A term calculus for Intuitionistic Linear Logic

  • Nick Benton
  • Gavin Bierman
  • Valeria de Paiva
  • Martin Hyland
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 664)


In this paper we consider the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system differs from previous calculi (e.g. that of Abramsky [1]) and has two important properties which they lack. These are the substitution property (the set of valid deductions is closed under substitution) and subject reduction (reduction on terms is well-typed). We also consider term reduction arising from cut-elimination in the sequent calculus and normalisation in natural deduction. We explore the relationship between these and consider their computational content.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Nick Benton
    • 1
  • Gavin Bierman
    • 1
  • Valeria de Paiva
    • 1
  • Martin Hyland
    • 2
  1. 1.Computer LaboratoryUniversity of CambridgeUK
  2. 2.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeUK

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