Un Lambda-Calcul Atomique

International audienceNous introduisons un lambda-calcul avec partage explicite, le lambda-calcul atomique, dans lequel la duplication des sous-termes est faite pas à pas en fonction des constructeurs. Nous donnons une fonction de dénotation du lambda-calcul atomique dans le lambda-calcul et montrons que le lambda-calcul atomique simule la -réduction et préserve la normalisation forte. Nous donnons aussi un système de type pour le lambda-calcul atomique et montrons que la réduction préserve le type

On Constructive Existence

International audienceBaaz and Fermueller gave in 2003 an original characterization of constructive existence in classical logic. In this paper, we give a simple proof of this result based on cut-elimination in sequent calculus. The interest of this proof besides its simplicity is that it allows in particular to generalize the result to other logics enjoying cut-elimination. We also briefly discuss the significance of the characterization itself

Spinal Atomic Lambda-Calculus

International audienceWe present the spinal atomic λ-calculus, a typed λ-calculus with explicit sharing and atomic duplication that achieves spinal full laziness: duplicating only the direct paths between a binder and bound variables is enough for beta reduction to proceed. We show this calculus is the result of a Curry-Howard style interpretation of a deep-inference proof system, and prove that it has natural properties with respect to the λ-calculus: confluence and preservation of strong normalisation