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On the Expressive Power of Multiple Heads in CHR

On the Expressive Power of Multiple Heads in CHR On the Expressive Power of Multiple Heads in CHR CINZIA DI GIUSTO, INRIA Rh ne Alpes o ` MAURIZIO GABBRIELLI, Focus INRIA, Universita di Bologna ` MARIA CHIARA MEO, Universita di Chieti Pescara Constraint Handling Rules (CHR) is a committed-choice declarative language that has been originally designed for writing constraint solvers and is nowadays a general purpose language. CHR programs consist of multiheaded 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 rst part of this article we analyze the Turing completeness of CHR with respect to the underlying 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 multiheaded 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

On the Expressive Power of Multiple Heads in CHR

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2012 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2071368.2071374
Publisher site
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Abstract

On the Expressive Power of Multiple Heads in CHR CINZIA DI GIUSTO, INRIA Rh ne Alpes o ` MAURIZIO GABBRIELLI, Focus INRIA, Universita di Bologna ` MARIA CHIARA MEO, Universita di Chieti Pescara Constraint Handling Rules (CHR) is a committed-choice declarative language that has been originally designed for writing constraint solvers and is nowadays a general purpose language. CHR programs consist of multiheaded 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 rst part of this article we analyze the Turing completeness of CHR with respect to the underlying 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 multiheaded 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

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Jan 1, 2012

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