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Automated Proofs of Unique Normal Forms w.r.t. Conversion for Term Rewriting Systems

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Frontiers of Combining Systems (FroCoS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11715))

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Abstract

The notion of normal forms is ubiquitous in various equivalent transformations. Confluence (CR), one of the central properties of term rewriting systems (TRSs), concerns uniqueness of normal forms. Yet another such property, which is weaker than confluence, is the property of unique normal forms w.r.t. conversion (UNC). Recently, automated confluence proof of TRSs has caught attentions; some powerful confluence tools integrating multiple methods for (dis)proving the CR property of TRSs have been developed. In contrast, there have been little efforts on (dis)proving the UNC property automatically yet. In this paper, we report on a UNC prover combining several methods for (dis)proving the UNC property. We present an equivalent transformation of TRSs preserving UNC, as well as some new criteria for (dis)proving UNC.

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Notes

  1. 1.

    The uniqueness of normal forms w.r.t. conversion is also often abbreviated as UN in the literature; here, we prefer UNC to distinguish it from a similar but different notion of unique normal forms w.r.t. reduction (UNR), following the convention employed in CoCo (Confluence Competition).

  2. 2.

    http://project-coco.uibk.ac.at/.

  3. 3.

    Cops can be accessed from http://cops.uibk.ac.at/, which consists of 1137 problems at the time of experiment.

  4. 4.

    This was obtained by a query ‘trs !confluent !terminating’ in Cops at the time of experiment.

  5. 5.

    The recent version of CSI had been extended with some other techniques.

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Acknowledgements

Thanks are due to the anonymous reviewers of the previous versions of the paper. This work is partially supported by JSPS KAKENHI No. 18K11158.

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Authors and Affiliations

  1. School of Natural Sciences, Niigata University, Niigata, Japan

    Takahito Aoto

  2. RIEC, Tohoku University, Sendai, Japan

    Yoshihito Toyama

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  1. Takahito Aoto
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  2. Yoshihito Toyama
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Correspondence to Takahito Aoto .

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  1. CNRS, University of Toulouse, Toulouse, France

    Andreas Herzig

  2. Middlesex University London, London, UK

    Andrei Popescu

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Aoto, T., Toyama, Y. (2019). Automated Proofs of Unique Normal Forms w.r.t. Conversion for Term Rewriting Systems. In: Herzig, A., Popescu, A. (eds) Frontiers of Combining Systems. FroCoS 2019. Lecture Notes in Computer Science(), vol 11715. Springer, Cham. https://doi.org/10.1007/978-3-030-29007-8_19

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  • DOI: https://doi.org/10.1007/978-3-030-29007-8_19

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