Focalisation and Classical Realisability (version with appendices)

Guillaume Munch-Maccagnoni (1, 2)

1 PPS - Preuves, Programmes et Systèmes
2 PI.R2 - Design, study and implementation of languages for proofs and programs

We 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.

Mots clés: focalization; realizability; sequent calculus; classical logic; linear logic; typing

Domaines: Logique en informatique [cs.LO]

Guillaume Munch-Maccagnoni. Focalisation and Classical Realisability (version with appendices). 18th EACSL Annual Conference on Computer Science Logic - CSL 09, Sep 2009, Coimbra, Portugal. pp.409-423, ⟨10.1007/978-3-642-04027-6_30⟩. ⟨inria-00409793v2⟩