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λ-calculi with explicit substitutions and composition which preserve β-strong normalization

Extended abstract
  • Maria C. F. Ferreira
  • Delia Kesner
  • Laurence Puel
Lambda-Calculus and Rewriting
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1139)

Abstract

We study preservation of β-strong normalization by λ d and λ dn , two confluent λ-calculi with explicit substitutions defined in [10]; the particularity of these calculi is that both have a composition operator for substitutions. We develop an abstract simulation technique allowing to reduce preservation of β-strong normalization of one calculus to that of another one, and apply said technique to reduce preservation of β-strong normalization of λ d and λ dn to that of λ f , another calculus 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 composition and preserving β- strong normalization. We also apply our technique to reduce preservation of β-strong normalization of the calculus λ v in [14] to that of λ f .

Keywords

Composition Operator Simulation Technique Reduction Rule Open Term Reduction Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Maria C. F. Ferreira
    • 1
  • Delia Kesner
    • 2
  • Laurence Puel
    • 2
  1. 1.Dep. de Informática, Fac. de Ciências e TecnologiaUniv. Nova de LisboaMonte de CaparicaPortugal
  2. 2.CNRS & Lab. de Rech. en Informatique, Bat 490Univ. de Paris-SudOrsay CedexFrance

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