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An Extensional Böhm Model

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Rewriting Techniques and Applications (RTA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2378))

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Abstract

We show the existence of an infinitary confluent and normalising extension of the finite extensional lambda calculus with beta and eta. Besides infinite beta reductions also infinite eta reductions are possible in this extension, and terms without head normal form can be reduced to bottom. As corollaries we obtain a simple, syntax based construction of an extensional Böhm model of the finite lambda calculus; and a simple, syntax based proof that two lambda terms have the same semantics in this model if and only if they have the same eta-Böhm tree if and only if they are observationally equivalent wrt to beta normal forms. The confluence proof reduces confluence of beta, bottom and eta via infinitary commutation and postponement arguments to confluence of beta and bottom and confluence of eta.

We give counterexamples against confluence of similar extensions based on the identification of the terms without weak head normal form and the terms without top normal form (rootactive terms) respectively.

Partially supported by IST-2001-322222 MIKADO; IST-2001-33477 DART.

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Author information

Authors and Affiliations

  1. Departimento di Informatica, Università di Torino, Corso Svizzera 185, 10149, Torino, Italy

    Paula Severi

  2. Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, UK

    Fer-Jan de Vries

Authors
  1. Paula Severi
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  2. Fer-Jan de Vries
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Editor information

Editors and Affiliations

  1. LIFL Bâtiment M3, Université de Lille 1, Cité Scientifique, 59655, Villeneuve d’Ascq cedex, France

    Sophie Tison

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© 2002 Springer-Verlag Berlin Heidelberg

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Severi, P., de Vries, FJ. (2002). An Extensional Böhm Model. In: Tison, S. (eds) Rewriting Techniques and Applications. RTA 2002. Lecture Notes in Computer Science, vol 2378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45610-4_12

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  • DOI: https://doi.org/10.1007/3-540-45610-4_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43916-5

  • Online ISBN: 978-3-540-45610-0

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