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International Conference on Rewriting Techniques and Applications

RTA 2008: Rewriting Techniques and Applications pp 172–186Cite as

On Normalisation of Infinitary Combinatory Reduction Systems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5117))

Abstract

For fully-extended, orthogonal infinitary Combinatory Reduction Systems, we prove that terms with perpetual reductions starting from them do not have (head) normal forms. Using this, we show that

  1. 1

    needed reduction strategies are normalising for fully-extended, orthogonal infinitary Combinatory Reduction Systems, and that

  2. 1

    weak and strong normalisation coincide for such systems as a whole and, in case reductions are non-erasing, also for terms.

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Authors and Affiliations

  1. Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

    Jeroen Ketema

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  1. Jeroen Ketema
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Andrei Voronkov

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Ketema, J. (2008). On Normalisation of Infinitary Combinatory Reduction Systems. In: Voronkov, A. (eds) Rewriting Techniques and Applications. RTA 2008. Lecture Notes in Computer Science, vol 5117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70590-1_12

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  • DOI: https://doi.org/10.1007/978-3-540-70590-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70588-8

  • Online ISBN: 978-3-540-70590-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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