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Volumn 3634, Issue , 2005, Pages 477-492

Light functional interpretation: An optimization of Gödel's technique towards the extraction of (more) efficient programs from (classical) proofs

Author keywords

Berger's uniform quantifiers; Complexity of extracted programs; G del's Functional interpretation; Program extraction from (classical) proofs; Proof Mining; Proof Carrying code

Indexed keywords

FUNCTIONS; MATHEMATICAL MODELS; OPTIMIZATION; THEOREM PROVING;

EID: 26944475514     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11538363_33     Document Type: Conference Paper
Times cited : (8)

References (38)
  • 1
    • 0034561991 scopus 로고    scopus 로고
    • Interpreting classical theories in constructive ones
    • J. Avigad. Interpreting classical theories in constructive ones. The Journal of Symbolic Logic, 65(4):1785-1812, 2000.
    • (2000) The Journal of Symbolic Logic , vol.65 , Issue.4 , pp. 1785-1812
    • Avigad, J.1
  • 2
    • 77956698231 scopus 로고    scopus 로고
    • Gödel's functional ('Dialectica') interpretation
    • S.R. Buss, editor, volume 137 Studies in Logic and the Foundations of Mathematics. Elsevier
    • J. Avigad and S. Feferman. Gödel's functional ('Dialectica') interpretation. In S.R. Buss, editor, Handbook of Proof Theory, volume 137 of Studies in Logic and the Foundations of Mathematics, pages 337-405. Elsevier, 1998.
    • (1998) Handbook of Proof Theory , pp. 337-405
    • Avigad, J.1    Feferman, S.2
  • 3
    • 84968335869 scopus 로고
    • Extracting constructive content from classical logic via control-like reductions
    • M. Bezem and J.F. Groote, editors, Typed Lambda Calculi and Applications
    • F. Barbanera and S. Berardi. Extracting constructive content from classical logic via control-like reductions. In M. Bezem and J.F. Groote, editors, Typed Lambda Calculi and Applications, pages 45-59. LNCS Vol. 664, 1993.
    • (1993) LNCS , vol.664 , pp. 45-59
    • Barbanera, F.1    Berardi, S.2
  • 5
    • 14744276178 scopus 로고    scopus 로고
    • Uniform heyting arithmetic
    • May. Festschrift for H. Schwichtenberg's 60th birthday
    • U. Berger. Uniform Heyting Arithmetic. Annals of Pure and Applied Logic, 133(1-3): 125-148, May 2005. Festschrift for H. Schwichtenberg's 60th birthday.
    • (2005) Annals of Pure and Applied Logic , vol.133 , Issue.1-3 , pp. 125-148
    • Berger, U.1
  • 7
    • 0035252984 scopus 로고    scopus 로고
    • The Warshall algorithm and Dickson's Lemma: Two examples of realistic program extraction
    • U. Berger, H. Schwichtenberg, and M. Seisenberger. The Warshall algorithm and Dickson's lemma: Two examples of realistic program extraction. Journal of Automated Reasoning, 26:205-221, 2001.
    • (2001) Journal of Automated Reasoning , vol.26 , pp. 205-221
    • Berger, U.1    Schwichtenberg, H.2    Seisenberger, M.3
  • 8
    • 0002476022 scopus 로고
    • Finding computational content in classical proofs
    • G. Huet and G. Plotkin, editors. Cambridge University Press
    • R.L. Constable and C. Murthy. Finding computational content in classical proofs. In G. Huet and G. Plotkin, editors, Logical Frameworks, pages 341-362. Cambridge University Press, 1991.
    • (1991) Logical Frameworks , pp. 341-362
    • Constable, R.L.1    Murthy, C.2
  • 9
    • 85016922087 scopus 로고    scopus 로고
    • A new method for establishing conservativity of classical systems over their intuitionistic version
    • T. Coquand and M. Hofmann. A new method for establishing conservativity of classical systems over their intuitionistic version. Mathematical Structures in Computer Science, 9(4):323-333, 1999.
    • (1999) Mathematical Structures in Computer Science , vol.9 , Issue.4 , pp. 323-333
    • Coquand, T.1    Hofmann, M.2
  • 10
    • 0002870034 scopus 로고
    • Eine Variante zur Dialectica Interpretation der Heyting Arithmetik endlicher Typen
    • J. Diller and W. Nahm. Eine Variante zur Dialectica Interpretation der Heyting Arithmetik endlicher Typen. Archiv für Mathematische Logik und Grundlagenforschung, 16:49-66, 1974.
    • (1974) Archiv für Mathematische Logik und Grundlagenforschung , vol.16 , pp. 49-66
    • Diller, J.1    Nahm, W.2
  • 11
    • 85056018189 scopus 로고    scopus 로고
    • Bounded functional interpretation
    • To appear, see Elseviers's Science Direct on the Internet
    • F. Ferreira and P. Oliva. Bounded Functional Interpretation. Annals of Pure and Applied Logic, 48 pp., To appear, see Elseviers's Science Direct on the Internet.
    • Annals of Pure and Applied Logic
    • Ferreira, F.1    Oliva, P.2
  • 12
    • 0001796972 scopus 로고
    • Classical and intuitionistically provably recursive functions
    • G.H. Müller and D.S. Scott, editors, Higher Set Theory. Springer Verlag
    • H. Friedman. Classical and intuitionistically provably recursive functions. In G.H. Müller and D.S. Scott, editors, Higher Set Theory, volume 669 of Lecture Notes in Mathematics, pages 21-27. Springer Verlag, 1978.
    • (1978) Lecture Notes in Mathematics , vol.669 , pp. 21-27
    • Friedman, H.1
  • 13
    • 84977256167 scopus 로고
    • Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes
    • K. Gödel. Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Dialectica, 12:280-287, 1958.
    • (1958) Dialectica , vol.12 , pp. 280-287
    • Gödel, K.1
  • 14
    • 26944463645 scopus 로고    scopus 로고
    • M.-D. Hernest. Technical Appendix to this paper. See the author's web-page
    • M.-D. Hernest. Technical Appendix to this paper. See the author's web-page.
  • 15
    • 21544465455 scopus 로고    scopus 로고
    • A comparison between two techniques of program extraction from classical proofs
    • M. Baaz, J. Makovsky, and A. Voronkov, editors, CSL 2003: Extended Posters. Springer Verlag
    • M.-D. Hernest. A comparison between two techniques of program extraction from classical proofs. In M. Baaz, J. Makovsky, and A. Voronkov, editors, CSL 2003: Extended Posters, vol. VIII of Kurt Gödel Society's Collegium Logicum, pp. 99-102. Springer Verlag, 2004.
    • (2004) Kurt Gödel Society's Collegium Logicum , vol.8 , pp. 99-102
    • Hernest, M.-D.1
  • 16
    • 18544381384 scopus 로고    scopus 로고
    • A complexity analysis of functional interpretations
    • 10 June
    • M.-D. Hernest and U. Kohlenbach. A complexity analysis of functional interpretations. Theoretical Computer Science, 338(1-3):200-246, 10 June 2005.
    • (2005) Theoretical Computer Science , vol.338 , Issue.1-3 , pp. 200-246
    • Hernest, M.-D.1    Kohlenbach, U.2
  • 18
    • 0008000980 scopus 로고
    • Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus
    • I. Johansson. Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus. Compositio Matematica, 4:119-136, 1936.
    • (1936) Compositio Matematica , vol.4 , pp. 119-136
    • Johansson, I.1
  • 19
    • 8744281788 scopus 로고    scopus 로고
    • Master's thesis, Departments of Mathematics and Philosophy, University of Roskilde, Roskilde, Denmark
    • K.F. Jørgensen. Finite type arithmetic. Master's thesis, Departments of Mathematics and Philosophy, University of Roskilde, Roskilde, Denmark, 2001.
    • (2001) Finite Type Arithmetic
    • Jørgensen, K.F.1
  • 20
    • 26944455746 scopus 로고    scopus 로고
    • Proof Interpretations and the computational content of proofs
    • latest version in the author's web page
    • U. Kohlenbach. Proof Interpretations and the Computational Content of Proofs. Lecture Course, latest version in the author's web page.
    • Lecture Course
    • Kohlenbach, U.1
  • 21
    • 0001154964 scopus 로고    scopus 로고
    • Analysing proofs in analysis
    • W. Hodges, M. Hyland, C. Steinhorn, and J. Truss, editors, European Logic Colloquium. Oxford University Press
    • U. Kohlenbach. Analysing proofs in Analysis. In W. Hodges, M. Hyland, C. Steinhorn, and J. Truss, editors, Logic: from Foundations to Applications, Keele, 1993, European Logic Colloquium, pages 225-260. Oxford University Press, 1996.
    • (1996) Logic: from Foundations to Applications, Keele, 1993 , pp. 225-260
    • Kohlenbach, U.1
  • 23
    • 0001776862 scopus 로고
    • Interpretation of analysis by means of constructive functionals of finite types
    • A. Heyting, editor. North-Holland Publishing Company
    • G. Kreisel. Interpretation of analysis by means of constructive functionals of finite types. In A. Heyting, editor, Constructivity in Mathematics, pages 101-128. North-Holland Publishing Company, 1959.
    • (1959) Constructivity in Mathematics , pp. 101-128
    • Kreisel, G.1
  • 24
    • 4243128737 scopus 로고
    • Classical logic, storage operators and second-order lambda-calculus
    • J.-L. Krivine. Classical logic, storage operators and second-order lambda-calculus. Annals of Pure and Applied Logic, 68:53-78, 1994.
    • (1994) Annals of Pure and Applied Logic , vol.68 , pp. 53-78
    • Krivine, J.-L.1
  • 25
    • 0000275420 scopus 로고
    • Syntactic translations and provably recursive functions
    • September
    • D. Leivant. Syntactic translations and provably recursive functions. The Journal of Symbolic Logic, 50(3):682-688, September 1985.
    • (1985) The Journal of Symbolic Logic , vol.50 , Issue.3 , pp. 682-688
    • Leivant, D.1
  • 26
    • 4544380231 scopus 로고
    • Extensional gödel functional interpretation
    • Springer Verlag
    • H. Luckhardt. Extensional Gödel Functional Interpretation, volume 306 of Lecture Notes in Mathematics. Springer Verlag, 1973.
    • (1973) Lecture Notes in Mathematics , vol.306
    • Luckhardt, H.1
  • 27
    • 2442550479 scopus 로고    scopus 로고
    • Bounds extracted by Kreisel from ineffective proofs
    • P. Odifreddi, editor. A.K. Peters, Wellesley, MA
    • H. Luckhardt. Bounds extracted by Kreisel from ineffective proofs. In P. Odifreddi, editor, Kreiseliana: About and around Georg Kreisel, pp. 289-300. A.K. Peters, Wellesley, MA, 1996.
    • (1996) Kreiseliana: about and Around Georg Kreisel , pp. 289-300
    • Luckhardt, H.1
  • 28
    • 0003834856 scopus 로고
    • Extracting constructive content from classical proofs
    • Dep.of Comp.Science, Cornell Univ., Ithaca, NY, U.S.A.. PhD thesis
    • C. Murthy. Extracting constructive content from classical proofs. Tech. Report 90-1151, Dep.of Comp.Science, Cornell Univ., Ithaca, NY, U.S.A.,1990. PhD thesis.
    • (1990) Tech. Report , vol.90 , Issue.1151
    • Murthy, C.1
  • 29
    • 14644424669 scopus 로고    scopus 로고
    • Elementary arithmetic
    • May Festschrift for H. Schwichtenberg's 60s
    • G.E. Ostrin and S.S. Wainer. Elementary arithmetic. Annals of Pure, and Applied Logic, 133(1-3):275-292, May 2005. Festschrift for H. Schwichtenberg's 60s.
    • (2005) Annals of Pure, and Applied Logic , vol.133 , Issue.1-3 , pp. 275-292
    • Ostrin, G.E.1    Wainer, S.S.2
  • 30
    • 84944098890 scopus 로고
    • λμ-calculus: An algorithmic interpretation of classical natural deduction
    • Proc. of Log. Prog. and Automatic Reasoning, St. Petersburg. Springer Verlag, Berlin, Heidelberg, New York
    • M. Parigot. λμ-calculus: an algorithmic interpretation of classical natural deduction. In Proc. of Log. Prog. and Automatic Reasoning, St. Petersburg, volume 624 of LNCS, pages 190-201. Springer Verlag, Berlin, Heidelberg, New York, 1992.
    • (1992) LNCS , vol.624 , pp. 190-201
    • Parigot, M.1
  • 32
    • 4243103715 scopus 로고    scopus 로고
    • Getting results from programs extracted from classical proofs
    • C. Raffalli. Getting results from programs extracted from classical proofs. Theoretical Computer Science, 323(1-3):49-70, 2004.
    • (2004) Theoretical Computer Science , vol.323 , Issue.1-3 , pp. 49-70
    • Raffalli, C.1
  • 34
    • 26944461397 scopus 로고    scopus 로고
    • Lecture course on program-extraction from (classical) proofs. Author's page or MINLOG distrib
    • H. Schwichtenberg. Minimal logic for computable functions. Lecture course on program-extraction from (classical) proofs. Author's page or MINLOG distrib. [36].
    • Minimal Logic for Computable Functions , Issue.36
    • Schwichtenberg, H.1
  • 35
    • 26944477989 scopus 로고    scopus 로고
    • Monotone majorizable functionals
    • H. Schwichtenberg. Monotone majorizable functionals. Studia Logica, 62:283-289, 1999.
    • (1999) Studia Logica , vol.62 , pp. 283-289
    • Schwichtenberg, H.1
  • 36
    • 26944496611 scopus 로고    scopus 로고
    • Proof- And program-extraction system MINLOG
    • H. Schwichtenberg and Others. Proof- and program-extraction system MINLOG. Free code and documentation at http://www.minlog-system.de.
    • Free Code and Documentation
    • Schwichtenberg, H.1
  • 38
    • 0003315261 scopus 로고
    • Metamathematical investigation of intuitionistic arithmetic and analysis
    • Springer-Verlag
    • A.S. Troelstra, editor. Metamathematical investigation of intuitionistic Arithmetic and Analysis, volume 344 of Lecture Notes in Mathematics. Springer-Verlag, 1973.
    • (1973) Lecture Notes in Mathematics , vol.344
    • Troelstra, A.S.1


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