Applying Interval Arithmetic to Real, Integer, and Boolean Constraints

We present in this paper a uni ed processing for Real, Integer and Boolean Constraints based on a general narrowing algorithm which applies to any n-ary relation on <. The basic idea is to de ne, for every such relation , a narrowing function ! based on the approximation of by a Cartesian product of intervals whose bounds are oating point numbers. We then focus on non-convex relations and establish several properties. The more important of these properties is applied to justify the computation of usual relations de ned in terms of intersections of simpler relations. We extend the scope of the narrowing algorithm used in the language BNR-Prolog to integer and disequality constraints, to Boolean constraints and to relations mixing numerical and Boolean values. As a result, we propose a new Constraint Logic Programming language called CLP(BNR), where BNR stands for Booleans, Naturals and Reals. In this language, constraints are expressed in a unique structure, allowing the mixing of real numbers, integers and Booleans. We end with the presentation of several examples showing the advantages of such an approach from the point of view of the expressiveness, and give some preliminary computational results from a prototype.