A Multi-level Approach to Program Synthesis

  • W. Bibel
  • D. Korn
  • C. Kreitz
  • F. Kurucz
  • J. Otten
  • S. Schmitt
  • G. Stolpmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1463)

Abstract

We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at different levels of abstraction. Besides providing an overall view we summarize the individual research results achieved in the course of this development.

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References

  1. 1.
    D. Basin & T. Walsh. A calculus for and termination of rippling. Journal of Automated Reasoning, 16(1–2), pp. 147–180, 1996.MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    J. L. Bates & R. L. Constable. Proofs as programs. ACM Transactions on Programming Languages and Systems, 7(1):113–136, 1985.MATHCrossRefGoogle Scholar
  3. 3.
    J. Van Benthem Correspondence Theory In D. Gabbay & F. Guenther, eds., Handbook of Philosophical Logic, II, pp. 167–247, Reidel, 1984.Google Scholar
  4. 4.
    W. Bibel. On matrices with connections. Journal of the ACM, 28(633–645), 1981.Google Scholar
  5. 5.
    W. Bibel. Automated Theorem Proving. Vieweg Verlag, 1987.Google Scholar
  6. 6.
    W. Bibel. Toward predicative programming. In M. R. Lowry & R. McCartney, eds., Automating Software Design, pp. 405–424, AAAI Press / The MIT Press, 1991.Google Scholar
  7. 7.
    W. Bibel, S. Brüning, U. Egly, T. Rath. Komet. In 12 th Conference on Automated Deduction, LNAI 814, pp. 783–787. Springer Verlag, 1994.Google Scholar
  8. 8.
    W. Bibel, D. Korn, C. Kreitz, S. Schmitt. Problem-oriented applications of automated theorem proving. In J. Calmet & C. Limongelli, eds., Design and Implementation of Symbolic Computation Systems, LNCS 1126, Springer Verlag, pp. 1–21, 1996.Google Scholar
  9. 9.
    A. Bundy, F. van Harmelen, A. Ireland, A. Smaill. Rippling: a heuristic for guiding inductive proofs. ArtiFIcial Intelligence, 1992.Google Scholar
  10. 10.
    R. L. Constable, et. al. Implementing Mathematics with the NuPRL proof development system. Prentice Hall, 1986.Google Scholar
  11. 11.
    M. Davis & H. Putnam. A computing procedure for quantification theory. Journal of the ACM, 7:201–215, 1960.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    M. Davis, G. Logemann, D. Loveland. A machine program for theorem-proving. Communications of the ACM, 5:394–397, 1962.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    M. C. Fitting. First-Order Logic and Automated Theorem Proving. Springer Verlag, 1990.Google Scholar
  14. 14.
    G. Gentzen. Untersuchungen über das logische Schließen. Mathematische Zeitschrift, 39:176–210, 405–431, 1935.CrossRefMathSciNetGoogle Scholar
  15. 15.
    P. Jackson. NuPRL’s Metalanguage ML. Reference Manual and User’s Guide, Cornell University, 1994.Google Scholar
  16. 16.
    P. Jackson. The NuPRL Proof Development System, Version 4.1. Reference Manual and User’s Guide, Cornell University, 1994.Google Scholar
  17. 17.
    D. Korn & C. Kreitz. Deciding intuitionistic propositional logic via translation into classical logic. In W. McCune, ed., 14 th Conference on Automated Deduction, LNAI 1249, pp. 131–145, Springer Verlag, 1997.Google Scholar
  18. 18.
    C. Kreitz. METASYNTHESIS: Deriving Programs that Develop Programs. Thesis for Habilitation, TH Darmstadt, 1992. Forschungsbericht AIDA-93-03.Google Scholar
  19. 19.
    C. Kreitz. Formal mathematics for verifiably correct program synthesis. Journal of the IGPL, 4(1):75–94, 1996.MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    C. Kreitz. Formal reasoning about communication systems I: Embedding ML into type theory. Technical Report TR 97-1637, Cornell University, 1997.Google Scholar
  21. 21.
    C. Kreitz, H. Mantel, J. Otten, S. Schmitt. Connection-Based Proof Construction in Linear Logic. In W. McCune, ed., 14 th Conference on Automated Deduction, LNAI 1249, pp. 207–221, Springer Verlag, 1997.Google Scholar
  22. 22.
    C. Kreitz, J. Otten, S. Schmitt. Guiding Program Development Systems by a Connection Based Proof Strategy. In M. Proietti, ed., 5th International Workshop on Logic Program Synthesis and Transformation, LNCS 1048, pp. 137–151. Springer Verlag, 1996.Google Scholar
  23. 23.
    F. Kurucz. Realisierung verschiedender Induktionsstrategien basierend auf dem Rippling-Kalkül. Diplomarbeit, TH Darmstadt, 1997.Google Scholar
  24. 24.
    R. Letz, J. Schumann, S. Bayerl, W. Bibel. Setheo: A high-performance theorem prover. Journal of Automated Reasoning, 8:183–212, 1992.MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    T. van thanh Liem. Induktion im NuPRL System. Diplomarbeit, TH Darmstadt, 1996.Google Scholar
  26. 26.
    R. C. Moore. Reasoning about Knowledge and Action IJCAI-77, pp 223–227, 1977.Google Scholar
  27. 27.
    H. J. Ohlbach. Semantics-Based Translation Methods for Modal Logics Journal of Logic and Computation, 1(6), pp 691–746, 1991.MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    J. Otten. ileanTAP: An intuitionistic theorem prover. In Didier Galmiche, ed., International Conference TABLEAUX’ 97. LNAI 1227, pp. 307–312, Springer Verlag, 1997.Google Scholar
  29. 29.
    J. Otten. On the advantage of a non-clausal Davis-Putnam procedure. Forschungsbericht AIDA-97-01, TH Darmstadt, 1997.Google Scholar
  30. 30.
    J. Otten & C. Kreitz. A connection based proof method for intuitionistic logic. In P. Baumgartner, R. Hähnle, J. Posegga, eds., 4 th Workshop on Theorem Proving with Analytic Tableaux and Related Methods, LNAI 918, pp. 122–137, Springer Verlag, 1995.Google Scholar
  31. 31.
    J. Otten & C. Kreitz. T-String-Unification: Unifying Prefixes in Non-Classical Proof Methods. In U. Moscato, ed., 5 th Workshop on Theorem Proving with Analytic Tableaux and Related Methods, LNAI 1071, pp. 244–260, Springer Verlag, 1996.Google Scholar
  32. 32.
    J. Otten & C. Kreitz. A Uniform Proof Procedure for Classical and Non-classical Logics. In G. Görz & S. Hölldobler, eds., KI-96: Advances in Artificial Intelligence, LNAI 1137, pp. 307–319. Springer Verlag, 1996.Google Scholar
  33. 33.
    D. Plaisted & S. Greenbaum. A structure-preserving clause form translation. Journal of Symbolic Computation, 2:293–304, 1986.MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    S. Schmitt. Avoiding redundancy in proof reconstruction 1 st International Workshop on Proof Transformation and Presentation, Schloß Dagstuhl, Germany, 1997.Google Scholar
  35. 35.
    S. Schmitt. Building Efficient Conversion Procedures using Proof Knowledge. Technical Report, TH Darmstadt, 1997.Google Scholar
  36. 36.
    S. Schmitt & C. Kreitz. On transforming intuitionistic matrix proofs into standard-sequent proofs. In P. Baumgartner, R. Hähnle, J. Posegga, eds., 4 th Workshop on Theorem Proving with Analytic Tableaux and Related Methods, LNAI 918, pp. 106–121. Springer Verlag, 1995.Google Scholar
  37. 37.
    S. Schmitt & C. Kreitz. Converting non-classical matrix proofs into sequent-style systems. In M. McRobbie & J. Slaney, eds., 13 th Conference on Automated Deduction, LNAI 1104, pp. 418–432. Springer Verlag, 1996.Google Scholar
  38. 38.
    S. Schmitt & C. Kreitz. A uniform procedure for converting non-classical matrix proofs into sequent-style systems. Technical Report AIDA-96-01, TH Darmstadt 1996.Google Scholar
  39. 39.
    D. R. Smith. Structure and design of global search algorithms. Technical Report KES.U.87.12, Kestrel Institute, 1987.Google Scholar
  40. 40.
    D. R. Smith & M. R. Lowry. Algorithm theories and design tactics. Science of Computer Programming, 14(2–3):305–321, 1990.CrossRefMATHMathSciNetGoogle Scholar
  41. 41.
    D. R. Smith & E. A. Parra. Transformational approach to transportation scheduling. 8 th Knowledge-Based Software Engineering Conference, pp. 60–68, 1993.Google Scholar
  42. 42.
    G. Stolpmann. Datentypen und Programmsynthese. Studienarbeit, TH Darmstadt, 1996.Google Scholar
  43. 43.
    G. Stolpmann. Schematische Konstruktion von Globalsuchalgorithmen. Diplomarbeit, TH Darmstadt, 1997.Google Scholar
  44. 44.
    L. Wallen. Automated deduction in nonclassical logic. MIT Press, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • W. Bibel
    • 1
  • D. Korn
    • 1
  • C. Kreitz
    • 2
  • F. Kurucz
    • 1
  • J. Otten
    • 2
  • S. Schmitt
    • 1
  • G. Stolpmann
    • 1
  1. 1.Fachgebiet Intellektik, Fachbereich InformatikDarmstadt University of TechnologyDarmstadtGermany
  2. 2.Department of Computer ScienceCornell UniversityIthacaUSA

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