Foundational issues in implementing constraint logic programming systems

Implementations of Constraint Logic Programming (CLP) systems are often incomplete with respect to the theories they are intended to implement. This paper studies two issues that arise in dealing with these incomplete implementations. First, the notion of “satisfiability function” (the analogue of unification) is formally defined, and the question of which such functions are reasonable is studied. Second, techniques are given, based on the notion of satisfiability function, for formally (proof-theoretically) specifying an intended CLP theory or characterizing an existing CLP system. Such proof-theoretic characterizations have applications in proving soundness and completeness results, and proving properties of programs. Notions from substructural logic and the notion of Henkinness of the theory are shown to be important here.