Skip to main content

The completion of typed logic programs and SLDNF-resolution

  • Conference paper
  • First Online:
Logic Programming and Automated Reasoning (LPAR 1993)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 698))

Abstract

We consider logic programming languages with a parametric type system, first described by Mycroft and O'Keefe, that allows generic polymorphism. It is well known that provided certain conditions hold typed definite logic programs do not go wrong under SLD-resolution. Previous work has looked at how these conditions may be avoided by adding run-time type checking to the SLD-resolution. However, only definite programs have been considered and the program's theory was assumed to be given by the statements of the program and not its completion. This paper establishes results showing that the conditions are also necessary for almost all typed logic programs if the declarative semantics is the completion semantics and the procedural semantics is based on SLDNF-resolution.

The author gratefully acknowledges support from SERC under grant GR/H 79862

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. L. Clark. Negation as failure. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 293–322. Plenum Press, 1978.

    Google Scholar 

  2. R. Dietrich and F. Hagl. A polymorphic type system with subtypes for Prolog. In H. Ganzinger, editor, Proceedings of the 2nd European Symposium on Programming, Nancy, France, pages 79–93. LNCS 300, Springer-Verlag, 1988.

    Google Scholar 

  3. M. Hanus. Horn clause programs with polymorphic types: Semantics and resolution. In J. Diaz and F. Orejas, editors, Proceedings of the Int. Joint Conf. on Theory and Practice of Software Development, Barcelona, Spain, pages 225–240. LNCS 352, Springer-Verlag, 1989.

    Google Scholar 

  4. P.M. Hill and J.W. Lloyd. The Gödel programming language. Technical Report CSTR-92-27, Department of Computer Science, University of Bristol, UK, 1992.

    Google Scholar 

  5. P.M. Hill and R.W. Topor. A semantics for typed logic programs. In F. Pfenning, editor, Types in Logic Programming, pages 1–62. MIT Press, 1992.

    Google Scholar 

  6. M. Kifer and J. Wu. A first-order theory of types and polymorphism in logic programming. Technical Report 90/23, Department of Computer Science, State University of New York at Stony Brook, USA, 1990.

    Google Scholar 

  7. T. K. Lakshman and U.S. Reddy. Typed Prolog: A semantic reconstruction of the Mycroft-O'Keefe type system. In F. Pfenning, editor, Types in Logic Programming. MIT Press, 1991.

    Google Scholar 

  8. J.W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 2nd ed., 1987.

    Google Scholar 

  9. A. Mycroft and R. A. O'Keefe. A polymorphic type system for Prolog. Artificial Intelligence, 23:295–307, 1984.

    MathSciNet  Google Scholar 

  10. G. Smolka. Logic Programming over Polymorphically Order-Sorted Types. PhD thesis, Universität Kaiserslautern, May 1989.

    Google Scholar 

  11. D.A. Wolfram, M.J. Maher, and J-L. Lassez. A unified treatment of resolution strategies for logic programs. In Proceedings of the 2nd Int. Conf. on Logic Programming, Uppsala, Sweden, pages 263–276, 1984.

    Google Scholar 

  12. E. Yardeni, T.W. Frühwirth, and E. Shapiro. Polymorphically typed logic programs. The Weitzmann Institute of Science and the Technical University of Vienna, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Andrei Voronkov

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hill, P.M. (1993). The completion of typed logic programs and SLDNF-resolution. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1993. Lecture Notes in Computer Science, vol 698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56944-8_52

Download citation

  • DOI: https://doi.org/10.1007/3-540-56944-8_52

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56944-2

  • Online ISBN: 978-3-540-47830-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics