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In the equivalent transformation (ET) model, where computation is regarded as ET using rules that constitute a program, this paper develops a theory for equality-constraint solving which unification does in the theory of logic programming. This paper clarifies the relationship between Constraint Solving Specializations for Equality (CSSEs) and unifiers. The concept of CSSE can be used to solve equality constraint in a clause, and promotes component-based programming. An algorithm for finding CSSEs in the domain including interval variables is constructed by combining simpler ET rules. Termination and correctness of the algorithm is proven.

Constraint Solving Specializations for Equality on an Interval-Variable Domain