In practice, a large part of most Prolog programs is in fact functional, the search facilities of Prolog are only rarely needed. In order to arrive at efficient implementations it is then convenient to make use of the cut operator provided by Prolog. Up to now, this operator has been regarded as an extra-logical control operator that destroys the declarative semantics of Prolog. In this paper we will show that this is not true. If the cut is used to implement functional predicates and if, furthermore, a certain discipline in its use is adhered to, then programs using the cut operator do possess a declarative semantics.