A Higher-Order Logic Programming Language with Constraints

  • Javier Leach
  • Susana Nieva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2024)


We present a framework for the combination of Constraint Logic Programming (tiCLP) and higher-order Hereditary Harrop Formulas (tihoHH). Our aim is to improve the expressiveness of traditional Logic Programming with the benefits of both fields: tiCLP and tihoHH. The result is denoted higher-order Hereditary Harrop Formulas with Constraints (hoHH(C)). The syntax of hoHH is introduced using lambda-terms and is enriched with a basic constraint system. Then an intuitionistic sequent calculus is defined for this combined logic, that preserves the property of an abstract logic programming language. In addition, a sound and complete procedure for goal solving is presented as a transformation system that explains the operational semantics.


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  1. 1.
    Clark, K.L., Negation as Failure, in: H. Gallaire and J. Minker (eds.), Logic and Databases 293–322, Plenum Press, 1978.Google Scholar
  2. 2.
    Felty, A., Implementing Tactics and Tacticals in a Higher-Order Logic Programming Language, Journal of Automated Reasoning 11(1):43–81 (1993).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Hanus, M. (ed.), Curry: an Integrated Functional Logic Language, Version 0.7, February 2, 2000. Available at http://www.informatik.uni-kiel.de/~curry/.
  4. 4.
    Jaffar, J. and Maher, M.J., Constraint Logic Programming: A Survey, Journal of Logic Programming 19(20):503–581 (1994).CrossRefMathSciNetGoogle Scholar
  5. 5.
    Leach, J., Nieva, S. and Rodrìguez-Artalejo, M., Constraint Logic Programming with Hereditary Harrop Formulas in: J. Maluszyʼnnski (ed.), ILPS’97 307–321, MIT Press, 1997.Google Scholar
  6. 6.
    Michaylov, S., Pfenning, F., Higher-Order Logic Programming as Constraint Logic Programming, in: Proc. of First Workshop on Principles and Practice of Constraint Programming, 221–229, Brown University, 1993.Google Scholar
  7. 7.
    Miller, D., A Logical Analysis of Modules in Logic Programming, Journal of Logic Programming 6(1,2):79–108 (1989).CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Miller, D., Nadathur, G., Pfenning, F. and Scedrov, A., Uniform Proofs as a Foundation for Logic Programming, Annals of Pure and Applied Logic 51:125–157 (1991).CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Miller, D., Nadathur, G. and Scedrov, A., Hereditary Harrop Formulas and Uniform Proof Systems, in: D. Gries (ed.), LICS’87 98–105, IEEE Comp. Soc. Press, 1987.Google Scholar
  10. 10.
    Nadathur, G. and Miller, D., An Overview of λ-Prolog, in: K.A. Bowen and R. A. Kowalski (eds.), ICLP’88 810–827, MIT Press, 1988.Google Scholar
  11. 11.
    Nerode, A., Some Lectures on Intuitionistic Logic, in: S. Homer, A. Nerode, R.A. Platek, G.E. Sacks, A. Scedrov (eds.), LCS’88 12–59, Springer LNM 1429, 1988.Google Scholar
  12. 12.
    Saraswat, V., The Category of Constraint Systems is Cartesian Closed, in: LICS’92 341–345, IEEE Comp. Soc. Press, 1992.Google Scholar
  13. 13.
    Tarski, A., A Decision Method for Elementary Algebra and Geometry, University of California Press, 1951.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Javier Leach
    • 1
  • Susana Nieva
    • 1
  1. 1.Dpto. de Sistemas Informáticos y ProgramaciónUniv. Complutense de MadridSpain

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