Advertisement

Mutual Exclusion by Interpolation

  • Jael Kriener
  • Andy King
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7294)

Abstract

The question of what constraints must hold for a predicate to behave as a (partial) function, is key to understanding the behaviour of a logic program. It has been shown how this question can be answered by combining backward analysis, a form of analysis that propagates determinacy requirements against the control flow, with a component for deriving so-called mutual exclusion conditions. The latter infers conditions sufficient to ensure that if one clause yields an answer then another cannot. This paper addresses the challenge of how to compute these conditions by showing that this problem can be reformulated as that of vertex enumeration. Whilst directly applicable in logic programming, the method might well also find application in reasoning about type classes.

Keywords

Logic Program Logic Programming Linear Inequality Type Class Mutual Exclusion 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Lu, L., King, A.: Determinacy Inference for Logic Programs. In: Sagiv, M. (ed.) ESOP 2005. LNCS, vol. 3444, pp. 108–123. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Kriener, J., King, A.: RedAlert: Determinacy Inference for Prolog. TPLP 11, 537–553 (2011)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Bossi, A., Cocco, N., Fabris, M.: Norms on Terms and their use in Proving Universal Termination of a Logic Program. TCS 124, 297–328 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Martin, J.C., King, A., Soper, P.: Typed Norms for Typed Logic Programs. In: Gallagher, J.P. (ed.) LOPSTR 1996. LNCS, vol. 1207, pp. 224–238. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    Weispfenning, V.: The Complexity of Linear Problems in Fields. Journal of Symbolic Computation 5, 3–27 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Craig, W.: Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory. J. Symb. Log. 22, 269–285 (1957)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Weissenbacher, G.: Program Analysis with Interpolants. PhD thesis, Magdalen College (2010), http://ora.ouls.ox.ac.uk/objects/uuid:6987de8b-92c2-4309-b762-f0b0b9a165e6
  8. 8.
    Krajíček, J.: Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic. J. Symb. Log. 62, 457–486 (1997)zbMATHCrossRefGoogle Scholar
  9. 9.
    Farkas, J.: Theorie der einfachen Ungleichungen. Journal für die Reine und Angewandte Mathematik 124, 1–27 (1902)Google Scholar
  10. 10.
    Avis, D.: lrs: A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm. In: Kalai, G., Ziegler, G.M. (eds.) Polytopes - Combinatorics and Computation, pp. 177–198. Birkhauser-Verlag (2000)Google Scholar
  11. 11.
    Goodman, J.E., O’Rourke, J. (eds.): Handbook of Discrete and Computational Geometry. CRC Press (2004)Google Scholar
  12. 12.
    Read, R.C.: Everyone a Winner. Annals of Discrete Mathematics 2, 107–120 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Peyton-Jones, S., Jones, M., Meijer, E.: Type Classes: an exploration of the design space. In: ACM SIGPLAN Haskell Workshop (1997)Google Scholar
  14. 14.
    Morris, J.G., Jones, M.P.: Instance Chains: Type Class Programming Without Overlapping Instances. In: Hudak, P., Weirich, S. (eds.) ICFP, pp. 375–386. ACM (2010)Google Scholar
  15. 15.
    The GHC Team: The Glorious Glasgow Haskell Compilation System User’s Guide, Version 7.2.1 (2011), http://www.haskell.org/ghc/docs/latest/html/users_guide
  16. 16.
    O’Keefe, R.A.: The Craft of Prolog. MIT Press (1990)Google Scholar
  17. 17.
    King, A., Lu, L.: Forward versus Backward Verification of Logic Programs. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 315–330. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Kovács, L., Voronkov, A.: Interpolation and Symbol Elimination. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 199–213. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Ziegler, G.M.: Lectures on Polytopes. Springer, New York (1995)Google Scholar
  20. 20.
    Bertsimas, D., Tsitsiklis, J.: Introduction to Linear Optimization, 1st edn. Athena Scientific (1997)Google Scholar
  21. 21.
    Avis, D., Fukuda, K.: Reverse search for enumeration. Discrete Applied Mathematics 65, 21–46 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Benoy, F., King, A.: Inferring Argument Size Relationships with CLP(R). In: Gallagher, J.P. (ed.) LOPSTR 1996. LNCS, vol. 1207, pp. 204–223. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  23. 23.
    Miné, A.: The Octagon Abstract Domain. HOSC 19, 31–100 (2006)zbMATHGoogle Scholar
  24. 24.
    Sozeau, M.: A New Look at Generalized Rewriting in Type Theory. Journal of Formalized Reasoning 2, 41–62 (2009)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Sahlin, D.: Determinacy Analysis for Full Prolog. In: Symposium on Partial Evaluation and Semantics-Based Program Manipulation, pp. 23–30. ACM (1991)Google Scholar
  26. 26.
    Mogensen, T.Æ.: A Semantics-Based Determinacy Analysis for Prolog with Cut. In: Bjorner, D., Broy, M., Pottosin, I.V. (eds.) PSI 1996. LNCS, vol. 1181, pp. 374–385. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  27. 27.
    Dawson, S., Ramakrishnan, C.R., Ramakrishnan, I.V., Sekar, R.C.: Extracting Determinacy in Logic Programs. In: Proceedings of the Tenth International Conference on Logic Programming, pp. 424–438. MIT Press (1993)Google Scholar
  28. 28.
    López-García, P., Bueno, F., Hermenegildo, M.V.: Automatic Inference of Determinacy and Mutual Exclusion for Logic Programs Using Mode and Type Analyses. New Generation Computing 28, 177–206 (2010)zbMATHCrossRefGoogle Scholar
  29. 29.
    McMillan, K.L.: Applications of Craig Interpolants in Model Checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 1–12. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  30. 30.
    Rybalchenko, A., Sofronie-Stokkermans, V.: Constraint solving for interpolation. Journal of Symbolic Computation 45, 1212–1233 (2010)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jael Kriener
    • 1
  • Andy King
    • 1
  1. 1.University of KentCanterburyUK

Personalised recommendations