Abstract
A direct support for scopes appears to be essential for logic programming languages, in those applications, like meta-programming, needing to distinguish between various levels of reasoning. However, dealing with scoping constructs in a logic programming language notably causes the set of constants to evolve dynamically during the computation, which creates difficulties in defining alternative evaluation strategies to the Top-Down one. We present in this paper a logic programming language of the λ-Prolog family, focusing on this quantificational scoping feature, for which we define a general intuitionistic resolution. This method extends the resolution defined by Robinson for Horn Clauses, and provides a general framework for evaluation strategies, encompassing Top-Down and Bottom-Up resolutions, as well as a basis to enhanced techniques combining goal-directed search and subcomputation sharing.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
C. Beeri and R. Ramakrishnan. On the power of magic. In Proceedings of the 6th Symposium on Principles of Database Systems, pages 269–283, 1987.
Jay Earley. An efficient context-free parsing algorithm. Communications A.C.M., 13(2):92–102, February 1970.
Moreno Falaschi, Giorgio Levi, Maurizio Martelli, and Catuscia Palamidessi. A new declarative semantics for logic languages. In Proceedings of ICLP'88, pages 993–1005, 1988.
Amy Felty. Specifying theorem provers in a higher-order logic programming language. In E. Lusk and R. Overbeek, editors, 9th International Conference on Automated Deduction. Springer Verlag, May 1988.
Gérard Huet. A unification algorithm for typed λ-calculus. Theoretical Computer Science, 1:27–57, 1975.
Alain Hui Bon Hoa. A bottom-up interpreter for a higher-order logic programming language. In Proceedings of PLILP 92. Spinger Verlag, August 1992.
Alain Hui Bon Hoa. Some kind of magic for a restriction of 1-lambda. In Dale Miller, editor, Proceedings of the 1992 λProlog Workshop, July 1992.
Robert Kowalski. Predicate logic as a programming language. In Proceedings of the IFIP 74 Congress, pages 569–574. North-Holland, 1974.
Bernard Lang. Complete evaluation of Horn Clauses: an automata theoretic approach. Research Report 813, INRIA, November 1988.
Maurizio Martelli, Allessandro Messora, and Catuscia Palamidessi. Fixpoint semantics of L λ. submitted to MFCS'94.
Dale Miller. A logic programming language with lambda-abstraction, function variables, and simple unification. Journal of Logic and Computation, 1:497–536, 1991.
Dale Miller. Unification under a mixed prefix. Journal of Symbolic Computation, 11, 1992.
Dale Miller and Gopalan Nadathur. A logic programming approach to manipulating formulas and programs. In Proceedings of the 4th Symposium on Logic Programming, pages 379–388. IEEE Press, 1987.
Dale Miller, Gopalan Nadathur, Frank Pfenning, and Andre Scedrov. Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic, 51:125–157, 1991.
Gopalan Nadathur. A proof procedure for the logic of Hereditary Harrop formulas. to appear in the Journal of Automated Reasoning.
Gopalan Nadathur. A Higher-Order Logic as the basis for Logic Programming. PhD thesis, University of Pennsylvania, 1987.
Gopalan Nadathur and Bharat Jarayaman. Implementation techniques for scoping constructs in logic programming. In Koichi Furukawa, editor, Proceedings of the Eigth International Conference on Logic Programming, pages 871–886, 1991.
Remo Pareschi and Dale Miller. Extending definite clause grammars with scoping constructs. In Proceedings of the 7th International Conference on Logic Programming, pages 373–389, 1990.
Lawrence C. Paulson. The foundation of a generic theorem prover. Journal of Automated Reasoning, 3:363–397, September 1989.
Fernando C. N. Pereira. Semantic interpretation as higher-order deduction. In Springer-Verlag, editor, Lecture Notes in Artificial Intelligence, pages 78–96, 1990.
Frank Pfenning. Elf: A language for logic definition and verified metaprogramming. In Fourth Annual Symposium on Logic in Computer Science, pages 313–321, Monterey, CA, June 1989.
H. Tamaki and T. Sato. OLD-resolution with tabulation. In E. Shapiro, editor, Proc. of Third Int. Conf. on Logic Programming, pages 84–98, London, 1986. Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hoa, A.H.B. (1994). Intuitionistic resolution for a logic programming language with scoping constructs. In: Hagiya, M., Mitchell, J.C. (eds) Theoretical Aspects of Computer Software. TACS 1994. Lecture Notes in Computer Science, vol 789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57887-0_93
Download citation
DOI: https://doi.org/10.1007/3-540-57887-0_93
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57887-1
Online ISBN: 978-3-540-48383-0
eBook Packages: Springer Book Archive