CSL 2010: Computer Science Logic pp 170-184 | Cite as

Exponentials with Infinite Multiplicities

  • Alberto Carraro
  • Thomas Ehrhard
  • Antonino Salibra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6247)

Abstract

Given a semi-ring with unit which satisfies some algebraic conditions, we define an exponential functor on the category of sets and relations which allows to define a denotational model of differential linear logic and of the lambda-calculus with resources. We show that, when the semi-ring has an element which is infinite in the sense that it is equal to its successor, this model does not validate the Taylor formula and that it is possible to build, in the associated Kleisli cartesian closed category, a model of the pure lambda-calculus which is not sensible. This is a quantitative analogue of the standard graph model construction in the category of Scott domains. We also provide examples of such semi-rings.

Keywords

lambda-calculus linear logic denotational semantics differential lambda-calculus resource lambda-calculus non sensible models 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alberto Carraro
    • 1
    • 2
  • Thomas Ehrhard
    • 2
  • Antonino Salibra
    • 1
  1. 1.Department of Computer ScienceCa’ Foscari UniversityVenice
  2. 2.Laboratory Preuves, Programmes & Systèmes UMR 7126University Paris Diderot, Paris 7 and CNRS 

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