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On the expressive power of multiple heads in CHR

By Cinzia Di Giusto and Maurizio Gabbrielli

Abstract

Constraint Handling Rules (CHR) is a committed-choice declarative language which has been originally designed for writing constraint solvers and which is nowadays a general purpose language. CHR programs consist of multi-headed guarded rules which allow to rewrite constraints into simpler ones until a solved form is reached. Many empirical evidences suggest that multiple heads augment the expressive power of the language, however no formal result in this direction has been proved, so far. In the first part of this paper we analyze the Turing completeness of CHR with respect to the underneath constraint theory. We prove that if the constraint theory is powerful enough then restricting to single head rules does not affect the Turing completeness of the language. On the other hand, differently from the case of the multi-headed language, the single head CHR language is not Turing powerful when the underlying signature (for the constraint theory) does not contain function symbols. In the second part we prove that, no matter which constraint theory is considered, under some reasonable assumptions it is not possible to encode the CHR language (with multi-headed rules) into a single headed language while preserving the semantics of the programs. We also show that

Topics: Categories and Subject Descriptors, D.3.2 [Programming Languages, Language Classifications—Constraint and logic languages, D.3.3 [Programming Languages, Language Constructs and Features—Concurrent programming structures, F.1.1 [Computation by Abstract Devices, Models of Computation—Relations between models, F.1.2 [Computation by Abstract Devices, Models of Computation—Parallelism and concurrency, F.3.3 [Logics and Meanings of Programs, Studies of Program Constructs—Control primitives General Terms, Languages, Theory Additional Key Words and Phrases, CHR, Language embedding, Expressiveness, Multiset Rewriting Systems
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