Confluence Modulo Equivalence in Constraint Handling Rules

Previous results on confluence for Constraint Handling Rules, CHR, are generalized to take into account user-defined state equivalence relations. This allows a much larger class of programs to enjoy the advantages of confluence, which include various optimization techniques and simplified correctness proofs. A new operational semantics for CHR is introduced that reduces notational overhead significantly and allows to consider confluence for programs with extra-logical and incomplete built-in predicates. Proofs of confluence are demonstrated for programs with redundant data representation, e.g., sets-as-lists, for dynamic programming algorithms with pruning as well as a Union-Find program, which are not covered by previous confluence notions for CHR.