Continuation semantics for PROLOG with cut

textabstractWe present a denotational continuation semantics for PROLOG with cut. First a uniform language B is studied, which captures the control flow aspects of PROLOG. The denotational semantics for B is proven equivalent to a transition system based operational semantics. The congruence proof relies on the representation of the operational semantics as a chain of approximations and on a convenient induction principle. Finally, we interpret the abstract language B such that we obtain equivalent denotational and operational models for PROLOG itself