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De Bruijn’s Automath and Pure Type Systems

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Thirty Five Years of Automating Mathematics

Part of the book series: Applied Logic Series ((APLS,volume 28))

Abstract

We study the position of the Automath systems within the framework of Pure Type Systems (PTSs). In [Barendregt, 1992; Geuvers, 1993], a rough relationship has been given between Automath and PTSs. That relationship ignores three of the most important features of Automath: definitions, parameters and П-reduction, because at the time, formulations of PTSs did not have these features. Since, PTSs have been extended with these features and in view of this, we revisit the correspondence between Automath and PTSs. This paper gives the most accurate description of Automath as a PTS so far.

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Authors
  1. Fairouz Kamareddine
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  2. Twan Laan
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  3. Rob Nederpelt
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Editor information

Editors and Affiliations

  1. School of Mathematical and Computer Sciences, Heriot-Watt University, Mountbatten Building, EH 14 4AS, Riccarton, Edinburgh, Scotland, UK

    Fairouz D. Kamareddine

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Kamareddine, F., Laan, T., Nederpelt, R. (2003). De Bruijn’s Automath and Pure Type Systems. In: Kamareddine, F.D. (eds) Thirty Five Years of Automating Mathematics. Applied Logic Series, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0253-9_5

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  • DOI: https://doi.org/10.1007/978-94-017-0253-9_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6440-0

  • Online ISBN: 978-94-017-0253-9

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