Promoting Constraints to First-Class Status

Abstract

This paper proposes to promote constraints to first-class status. In contrast to constraint propagation, which performs inference on values of variables, first-class constraints allow reasoning about the constraints themselves. This lets the programmer access the current state of a constraint and control a constraint’s behavior directly, thus making powerful new programming and inference techniques possible, as the combination of constraint propagation and rewriting constraints à la term rewriting. First-class constraints allow for true meta constraint programming. Promising applications in the field of combinatorial optimization include early unsatisfiability detection, constraint reformulation to improve propagation, garbage collection of redundant but not yet entailed constraints, and finding minimal inconsistent subsets of a given set of constraints for debugging immediately failing constraint programs.

We demonstrate the above-mentioned applications by means of examples. The experiments were done with Mozart Oz but can be easily ported to other constraint solvers.