λCalculi with Explicit Substitutions Preserving Strong Normalization

  • Maria C. F. Ferreira
  • Delia Kesner
  • Laurence Puel
  • 20 Downloads

Abstract

This paper studies preservation of β-strong normalization by two different confluent λ-calculi with explicit substitutions defined in [96]; the particularity of these calculi, called λ d and λ dn respectively, is that both have a (weak) composition operator for substitutions. We apply an abstract simulation technique to reduce preservation of β-strong normalization of λ d and λ dn to that of another calculus, called λ f having no composition operator. Then, preservation of β-strong normalization of λ f is shown using the same technique as in [2]. As a consequence, λ d and λ dn become the first λ-calculi with explicit substitutions having (weak) composition and preserving β-strong normalization. As an aside, we also show how to apply our technique to reduce preservation of β-strong normalization of the calculus λ v in [20] to that of λ f .

Key wordsλ-Calculus, Explicit substitutions, Preservation of strong normalization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Maria C. F. Ferreira
    • 1
  • Delia Kesner
    • 2
  • Laurence Puel
    • 2
  1. 1.Dep. de Informática, Fac. de Ciências e Tecnologia, Univ. Nova de Lisboa, Quinta da Torre, P-2825 Monte da Caparica, Portugal, (e-mail: cf@di.fct.unl.pt)PT
  2. 2.CNRS and Laboratoire de Recherche en Informatique, Bat 490, Université de Paris-Sud, F-91405 Orsay Cedex, France, (e-mail: {kesner,puel}@lri.fr)FR

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