Time and Games
Résumé
We add the notion of time to denotational models of the $\lambda$-calculus. The denotation is no longer constant through reduction, but rather decreases with respect to an appropriate order. Categorically, we use a monad over a cartesian category, an order over the morphisms of the Kleisli category, and a Galois connection to model $\beta$-reduction. We define a generic monad (time as a resource), and an instance of this construction in game semantics, where our timings are precise enough to simulate parallelism through interleaving.
Domaines
Langage de programmation [cs.PL]
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