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.

We address in this paper the question of how to verify program properties in modern functional logic languages, where it is allowed the presence of non-deterministic functions with call-time choice semantics. The main problem to face is that for such kind of programs equational reasoning is not valid. We develop some logical conceptual tools providing sound reasoning mechanisms for these programs, in particular for proving properties valid in the initial model of a program. We show how CRWL, a well known logical framework for functional logic programming, can be easily mapped into logic programming, and we use this mapping as a starting point of our work. We explore then how to prove properties of the resulting logic programming translation by means of different existing interactive proof assistants, and afterwards we give some proposals trying to overcome the limitations of the approach, specially with respect to its theoretical strength.

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