Blot, Valentin - Typed realizability for first-order classical analysis

lmcs:1623 - Logical Methods in Computer Science, December 31, 2015, Volume 11, Issue 4
Typed realizability for first-order classical analysis

Authors: Blot, Valentin

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 G\"odel'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}02 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.


Source : oai:arXiv.org:1512.05313
DOI : 10.2168/LMCS-11(4:22)2015
Volume: Volume 11, Issue 4
Published on: December 31, 2015
Submitted on: April 15, 2015
Keywords: Computer Science - Logic in Computer Science


Share

Consultation statistics

This page has been seen 142 times.
This article's PDF has been downloaded 78 times.