A Linear-non-Linear Model for a Computational Call-by-Value Lambda Calculus (Extended Abstract)

  • Peter Selinger
  • Benoît Valiron
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4962)


We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda calculus is its linear type system, which includes a duplicability operator “!” as in linear logic. Another main feature is its call-by-value reduction strategy, together with a side-effect to model probabilistic measurements. The “!” operator gives rise to a comonad, as in the linear logic models of Seely, Bierman, and Benton. The side-effects give rise to a monad, as in Moggi’s computational lambda calculus. It is this combination of a monad and a comonad that makes the present paper interesting. We show that our categorical semantics is sound and complete.


Permeability Recombination Coherence Shoe 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Peter Selinger
    • 1
  • Benoît Valiron
    • 2
  1. 1.Dalhousie University 
  2. 2.University of Ottawa 

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