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A Parameterized Unfold/Fold Transformation Framework for Definite Logic Programs

  • Abhik Roychoudhury
  • K. Narayan Kumar
  • C. R. Ramakrishnan
  • I. V. Ramakrishnan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1702)

Abstract

Given a program P, an unfold/fold program transformation system derives a sequence of programs P = P 0, P 1, ..., P n , such that P i + 1 is derived from P i by application of either an unfolding or a folding step. Existing unfold/fold transformation systems for definite logic programs differ from one another mainly in the kind of folding transformations they permit at each step. Some allow folding using a single (possibly recursive) clause while others permit folding using multiple non-recursive clauses. However, none allow folding using multiple recursive clauses that are drawn from some previous program in the transformation sequence. In this paper we develop a parameterized framework for unfold/fold transformations by suitably abstracting and extending the proofs of existing transformation systems. Various existing unfold/fold transformation systems can be obtained by instantiating the parameters of the framework. This framework enables us to not only understand the relative strengths and limitations of these systems but also construct new transformation systems. Specifically we present a more general transformation system that permits folding using multiple recursive clauses that can be drawn from any previous program in the transformation sequence. This new transformation system is also obtained by instantiating our parameterized framework.

Keywords

Logic Program Transformation System Weakly Measure Transformation Sequence Total Correctness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aravindan, C., Dung, P.M.: On the correctness of unfold/fold transformations of normal and extended logic programs. Journal of Logic Programming, 295–322 (1995)Google Scholar
  2. 2.
    Bossi, A., Cocco, N., Dulli, S.: A method of specializing logic programs. ACM TOPLAS, 253–302 (1990)Google Scholar
  3. 3.
    Boulanger, D., Bruynooghe, M.: Deriving unfold/fold transformations of logic programs using extended OLDT-based abstract interpretation. Journal of Symbolic Computation, 495–521 (1993)Google Scholar
  4. 4.
    Cui, B., Dong, Y., Du, X., Narayan Kumar, K., Ramakrishnan, C.R., Ramakr, I.V.: Logic programming and model checking. In: Palamidessi, C., Meinke, K., Glaser, H. (eds.) ALP 1998 and PLILP 1998. LNCS, vol. 1490, pp. 1–20. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Etalle, S., Gabrielli, M., Meo, M.C.: Unfold/fold transformations of CCP programs. In: Proceedings of CONCUR (1998)Google Scholar
  6. 6.
    Francesco, N.D., Santone, A.: A transformation system for concurrent processes. Acta Informatica 35(12), 1037–1073 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gergatsoulis, M., Katzouraki, M.: Unfold/fold transformations for definite clause programs. In: Penjam, J. (ed.) PLILP 1994. LNCS, vol. 844, Springer, Heidelberg (1994)Google Scholar
  8. 8.
    Kanamori, T., Fujita, H.: Unfold/fold transformation of logic programs with counters. USA-Japan Seminar on Logics of Programs (1987)Google Scholar
  9. 9.
    Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1993)zbMATHGoogle Scholar
  10. 10.
    Maher, M.J.: Correctness of a logic program transformation system. Technical report, IBM T.J. Watson Research Center (1987)Google Scholar
  11. 11.
    Pettorossi, A., Proietti, M. (eds.): Transformation of logic programs. Handbook of Logic in Artificial Intelligence, vol. 5, pp. 697–787. Oxford University Press, Oxford (1998)Google Scholar
  12. 12.
    Pettorossi, A., Proietti, M., Renault, S.: Reducing nondeterminism while specializing logic programs. Proceedings of POPL, 414–427 (1997)Google Scholar
  13. 13.
    Roychoudhury, A., Narayan Kumar, K., Ramakrishnan, C.R., Ramakrishnan, I.V.: A generalized unfold/fold transformation system for definite logic programs. Technical Report 98/37, Dept. of Computer Science, SUNY Stony Brook (1998)Google Scholar
  14. 14.
    Roychoudhury, A., Narayan Kumar, K., Ramakrishnan, C.R., Ramakrishnan, I.V.: Proofs by program transformations. Accepted for LOPSTR (1999)Google Scholar
  15. 15.
    Roychoudhury, A., Narayan Kumar, K., Ramakrishnan, I.V.: Beyond TamakiSato style unfold/fold transformations for normal logic programs. Technical Report 99/21, Dept. of Computer Science, SUNY Stony Brook (1999)Google Scholar
  16. 16.
    Roychoudhury, A., Ramakrishnan, C.R., Ramakrishnan, I.V., Smolka, S.A.: Tabulation based Induction proofs with applications to Automated Verification. In: Workshop on Tabulation in Parsing and Deduction, pp. 83–88 (1998)Google Scholar
  17. 17.
    Sands, D.: Total correctness by local improvement in the transformation of functional programs. ACM TOPLAS 18(2), 175–234 (1996)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Seki, H.: Unfold/fold transformation of stratified programs. Theoretical Computer Science, 107–139 (1991)Google Scholar
  19. 19.
    Seki, H.: Unfold/fold transformation of general logic programs for well-founded semantics. Journal of Logic Programming, 5–23 (1993)Google Scholar
  20. 20.
    Tamaki, H., Sato, T.: Unfold/fold transformations of logic programs. In: Proceedings of International Conference on Logic Programming, pp. 127–138 (1984)Google Scholar
  21. 21.
    Tamaki, H., Sato, T.: A generalized correctness proof of the unfold/ fold logic program transformation. Technical report, Ibaraki University, Japan (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Abhik Roychoudhury
    • 1
  • K. Narayan Kumar
    • 1
    • 2
  • C. R. Ramakrishnan
    • 1
  • I. V. Ramakrishnan
    • 1
  1. 1.Dept. of Computer ScienceSUNY Stony BrookStony BrookUSA
  2. 2.Chennai Mathematical InstituteChennaiIndia

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