Differential Linear Logic and Polarization

  • Authors:
  • Lionel Vaux

  • Affiliations:
  • Laboratoire de Mathématiques de l'Université de Savoie, UMR 5127 CNRS, Le Bourget-du-Lac Cedex, France 73376

  • Venue:
  • TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
  • Year:
  • 2009

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Abstract

We extend Ehrhard---Regnier's differential linear logic along the lines of Laurent's polarization. We provide a denotational semantics of this new system in the well-known relational model of linear logic, extending canonically the semantics of both differential and polarized linear logics: this justifies our choice of cut elimination rules. Then we show this polarized differential linear logic refines the recently introduced convolution ${\bar\lambda}\mu$-calculus, the same as linear logic decomposes *** -calculus.