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International Workshop on Computer Science Logic

CSL 2005: Computer Science Logic pp 477–492Cite as

Light Functional Interpretation

An Optimization of Gödel’s Technique Towards the Extraction of (More) Efficient Programs from (Classical) Proofs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3634))

Abstract

We give a Natural Deduction formulation of an adaptation of Gödel’s functional (Dialectica) interpretation to the extraction of (more) efficient programs from (classical) proofs. We adapt Jørgensen’s formulation of pure Dialectica translation by eliminating his “Contraction Lemma” and allowing free variables in the extracted terms (which is more suitable in a Natural Deduction setting). We also adapt Berger’s uniform existential and universal quantifiers to the Dialectica-extraction context. The use of such quantifiers without computational meaning permits the identification and isolation of contraction formulas which would otherwise be redundantly included in the pure-Dialectica extracted terms. In the end we sketch the possible combination of our refinement of Gödel’s Dialectica interpretation with its adaptation to the extraction of bounds due to Kohlenbach into a light monotone functional interpretation.

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique (LIX), École Polytechnique, F-91128, Palaiseau, France

    Mircea-Dan Hernest

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  1. Mircea-Dan Hernest
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Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, Oxford, United Kingdom

    Luke Ong

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Hernest, MD. (2005). Light Functional Interpretation. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_33

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  • DOI: https://doi.org/10.1007/11538363_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28231-0

  • Online ISBN: 978-3-540-31897-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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