Structures de réalisabilité, RAM et ultrafiltre sur N

34 p.We show how to transform into programs the proofs in classical Analysis which use the existence of an ultrafilter on the integers. The method mixes the classical realizability introduced by the author, with the ``forcing'' of P. Cohen. The programs we obtain, use read and write instructions in random access memory

Focalisation and Classical Realisability (version with appendices)

The original publication is avalaible at : www.springerlink.comInternational audienceWe develop a polarised variant of Curien and Herbelin's lambda-bar-mu-mu-tilde calculus suitable for sequent calculi that admit a focalising cut elimination (i.e. whose proofs are focalised when cut-free), such as Girard's classical logic LC or linear logic. This gives a setting in which Krivine's classical realisability extends naturally (in particular to call-by-value), with a presentation in terms of orthogonality. We give examples of applications to the theory of programming languages