Reductions, intersection types, and explicit substitutions

  • Dan Doughertyy
  • Pierre Lescanne
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2044)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Dan Doughertyy
    • 1
  • Pierre Lescanne
    • 2
  1. 1.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA
  2. 2.Laboratoire de l’Informatique du Parallélismeécole Normale Supérieure de LyonLyon 07France

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