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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
K. L. Clark. Negation as failure. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 293–322. Plenum Press, 1978.
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.
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.
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.
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.
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.
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.
J.W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 2nd ed., 1987.
A. Mycroft and R. A. O'Keefe. A polymorphic type system for Prolog. Artificial Intelligence, 23:295–307, 1984.
G. Smolka. Logic Programming over Polymorphically Order-Sorted Types. PhD thesis, Universität Kaiserslautern, May 1989.
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.
E. Yardeni, T.W. Frühwirth, and E. Shapiro. Polymorphically typed logic programs. The Weitzmann Institute of Science and the Technical University of Vienna, 1990.
Author information
Authors and Affiliations
Editor information
Rights 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