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

Peter Selinger, Benoît Valiron
Foundations of Software Science and Computational Structures  
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
more » ... onad, 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.
doi:10.1007/978-3-540-78499-9_7 dblp:conf/fossacs/SelingerV08 fatcat:sc5e6vnzhrbzbkyjuuxa4lespa