Typed realizability for first-order classical analysis

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• Valentin Blot, Mathematical foundations group, computer science department, University of Bath
• Friday 27 November 2015, 14:00-15:00
• FW26.

If you have a question about this talk, please contact Ohad Kammar.

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 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.


This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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