On Normalisation of Infinitary Combinatory Reduction Systems

  • Jeroen Ketema
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5117)


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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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jeroen Ketema
    • 1
  1. 1.Research Institute of Electrical CommunicationTohoku UniversitySendaiJapan

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