A Terminating and Confluent Linear Lambda Calculus

  • Yo Ohta
  • Masahito Hasegawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4098)


We present a rewriting system for the linear lambda calculus corresponding to the {!, \(\multimap\)}-fragment of intuitionistic linear logic. This rewriting system is shown to be strongly normalizing, and Church-Rosser modulo the trivial commuting conversion. Thus it provides a simple decision method for the equational theory of the linear lambda calculus. As an application we prove the strong normalization of the simply typed computational lambda calculus by giving a reduction-preserving translation into the linear lambda calculus.


Equational Theory Linear Logic Reduction Rule Springer Lecture Note Strong Normalization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yo Ohta
    • 1
  • Masahito Hasegawa
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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