An efficient algorithm for automatic equational unifier generation

In the field of automated deduction, natural language understanding, theorem proving and rewriting theory, unification theory is a very fundamental process. Nowadays researchers have designed several efficient unification algorithms and many automated tools have also been developed. However, there is no efficient practice of an E-unifier generator. In this paper, we propose an efficient method to construct an E-unifier generator. Firstly we implement an algorithm for syntactic unification. Via the bijection between terms and shapes of trees, we can get the correlative set of terms by the transformation of shapes of trees. After these operations, we expand the syntactic unification solution to E-unification. This proposal is able to solve E-unification problems in which case the Diophantine Equations is unable to help. Hence, the method is practical enough for other research works.¹