On Completion of Constraint Handling Rules

Constraint Handling Rules (CHR) is a high-level language for writing constraint solvers either from scratch or by modifying existing solvers. An important property of any constraint solver is confluence: The result of a computation should be independent from the order in which constraints arrive and in which rules are applied. In previous work [1], a sufficient and necessary condition for the confluence of terminating CHR programs was given by adapting and extending results about conditional term rewriting systems. In this paper we investigate so-called completion methods that make a non-confluent CHR program confluent by adding new rules. As it turns out, completion can also exhibit inconsistency of a CHR program. Moreover, as shown in this paper, completion can be used to define new constraints in terms of already existing constraints and to derive constraint solvers for them