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.


Quantum Computation Natural Transformation Categorical Semantic Operational Semantic Monoidal Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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