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Realizability Proof for Normalization of Full Differential Linear Logic

  • Stéphane Gimenez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6690)

Abstract

Realizability methods allowed to prove normalization results on many typed calculi. Girard adapted these methods to systems of nets and managed to prove normalization of second order Linear Logic [4]. Our contribution is to provide an extension of this proof that embrace Full Differential Linear Logic (a logic that can describe both single-use resources and inexhaustible resources). Anchored within the realizability framework our proof is modular enough so that further extensions (to second order, to additive constructs or to any other independent feature that can be dealt with using realizability) come for free.

Keywords

Linear Logic Proof Nets Differential Linear Logic Differential Interaction Nets Realizability Weak Normalization 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Stéphane Gimenez
    • 1
  1. 1.Laboratoire PPSUniversité Paris-DiderotParis 7France

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