Section: New Results

Realizability semantics of abstract focusing, formalized

Participant : Stéphane Graham-Lengrand.

In [21] we presented a parametric system for abstract focusing, building on Zeilberger's work  [87] , and parametrically capturing classical and intuitionistic focused systems. We presented its semantics, building on Munch-Maccagnoni's work  [80] , in terms of abstract realizability models (which were independently identified by Krivine). The goal was to emphasize the similarities and differences between focusing and realizability, in the way they exploit the polarities of formulae. The system and its semantics led to a substantially formalisation in the proof assistant Coq.