Typed realizability for first-order classical analysis

Valentin Blot
University of Bath
https://valentinblot.org/pro/

Date(s) : 10/12/2015   iCal
14 h 00 min - 15 h 00 min

We describe a realizability framework for classical first-order logic in which realizers live in (a model of) typed lambda-mu-calculus. This allows a direct interpretation of classical proofs, avoiding the usual negative translation to intuitionistic logic. We prove that (the interpretations of) the usual terms of Gödel’s system T realize the axioms of Peano arithmetic, and that under some assumptions on the computational model, the bar recursion operator realizes the axiom of dependent choice. We also perform a proper analysis of relativization, which allows for less technical proofs of adequacy. Extraction of algorithms from proofs of pi-0-2 formulas relies on a novel implementation of Friedman’s trick exploiting the control possibilities of the language. This allows to have extracted programs with simpler types than in the case of negative translation followed by intuitionistic realizability.

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