Strong Normalization of the Typed λws-Calculus

  • René David
  • Bruno Guillaume
Conference paper

DOI: 10.1007/978-3-540-45220-1_15

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2803)
Cite this paper as:
David R., Guillaume B. (2003) Strong Normalization of the Typed λws-Calculus. In: Baaz M., Makowsky J.A. (eds) Computer Science Logic. CSL 2003. Lecture Notes in Computer Science, vol 2803. Springer, Berlin, Heidelberg


The λws-calculus is a λ-calculus with explicit substitutions introduced in [4]. It satisfies the desired properties of such a calculus: step by step simulation of β, confluence on terms with meta-variables and preservation of the strong normalization. It was conjectured in [4] that simply typed terms of λws are strongly normalizable. This was proved in [7] by Di Cosmo & al. by using a translation of λws into the proof nets of linear logic. We give here a direct and elementary proof of this result. The strong normalization is also proved for terms typable with second order types (the extension of Girard’s system F). This is a new result.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • René David
    • 1
  • Bruno Guillaume
    • 2
  1. 1.Université de SavoieLe Bourget du Lac
  2. 2.LORIA / INRIA LorraineVandœuvre-lès-Nancy

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