Heterogeneous Constraint Solving

Most CLP languages designed in the past few years feature at least some combination of constraint solving capabilities. These combinations can take m ultiple forms since they achieve either the mixing of diierent domains or the use of diierent algorithms over the same domain. These solvers are also very diierent in nature. Some of them perform complete constraint solving while others are based on propagation methods. This paper is an attempt to design a uniied framework describing the cooperation of constraint solving methods. Most techniques used in constraint-based systems are shown to be implementations of operators called constraint narrowing operators. A generalized notion of arc-consistency, called weak arc-consistency is proposed and is used to model heterogeneous constraint solving. We p r o vide conditions on the constraint solving algorithms which guarantee termination, correctness and connuence of the resulting combined solver. This framework is shown to be general enough to describe the operational semantics of the basic constraint solving mechanisms in a number of current CLP systems.