Lazy Unification with Simplification

Unification in the presence of an equational theory is an important problem in theorem-proving and in the integration of functional and logic programming languages. This paper presents an improvement of the proposed lazy unification methods by incorporating simplification into the unification process. Since simplification is a deterministic computation process, more efficient unification algorithms can be achieved. Moreover, simplification reduces the search space so that in some cases infinite search spaces are reduced to finite ones. We show soundness and completeness of our method for equational theories represented by ground confluent and terminating rewrite systems which is a reasonable class w.r.t.\ functional logic programming