  Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are
two well known ways to enhance the expressivity of Horn clauses. In this paper,
we present a novel combination of these two approaches. We show how to enrich
the syntax and proof theory of HH with the help of a given constraint system,
in such a way that the key property of HH as a logic programming language
(namely, the existence of uniform proofs) is preserved. We also present a
procedure for goal solving, showing its soundness and completeness for
computing answer constraints. As a consequence of this result, we obtain a new
strong completeness theorem for CLP that avoids the need to build disjunctions
of computed answers, as well as a more abstract formulation of a known
completeness theorem for HH.
