Observable Confluence for Constraint Handling Rules

Constraint Handling Rules (CHRs) are a powerful rule based language for specifying constraint solvers. Critical for any rule based language is the notion of confluence, and for terminating CHRs there is a decidable test for confluence. But many CHR programs that in practice are confluent fail this confluence test. The problem is that the states that illustrate non-confluence are not reachable in practice. In this paper we introduce the notion of observable confluence, a weaker notion of confluence which takes into account whether states are observable. We show for an important class of non-confluent programs arising from Haskell type class programs with functional dependencies, that they are observable confluent.