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International Symposium on Logic-Based Program Synthesis and Transformation

LOPSTR 2014: Logic-Based Program Synthesis and Transformation pp 41–58Cite as

Confluence Modulo Equivalence in Constraint Handling Rules

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8981))

Abstract

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 significantly reduces notational overhead 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.

M.H. Kirkeby—The second author’s contribution has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no 318337, ENTRA - Whole-Systems Energy Transparency.

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Notes

  1. 1.

    It may be the case that \(\pi '_1\) was produced and pruned at an earlier stage, so the propagation history prevents the creation of \(\pi '_1\) anew. A detailed argument can show, that in this case, there will be another constraints \(\pi ''_1\) in the store similar to \(\pi '_1\) but with a \(\ge \) probability, and \(\pi ''_1\) can be used for pruning \(\pi '_2\) and obtain the desired result in that way.

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Authors and Affiliations

  1. Research group PLIS: Programming, Logic and Intelligent Systems Department of Communication, Business and Information Technologies, Roskilde University, Roskilde, Denmark

    Henning Christiansen & Maja H. Kirkeby

Authors
  1. Henning Christiansen
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  2. Maja H. Kirkeby
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Correspondence to Henning Christiansen .

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Editors and Affiliations

  1. IASI-CNR, Rome, Italy

    Maurizio Proietti

  2. Nagoya Institute of Technology, Nagoya, Japan

    Hirohisa Seki

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Christiansen, H., Kirkeby, M.H. (2015). Confluence Modulo Equivalence in Constraint Handling Rules. In: Proietti, M., Seki, H. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2014. Lecture Notes in Computer Science(), vol 8981. Springer, Cham. https://doi.org/10.1007/978-3-319-17822-6_3

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  • DOI: https://doi.org/10.1007/978-3-319-17822-6_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17821-9

  • Online ISBN: 978-3-319-17822-6

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