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Confluence and Commutation for Nominal Rewriting Systems with Atom-Variables

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Book cover Logic-Based Program Synthesis and Transformation (LOPSTR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12561))

Abstract

Nominal rewriting was introduced as an extension of first-order term rewriting by a binding mechanism based on the nominal approach. Recently, a new format of nominal rewriting has been introduced where rewrite rules are defined with atom-variables rather than atoms. In this paper, we investigate the difference between the new format and the original nominal rewriting, and prove confluence and commutation for some classes of rewriting systems whose rewrite rules have no proper overlaps which are computed using nominal unification with atom-variables. The properties we prove are expected to be used in a form of program transformation that is realised as an equivalence transformation of rewriting systems.

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Notes

  1. 1.

    In usual papers on rewriting systems with binders such as \(\lambda \)-calculus, meta-variables are used to specify rewrite rules instead of (term-)variables and atom-variables used here. The reason we include those variables in the language to describe rewrite rules is that the set of rewrite rules should keep finite, which is essential when considering some kind of unification procedure to compute overlaps, critical pairs, etc.

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Acknowledgements

We are grateful to the anonymous referees for valuable comments. The first author thanks Makoto Hamana for useful discussions. This work was partly supported by JSPS KAKENHI Grant Numbers JP17K00005, JP18K11158, JP19K11891 and JP20H04164.

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Authors and Affiliations

  1. RIEC, Tohoku University, Sendai, Japan

    Kentaro Kikuchi

  2. Faculty of Engineering, Niigata University, Niigata, Japan

    Takahito Aoto

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  1. Kentaro Kikuchi
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  2. Takahito Aoto
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Correspondence to Kentaro Kikuchi .

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  1. King’s College London, London, UK

    Maribel Fernández

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Kikuchi, K., Aoto, T. (2021). Confluence and Commutation for Nominal Rewriting Systems with Atom-Variables. In: Fernández, M. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2020. Lecture Notes in Computer Science(), vol 12561. Springer, Cham. https://doi.org/10.1007/978-3-030-68446-4_3

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  • DOI: https://doi.org/10.1007/978-3-030-68446-4_3

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  • Online ISBN: 978-3-030-68446-4

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