Focalisation and classical realisability

Authors:
Guillaume Munch-Maccagnoni
Affiliations:
Université Paris 7
Venue:
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Year:
2009

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Abstract

We develop a polarised variant of Curien and Herbelin's λµµ 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-byvalue), with a presentation in terms of orthogonality. We give examples of applications to the theory of programming languages.