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Light functional interpretation
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Hybrid Functional Interpretations
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
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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 semi-classical proof is available in MinLog's library of examples. The term of Godel'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 meta-algorithm is much better than the T-program extracted by means of the pure Godel Dialectica Interpretation. It is also strictly less complex than the result obtained by means of the refined A-translation 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 Kripke-style refined A-translation. Although syntactically different, it also has the same computational complexity as the original program yielded by the refined A-translation from the undistorted input classical Fibonacci proof.