Convolution \(\bar\lambda\mu\)-Calculus

  • Lionel Vaux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4583)


We define an extension of Herbelin’s \(\bar\lambda\mu\)-calculus, introducing a product operation on contexts (in the sense of lists of arguments, or stacks in environment machines), similar to the convolution product of distributions. This is the computational couterpart of some new semantical constructions, extending models of Ehrhard-Regnier’s differential interaction nets, along the lines of Laurent’s polarization of linear logic. We demonstrate this correspondence by providing this calculus with a denotational semantics inside a lambda-model in the category of sets and relations.


Relational Semantic Classical Logic Intuitionistic Logic Linear Logic Reduction Rule 
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© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Lionel Vaux
    • 1
  1. 1.Institut de Mathématiques de Luminy, MarseilleFrance

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