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On Continuous Normalization

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Computer Science Logic (CSL 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2471))

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Abstract

This work aims at explaining the syntactical properties of continuous normalization, as introduced in proof theory by Mints, and further studied by Ruckert, Buchholz and Schwichtenberg. In an extension of the untyped coinductive λ-calculus by void construcors (so-called repetition rules), a primitive recursive normalization function is defined. Compared with other formulations of continuous normalization, this definition is much simpler and therefore suitable for analysis in a coalgebraic setting. It is shown to be continuous w.r.t. the natural topology on non-wellfounded terms with the identity as modulus of continuity. The number of repetition rules is locally related to the number of β-reductions necessary to reach the normal form (as represented by the Böhm tree) and the number of applications appearing in this normal form.

Supported by the “Graduiertenkolleg Logik in der Informatik” of the Deutsche Forschungsgemeinschaft

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Authors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstrasse 39, 80333, München, Germany

    Klaus Aehlig & Felix Joachimski

Authors
  1. Klaus Aehlig
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  2. Felix Joachimski
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Editors and Affiliations

  1. Laboratory for Foundations of Computer Science Division of Informatics, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Julian Bradfield

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© 2002 Springer-Verlag Berlin Heidelberg

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Aehlig, K., Joachimski, F. (2002). On Continuous Normalization. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_5

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  • DOI: https://doi.org/10.1007/3-540-45793-3_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44240-0

  • Online ISBN: 978-3-540-45793-0

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