A Universal Unification Algorithm Based on Unification-Driven Leftmost Outermost Narrowing

  Heinz FabenderHeiko Vogler

Abstract:

  We formalize a universal unification algorithm for the class of equational theories which is induced by the class of canonical, totally-defined, not strictly subunifiable term rewriting sytems (for short ctn- trs ). For a ctn-trs and for two terms and , the algorithm computes a ground-complete set of ()-unifiers of and , where is the set of rewrite rules of viewed as equations and is the set of constructor symbols. The algorithm is based on the unification-driven leftmost outermost narrowing relation (for short: ulo narrowing relation ďwhich is introduced in this paper. The ulo narrowing relation interleaves leftmost outermost narrowing steps with decomposition steps taken from the usual unification of terms. In its turn, every decomposition step involves a consistency check on constructor symbols combined with a particular form of the occur check. Since decomposition can be stopped earlier than in other univeral unification algorithms for ctn-trs's. We give a proof that our algorithm really is a universal unification algorithm.

 Gyenizse Pal 1996. Szeptember 4. Szerda 13:07:28 MET DST