Simple Proofs of Characterizing Strong Normalization for Explicit Substitution Calculi

  • Kentaro Kikuchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4533)


We present a method of lifting to explicit substitution calculi some characterizations of the strongly normalizing terms of λ-calculus by means of intersection type systems. The method is first illustrated by applying to a composition-free calculus of explicit substitutions, yielding a simpler proof than the previous one by Lengrand et al. Then we present a new intersection type system in the style of sequent calculus, and show that it characterizes the strongly normalizing terms of Dyckhoff and Urban’s extension of Herbelin’s explicit substitution calculus.


Intersection Type Simple Proof Reduction Rule Natural Deduction Sequent Calculus 
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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Kentaro Kikuchi
    • 1
  1. 1.RIEC, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577Japan

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