. We are investigating the use of a class of logical formulas to define constraint theories and implement constraint solvers at the same time. The representation of constraint evaluation in a declarative formalism greatly facilitates the prototyping, extension, specialization and combination of constraint solvers. In our approach, constraint evaluation is specified using multiheaded guarded clauses called constraint handling rules (CHRs). CHRs define determinate conditional rewrite systems that express how conjunctions of constraints propagate and simplify. In this paper we concentrate on CHRs as an extension for constraint logic programming languages. Into such languages, the CHRs can be tightly integrated. They can make use of any hard-wired solvers already built into the host language. Program clauses can be used to specify the non-deterministic behavior of constraints, i.e. to introduce search by constraints. In this way our approach merges the advantages of constraints (eager simp...

. A fundamental question in programming language semantics is when two programs should be considered equivalent. In this paper we introduce a notion of operational equivalence for CHR programs and user-defined constraints. Constraint Handling Rules (CHR) is a highlevel language for writing constraint solvers either from scratch or by modifying existing solvers. We give a decidable, sufficient and necessary syntactic condition for operational equivalence of terminating and confluent CHR programs. For practical reasons, we also investigate a notion of operational equivalence for user-defined constraints that are defined in different programs. We give a sufficient syntactic condition for constraints defined in terminating and confluent CHR programs. For a subclass of programs which have only one user-defined constraint in common, we are able to give a sufficient and necessary syntactic condition. 1 Introduction Constraint Handling Rules (CHR) [Fru98] is essentially a committed-choice lan...