Structure sharing for quantified terms: Fundamentals

Structure sharing is used in symbolic computation to share a common top level between terms with different lower levels. It is widely used in the implementation of Prolog interpreters and is of interest for the implementation of automatic theorem provers, interactive proof editors and verification systems. Previously, structure sharing has been applied only to free-variable terms. In this paper we extend the structure sharing technique to quantified terms. We give an efficient unification algorithm of our structure sharing representation of quantified terms, and we prove the correctness of the algorithm