A Confluence Checker for Constraint Handling Rules with Persistent Constraints

In the abstract operational semantics of Constraint Handling Rules (CHR), propagation rules, i.e. rules that only add information, can be applied again and again. This trivial non-termination is typically avoided by a propagation history. A more declarative approach are persistent constraints. Constraints that are introduced by propagation rules are made persistent and cannot be removed. Now a propagation rule is only applied, if its derived constraints are not already persistent. The operational semantics with persistent constraints ω! differs substantially from other operational semantics, hence the standard confluence test cannot be applied. In this paper, a confluence test for ω! is presented. Since ω! breaks monotonicity of CHR, a weaker property is established that is shown to suffice for a decidable confluence criterion for terminating ω! programs. The confluence test is implemented using a source to source transformation.