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International Workshop on Coalgebraic Methods in Computer Science

CMCS 2012: Coalgebraic Methods in Computer Science pp 130–149Cite as

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An Alpha-Corecursion Principle for the Infinitary Lambda Calculus

An Alpha-Corecursion Principle for the Infinitary Lambda Calculus

  • Alexander Kurz18,
  • Daniela Petrişan18,
  • Paula Severi18 &
  • …
  • Fer-Jan de Vries18 
  • Conference paper
  • 574 Accesses

  • 2 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7399)

Abstract

Gabbay and Pitts proved that lambda-terms up to alpha-equivalence constitute an initial algebra for a certain endofunctor on the category of nominal sets. We show that the terms of the infinitary lambda-calculus form the final coalgebra for the same functor. This allows us to give a corecursion principle for alpha-equivalence classes of finite and infinite terms. As an application, we give corecursive definitions of substitution and of infinite normal forms (Böhm, Lévy-Longo and Berarducci trees).

Keywords

  • Normal Form
  • Cauchy Sequence
  • Free Variable
  • Ultrametric Space
  • Lambda Calculus

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. Department of Computer Science, University of Leicester, UK

    Alexander Kurz, Daniela Petrişan, Paula Severi & Fer-Jan de Vries

Authors
  1. Alexander Kurz
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  2. Daniela Petrişan
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  3. Paula Severi
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  4. Fer-Jan de Vries
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Editor information

Editors and Affiliations

  1. Research School of Information Sciences and Engineering, The Australian National University, 0200, Canberra, ACT, Australia

    Dirk Pattinson

  2. Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058, Erlangen, Germany

    Lutz Schröder

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Kurz, A., Petrişan, D., Severi, P., de Vries, FJ. (2012). An Alpha-Corecursion Principle for the Infinitary Lambda Calculus. In: Pattinson, D., Schröder, L. (eds) Coalgebraic Methods in Computer Science. CMCS 2012. Lecture Notes in Computer Science, vol 7399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32784-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-32784-1_8

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  • Print ISBN: 978-3-642-32783-4

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