A Comparison of Constraint Handling Rules with Equivalent Transformation Rules

We have proposed a novel computation framework called Equivalent Transformation (ET). The ET framework is a rewriting system in which computation is executed by rewriting rules. Rewriting rules of the ET framework are called Equivalent Transformation Rules (ETRs). The theory of ET guarantees the correctness of the computation by ETRs. Multi-head ETRs which have multiple atoms in their head part are valid ETRs. Constraint Handling Rules (CHR) are declarative language extension designed for writing user-defined constraints. CHR allows to use multi-head guarded rules for its computation. This paper compares the rewriting rules of ET and CHR, especially multi-head rules. We show that all CHR rules can be simply transformed into correct ETRs preserving their logical meanings. Examples of the correct ETRs which can not be represented as CHR rules are also given. Therefore CHR rules can be regarded as proper subclass of ETRs.