Operational Semantics and Confluence of Constraint Propagation Rules

Constraint Handling Rules (CHR) allow one to specify and implement both propagation and simpliication for user-deened constraints. Since a propagation rule is applicable again and again, we present in this paper for the rst time an operational semantics for CHR that avoids the termination problem with propagation rules. In previous work AFM96], a suucient and necessary condition for the connuence of terminating simpliication rules was given inspired by results about conditional term rewriting systems. Connuence ensures that the solver will always compute the same result for a given set of constraints independent of which rules are applied. The connuence of propagation rules was an open problem. This paper shows that we can also give a suucient and a necessary condition for connuence of terminating CHR programs with propagation rules based on the more reened operational semantics.