Correctness of unification without occur check in Prolog

For efficiency reasons, most Prolog implementations do not include an occur check in their unification algorithms and thus do not conform to the semantic model of first-order logic. We present a simple test which guarantees that unification without occur check is sound in programs satisfying the conditions of the test. We designate each argument position of every predicate as either an input or an output position and then describe a sufficient condition in terms of this designation for unification without occur check to be sound. Unification with occur check can be performed in places in the program where this condition is not satisfied. Two algorithms for implementing this test are described and compared