove soundness of the translation. Furthermore, a precise characterization of the shape of the unifiers allows us to easily reduce Left-Hole Context Unification to (the decidable problem of) Word Unification with Regular Constraints, obtaining then a decidability proof for an extension of Sequence Unification.