Equivalent Transformation for Member Constraints on the Term Domain

Abstract

While many conventional theories are based on the logic paradigm, our theory is based on the equivalent transformation (ET) paradigm, where computation is regarded as "equivalent transformation of declarative descriptions." In the ET paradigm, each domain is characterized by a mathematical structure called a "specialization system." The term domain, consisting of usual atoms and substitutions; is also formalized by a specialization system. The ET paradigm makes it possible to utilize not only the usual unfolding rule but also other equivalent transformation rules, which may often make execution more efficient without much additional cost. In this paper we develop a theory of two new equivalent transformation rules for member constraints in the term domain : the candidate elimination rule (CE rule) and the common pattern specialization rule (CPS rule). While the CE rule reduces the length of the candidate list of a member constraint, the CPS rule specializes the clause containing the given member constraint by unifying a common pattern of all the candidates with the first object of the member constraint. Natural language understanding examples show that, when used in preference to unfolding, these rules suppress clause splitting in the course of equivalent transformation, which makes computation more efficient.