Abstract
Gödel’s functional interpretation [1] can be used to extract programs from non-constructive proofs. Though correct by construction, the obtained terms can be computationally inefficient. One reason for slow execution is the re-evaluation of equal subterms due to the use of substitution during the extraction process. In the present paper we define a variant of the interpretation, which avoids subterm repetition and achieves an almost linear bound on the size of extracted programs.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Gödel, K.: Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Dialectica 12, 280–287 (1958)
Hernest, M.-D., Kohlenbach, U.: A complexity analysis of functional interpretations. Theor. Comput. Sci. 338(1-3), 200–246 (2005)
Hernest, M.-D., Trifonov, T.: Light Dialectica revisited. Submitted to APAL (2008), http://www.math.lmu.de/~trifonov/papers/ldrev.pdf .
Kohlenbach, U.: Applied Proof Theory: Proof Interpretations and their Use in Mathematics. Springer Monographs in Mathematics. Springer, Heidelberg (2008)
Kreisel, G.: Interpretation of analysis by means of constructive functionals of finite types. In: Heyting, A. (ed.) Constructivity in Mathematics, pp. 101–128. North-Holland Publishing Company, Amsterdam (1959)
Schwichtenberg, H.: Dialectica interpretation of well-founded induction. Mathematical Logic Quarterly 54(3), 229–239 (2008)
Trifonov, T.: Dialectica interpretation with fine computational control. In: CiE 2009, July 19-24. LNCS, vol. 5635, pp. 467–477. Springer, Heidelberg (2009)
Troelstra, A.S.: Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. LNM, vol. 344. Springer, Heidelberg (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Trifonov, T. (2010). Quasi-linear Dialectica Extraction. In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_46
Download citation
DOI: https://doi.org/10.1007/978-3-642-13962-8_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13961-1
Online ISBN: 978-3-642-13962-8
eBook Packages: Computer ScienceComputer Science (R0)