On Con uence of Constraint Handling

We introduce the notion of connuence for Constraint Handling Rules (CHR), a powerful language for writing constraint solvers. With CHR one simpliies and solves constraints by applying rules. Connuence guarantees that a CHR program will always compute the same result for a given set of constraints independent of which rules are applied. We give a decidable, suucient and necessary syntactic condition for connuence. Connuence turns out to be an essential syntactical property of CHR programs for two reasons. First, connuence implies correctness (as will be shown in this paper). In a correct CHR program, application of CHR rules preserves logical equivalence of the simpliied constraints. Secondly, even when the program is already correct, connuence is highly desirable. Otherwise, given some constraints , one computation may detect their inconsistency while another one may just simplify them into a still complex constraint. As a side-eeect, the paper also gives soundness and completeness results for CHR programs. Due to their special nature, and in particular correctness, these theorems are stronger than what holds for the related families of (concurrent) constraint programming languages.