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Light Dialectica program extraction from a classical Fibonacci proof
 PROCEEDINGS OF DCM’06 AT ICALP’06, ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE (ENTCS, 2007), 10PP., ACCEPTED FOR PUBLICATION, DOWNLOADABLE @ HTTP://WWW.BRICS.DK/ EDANHER
, 2007
"... We demonstrate program extraction by the Light Dialectica Interpretation (LDI) on a minimal logic proof of the classical existence of Fibonacci numbers. This semiclassical proof is available in MinLog’s library of examples. The term of Gödel’s T extracted by the LDI is, after strong normalization, ..."
Abstract

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We demonstrate program extraction by the Light Dialectica Interpretation (LDI) on a minimal logic proof of the classical existence of Fibonacci numbers. This semiclassical proof is available in MinLog’s library of examples. The term of Gödel’s T extracted by the LDI is, after strong normalization, exactly the usual recursive algorithm which defines the Fibonacci numbers (in pairs). This outcome of the Light Dialectica metaalgorithm is much better than the Tprogram extracted by means of the pure Gödel Dialectica Interpretation. It is also strictly less complex than the result obtained by means of the refined Atranslation technique of Berger, Buchholz and Schwichtenberg on an artificially distorted variant of the input proof, but otherwise it is identical with the term yielded by Berger’s Kripkestyle refined Atranslation. Although syntactically different, it also has the same computational complexity as the original program yielded by the refined Atranslation from the undistorted input classical Fibonacci proof.