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Perpetuality and uniform normalization

  • Lambda-Calculus
  • Conference paper
  • First Online:
Algebraic and Logic Programming (ALP 1997, HOA 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1298))

Abstract

We define a perpetual one-step reduction strategy which enables one to construct minimal (w.r.t. Lévy's ordering ⊴ on reductions) infinite reductions in Conditional Orthogonal Expression Reduction Systems. We use this strategy to derive two characterizations of perpetual redexes, i.e., redexes whose contractions retain the existence of infinite reductions. These characterizations generalize existing related criteria for perpetuality of redexes. We give a number of applications of our results, demonstrating their usefulness. In particular, we prove equivalence of weak and strong normalization (the uniform normalization property) for various restricted λ-calculi, which cannot be derived from previously known perpetuality criteria.

The UN property is called strong normalization in [B194].

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Authors and Affiliations

  1. NTT Basic Research Laboratories, 3-1 Moriaosato-Wakamiya, 243-01, Atsugi, Kanagawa, Japan

    Zurab Khasidashvili & Mizuhito Ogawa

Authors
  1. Zurab Khasidashvili
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  2. Mizuhito Ogawa
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Michael Hanus Jan Heering Karl Meinke

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© 1997 Springer-Verlag Berlin Heidelberg

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Khasidashvili, Z., Ogawa, M. (1997). Perpetuality and uniform normalization. In: Hanus, M., Heering, J., Meinke, K. (eds) Algebraic and Logic Programming. ALP HOA 1997 1997. Lecture Notes in Computer Science, vol 1298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027014

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  • DOI: https://doi.org/10.1007/BFb0027014

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63459-1

  • Online ISBN: 978-3-540-69555-4

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