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Reductions, intersection types, and explicit substitutions

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Typed Lambda Calculi and Applications (TLCA 2001)

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Abstract

The λ-calculus plays a key role in the foundations of logic and of programming language design, and in the implementation of logics and languages as well. The foundation of λ-calculus itself is β-conversion, which relates the primitive notions of abstraction and application in terms of substitution. Classical λ-calculus treats substitution as an atomic operation, but in the presence of variablebinding substitution it is a complex operation to define and to implement. So a more careful analysis is required if one is to reason about the correctness of compilers, theorem provers, or proof-checkers. Furthermore the actual cost of performing substitution should be considered when reasoning about complexity of implementations.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT, 06459, USA

    Dan Doughertyy

  2. Laboratoire de l’Informatique du Parallélisme, école Normale Supérieure de Lyon, 46, Allée d’Italie, 69364, Lyon 07, France

    Pierre Lescanne

Authors
  1. Dan Doughertyy
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  2. Pierre Lescanne
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Editor information

Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, USA

    Samson Abramsky

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© 2001 Springer-Verlag Berlin Heidelberg

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Doughertyy, D., Lescanne, P. (2001). Reductions, intersection types, and explicit substitutions. In: Abramsky, S. (eds) Typed Lambda Calculi and Applications. TLCA 2001. Lecture Notes in Computer Science, vol 2044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45413-6_13

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  • DOI: https://doi.org/10.1007/3-540-45413-6_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41960-0

  • Online ISBN: 978-3-540-45413-7

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