Strong Normalisation of Cut-Elimination That Simulates β-Reduction

  • Kentaro Kikuchi
  • Stéphane Lengrand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4962)

Abstract

This paper is concerned with strong normalisation of cut-elimination for a standard intuitionistic sequent calculus. The cut- elimination procedure is based on a rewrite system for proof-terms with cut-permutation rules allowing the simulation of β-reduction. Strong normalisation of the typed terms is inferred from that of the simply-typed λ-calculus, using the notions of safe and minimal reductions as well as a simulation in Nederpelt-Klop’s λI-calculus. It is also shown that the type-free terms enjoy the preservation of strong normalisation (PSN) property with respect to β-reduction in an isomorphic image of the type-free λ-calculus.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Kentaro Kikuchi
    • 1
  • Stéphane Lengrand
    • 2
  1. 1.RIECTohoku UniversityJapan
  2. 2.CNRSLaboratoire d’Informatique de l’Ecole PolytechniqueFrance

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