2009 | OriginalPaper | Chapter
Focalisation and Classical Realisability
Author : Guillaume Munch-Maccagnoni
Published in: Computer Science Logic
Publisher: Springer Berlin Heidelberg
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We develop a polarised variant of Curien and Herbelin’s
$\bar{\lambda}\mu\tilde{\mu}$
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.