  Completeness of a logic program means that the program produces all the
answers required by its specification. The cut is an important construct of
programming language Prolog. It prunes part of the search space, this may
result in a loss of completeness. This paper proposes a way of proving
completeness of programs with the cut. The semantics of the cut is formalized
by describing how SLD-trees are pruned. A sufficient condition for completeness
is presented, proved sound, and illustrated by examples.
