On proving left termination of constraint logic programs

The Constraint Logic Programming (CLP) Scheme merges logic programming with constraint solving over predefined domains. In this article, we study proof methods for universal left termination of constraint logic programs. We provide a sound and complete characterization of left termination for ideal CLP languages which generalizesacceptabilityof logic programs. The characterization is then refined to the notion ofpartial acceptability, which is well suited for automatic modular inference. We describe a theoretical framework for automation of the approach, which is implemented. For nonideal CLP languages and without any assumption on their incomplete constraint solvers, even the most basic sound termination criterion from logic programming does not lift. We focus on a specific system, namely CLP(R), by proposing some additional conditions that make (partial) acceptability sound.