A Direct Proof of Strong Normalization for an Extended Herbelin’s Calculus

  • Kentaro Kikuchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2998)

Abstract

Herbelin presented (at CSL’94) an explicit substitution calculus with a sequent calculus as a type system, in which reduction steps correspond to cut-elimination steps. The calculus, extended with some rules for substitution propagation, simulates β-reduction of ordinary λ-calculus. In this paper we present a proof of strong normalization for the typable terms of the calculus. The proof is a direct one in the sense that it does not depend on the result of strong normalization for the simply typed λ-calculus, unlike an earlier proof by Dyckhoff and Urban.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Kentaro Kikuchi
    • 1
  1. 1.Department of Mathematics and InformaticsChiba UniversityChibaJapan

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