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Communication Dans Un Congrès Année : 2008

A linear-non-linear model for a computational call-by-value lambda calculus (extended abstract)

Résumé

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.

Dates et versions

hal-00483903 , version 1 (17-05-2010)

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Citer

Peter Selinger, Benoît Valiron. A linear-non-linear model for a computational call-by-value lambda calculus (extended abstract). Foundation of Software Science and Computation Structures, Mar 2008, Budapest, Hungary. pp.81--96, ⟨10.1007/978-3-540-78499-9_7⟩. ⟨hal-00483903⟩
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