Skip to main content
SpringerLink
Log in

Directional type checking of logic programs

  • Conference paper
  • First Online:
Static Analysis (SAS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 864))

Included in the following conference series:

Abstract

We present an algorithm for automatic type checking of logic programs with respect to directional types that describe both the structure of terms and the directionality of predicates. The type checking problem is reduced to a decision problem on systems of inclusion constraints over set expressions. The solution to this decision problem provides an effective type checking procedure. We discuss some properties of the reduction algorithm, and present a proof of correctness. We present lower bound complexity results for the general type checking problem where types are given as arbitrary set expressions, as well as for the restrictive class of discriminative directional types. For discriminative directional types the type checking procedure is shown to be sound and complete.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. R. Apt and Sandro Etalle. On the Unification-free Prolog Programs. In Proceedings of the 1993 Conference on Mathematical Foundations of Computer Science, June 1993.

    Google Scholar 

  2. A. Aiken, D. Kozen, and E. Wimmers. Decidability of systems of set constraints with negative constraints. Technical Report 93-1362, Cornell University, June 1993.

    Google Scholar 

  3. K. R. Apt. Declarative Programming in Prolog. In D. Miller, editor, Proceedings of the International Logic Programming Symposium. MIT Press, November 1993.

    Google Scholar 

  4. K. R. Apt. Program Verification and Prolog. Technical report, CWI Amsterdam, January 1994.

    Google Scholar 

  5. A. Aiken and E. Wimmers. Solving Systems of Set Constraints. In Symposium on Logic in Computer Science, pages 329–340, June 1992.

    Google Scholar 

  6. A. Bossi and N. Cocco. Verifying Correctness of Logic Programs. In Proceedings of TAPSOFT 89, pages 96–110. LNCS 352, Springer Lecture Notes in Computer Science, 1989.

    Google Scholar 

  7. L. Bachmair, H. Ganzinger, and U. Waldmann. Set constraints are the monadic class. In Symposium on Logic in Computer Science, pages 75–83, June 1993.

    Google Scholar 

  8. F. Bronsard, T. K. Lakshman, and U. S. Reddy. A Directional Type System for Prolog: Unifying notions of Types and Directionality. Technical report UIUC-DCS, University of Illinois at Urbana-Champaign, December 1992.

    Google Scholar 

  9. F. Bronsard, T. K. Lakshman, and U. S. Reddy. A framework of directionality for proving termination of logic programs. In K. R. Apt, editor, Logic Programming: Proceedings of the 1992 Joint International Conference and Symposium, pages 321–335, November 1992.

    Google Scholar 

  10. M. Codish and B. Demoen. Deriving Type Dependencies for Logic Programs using Multiple Incarnations of PROP. In Proceedings of the Ist International Static Analysis Symposium. Springer Lecture Notes in Computer Science, September 1994. To appear.

    Google Scholar 

  11. P. De Boeck and B. Le Charlier. Mechanical Transformation of Logic Definitions augmented with Type Information into Prolog Procedures: Some Experiments. In Proceedings of (LOPSTR'93), July 1993.

    Google Scholar 

  12. S. K. Debray. Static inference of modes and data dependencies in logic programs. ACM Transactions on Programming Languages and Systems, 11(3):418–450, July 1989.

    Article  Google Scholar 

  13. Y. Deville. Logic Programming: Systematic Program Development. Addison Wesley, 1990.

    Google Scholar 

  14. P. De Boeck, and B. Le Charlier. Static type analysis of Prolog procedures for ensuring correctness. In Proceedings of Programming Language Implementation and Logic Programming (PLILP'90), volume 456 of Lecture Notes in Computer Science, pages 222–237, Linköping, Sweden, August 1990.

    Google Scholar 

  15. S. K. Debray, and P. Mishra. Denotational and operational semantics for Prolog. Journal of Logic Programming, 5(1):61–91, 1988.

    MathSciNet  Google Scholar 

  16. W. Drabent, and M. Małusziński. Inductive assertion method for logic programs. Theoretical Computer Science, 59:207–230, 1988.

    Article  Google Scholar 

  17. P. W. Dart, and J. Zobel. A Regular Type Language for Logic Programs, chapter in Types in Logic Programming, Frank Pfenning, editor, pages 157–187. MIT Press, Cambridge, MA, 1992.

    Google Scholar 

  18. T. Früwirth, E. Shapiro, M. Vardi, and E. Yardeni. Logic programs as types for logic programs. In Symposium on Logic in Computer Science, pages 300–309, July 1991.

    Google Scholar 

  19. S. Gregory. Parallel Logic Programming in PARLOG. Addison-Wesley, 1987.

    Google Scholar 

  20. R. Gilleron, S. Tison, and M. Tommasi. Solving Systems of Set Constraints with Negated Subset Relationships. In Foundations of Computer Science, pages 372–380, November 1993.

    Google Scholar 

  21. N. Heintze. Practical Aspects of Set Based Analysis. In K. R. Apt, editor, Logic Programming: Proceedings of the 1992 Joint International Conference and Symposium, pages 765–782. MIT Press, November 1992.

    Google Scholar 

  22. N. Heintze. Set Based Program Analysis. PhD thesis, Carnegie Mellon University, 1992.

    Google Scholar 

  23. Nevin Heintze. Set Constraints in Program Analysis. In Workshop on Global Compilation, Vancouver, CA, October 1993. Proceedings of the International Logic Programming Symposium.

    Google Scholar 

  24. N. Heintze and J. Jaffar. A Finite Presentation Theorem for approximating logic programs. In Proceedings of the Annual ACM Symposium on Principles of Programming Languages, pages 197–209, January 1990.

    Google Scholar 

  25. N. Heintze and J. Jaffar. A decision procedure for a class of set constraints. In Symposium on Logic in Computer Science, pages 42–51, June 1990.

    Google Scholar 

  26. N. Heintze, and J. Jaffar. Semantic Types for Logic Programs, chapter in Types in Logic Programming, Frank Pfenning, editor, pages 141–155. MIT Press, Cambridge, MA, 1992.

    Google Scholar 

  27. J. Henrard and B. Le Charlier. FOLON: An environment for Declarative Construction of Logic Programs. In M. Bruynooghe and M. Wirsing, editors, Proceedings of the Fourth International Workshop on Programming Language Implementation and Logic Programming (PLILP'92), volume 631 of Lecture Notes in Computer Science. Springer-Verlag, August 1992.

    Google Scholar 

  28. M. Hermenegiklo, R. Warren, and S. K. Debray. Global flow analysis as a practical compilation tool. Journal of Logic Programming, 13:349–366, 1992.

    Article  Google Scholar 

  29. D. Jacobs. A Pragmatic View of Types for Logic Programs, chapter in Types in Logic Programming, Frank Pfenning, editor, pages 217–228. MIT Press, Cambridge, MA, 1992.

    Google Scholar 

  30. G. Janssens, and M. Bruynooghe. Deriving descriptions of possible values of program variables by means of abstract interpretation. Journal of Logic Programming, 13(2):205–258, July 1992.

    Article  Google Scholar 

  31. D. Kozen. Lower bounds for natural proof systems. In IEEE Symposium on the Foundations of Computer Science, pages 254–266. IEEE Computer Society, 1977.

    Google Scholar 

  32. P. Mishra. Towards a theory of types in PROLOG. In Proceedings of the First IEEE Symposium in Logic Programming, pages 289–298, 1984.

    Google Scholar 

  33. P. Mishra and U. S. Reddy. Declaration-free type checking. In Proceedings of the Annual ACM Symposium on Principles of Programming Languages, pages 7–21, January 1985.

    Google Scholar 

  34. Lee Naish. Negation and control in Prolog. Lecture Notes in Computer Science 238. Springer-Verlag, 1986.

    Google Scholar 

  35. D. Pedreschi. A Proof Method for Run-time Properties of Prolog Programs. In Proceedings of the International Conference on Logic Programming, MIT Press, June 1994. To appear.

    Google Scholar 

  36. Yann Rouzaud and Lan Nguyen-Phoung. Integrating Modes and Subtypes into a Prolog Type-Checker. In K. R. Apt, editor, Logic Programming: Proceedings of the 1992 Joint International Conference and Symposium, pages 85–97. MIT Press, November 1992.

    Google Scholar 

  37. H. Seidl. Deciding equivalence of finite tree automata. SIAM Journal of Computing, 19(3):424–437, June 1990.

    Article  Google Scholar 

  38. E. Shapiro. The family of concurrent logic programming languages. ACM Computing Surveys, 21(3):412–510, May 1989.

    Article  Google Scholar 

  39. Z. Somogyi. A system of precise modes for logic programs. In Proceedings of the International Conference on Logic Programming, pages 769–787, June 1987.

    Google Scholar 

  40. J. L. Zachary, and K. Yelick. Moded Type Systems to Support Abstraction, chapter in Types in Logic Programming, Frank Pfenning, editor, pages 217–228. MIT Press, Cambridge, MA, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Division, University of California, Berkeley, 571 Evans, 94720, Berkeley, CA

    Alexander Aiken

  2. Department of Computer Science, University of Illinois at Urbana-Champaign, 1304 W. Springfield Ave, 61801, Urbana, IL

    T. K. Lakshman

Authors
  1. Alexander Aiken
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. K. Lakshman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Baudouin Le Charlier

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Aiken, A., Lakshman, T.K. (1994). Directional type checking of logic programs. In: Le Charlier, B. (eds) Static Analysis. SAS 1994. Lecture Notes in Computer Science, vol 864. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58485-4_32

Download citation

  • DOI: https://doi.org/10.1007/3-540-58485-4_32

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58485-8

  • Online ISBN: 978-3-540-49005-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation