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Explicit substitutions for the λΔ-calculus

  • Lambda-Calculus
  • Conference paper
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Book cover Algebraic and Logic Programming (ALP 1997, HOA 1997)

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

Abstract

The λΔ-calculus is a λ-calculus with a control-like operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce λδexp, an explicit substitution calculus for λΔ and study its properties. In particular, we show that λΔexp preserves strong normalisation, which provides us with the first example -moreover a very natural one indeed of explicit substitution calculus which is not structure-preserving and has the preservation of strong normalisation property. One particular application of this result is to prove that the simply typed version of λΔexp is strongly normalising.

In addition, we show that Plotkin's call-by-name continuation-passing style translation may be extended to λΔexp and that the extended translation preserves typing. This seems to be the first study of CPS translations for calculi of explicit substitutions.

This work is supported by NWO and the British council under UK/Dutch joint scientific research project JRP240 and EPSRC grant GR/K 25014.

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Author information

Authors and Affiliations

  1. CWI, P.O. Box 94079, 1090 GB, Amsterdam, the Netherlands

    Gilles Barthe

  2. Department of Computing Science, University of Glasgow, 17 Lilybank Gardens, G12 8QQ, Glasgow, Scotland, UK

    Fairouz Kamareddine & Alejandro Ríos

Authors
  1. Gilles Barthe
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  2. Fairouz Kamareddine
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  3. Alejandro Ríos
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Editor information

Michael Hanus Jan Heering Karl Meinke

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© 1997 Springer-Verlag Berlin Heidelberg

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Barthe, G., Kamareddine, F., Ríos, A. (1997). Explicit substitutions for the λΔ-calculus. 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/BFb0027012

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  • DOI: https://doi.org/10.1007/BFb0027012

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  • Print ISBN: 978-3-540-63459-1

  • Online ISBN: 978-3-540-69555-4

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