The Free Exponential Modality of Probabilistic Coherence Spaces

  • Raphaëlle Crubillé
  • Thomas Ehrhard
  • Michele PaganiEmail author
  • Christine Tasson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10203)


Probabilistic coherence spaces yield a model of linear logic and lambda-calculus with a linear algebra flavor. Formulas/types are associated with convex sets of \({\mathbb R^+}^{}\)-valued vectors, linear logic proofs with linear functions and \(\lambda \)-terms with entire functions, both mapping the convex set of their domain into the one of their codomain.

Previous results show that this model is particularly precise in describing the observational equivalences between probabilistic functional programs. We prove here that the exponential modality is the free commutative comonad, giving a further mark of canonicity to the model.



We thank Sam Staton, Hugh Steele, Lionel Vaux and the anonymous reviewers for useful comments and discussions. This work has been partly funded by the French project ANR-14-CE25-0005 Elica and by the French-Chinese project ANR-11-IS02-0002 and NSFC 61161130530 Locali.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Raphaëlle Crubillé
    • 1
  • Thomas Ehrhard
    • 1
  • Michele Pagani
    • 1
    Email author
  • Christine Tasson
    • 1
  1. 1.IRIF, UMR 8243, Université Paris Diderot, Sorbonne Paris CitéParisFrance

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