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Operational semantics of constraint logic programming over finite domains

  • Pascal van Hentenryck
  • Yves Deville
Session: Constraint Logic Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 528)

Abstract

Although the Constraint Logic Programming (CLP) theory [7] is an elegant generalization of the LP theory, it has some difficulties in capturing some operational aspects of actual CLP languages (e.g. [8, 6, 3, 12, 18, 19]). A difficulty comes from the intentional incompleteness of some constraint-solvers. Some constraints are simply delayed until they can be decided by the constraint-solver. Others are approximated, providing an active pruning of the search space without being actually decided by the constraint-solver.

This paper presents an extension of the Ask & Tell framework [14] in order to give a simple and precise operational semantics to (a class of) CLP languages with an incomplete constraint-solver. The basic idea is to identify a subset of the constraints (the basic constraints) for which there exists an efficient and complete constraint-solver. Non-basic constraints are handled through two new combinators, relaxed ask and relaxed tell, that are in fact relaxations of the standard ask and tell.

The extended framework is instantiated to CLP on finite domains, say CLP(F) [16, 6]. Arc-consistency is shown to be an efficient and complete constraint-solver for basic constraints. We also present how non-basic constraints can be approximated in CLP(F). The resulting semantics precisely describes the operational semantics of the language, enables the programmer to reason easily about the correctness and efficiency of his programs, and clarifies the links of CLP(F) with the CLP and Ask & Tell theories.

It is believed that the approach can be used as well to endow other CLP languages such as BNR-Prolog [12], CLP(Σ*) [19], and parts of Trilogy [18] with a precise operational semantics.

Keywords

Operational Semantic Relaxation Function Unary Constraint Finite Domain Binary Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    W Buttner and al. A General Framework for Constraint Handling in Prolog. Technical report, Siemens Technical Report, 1988.Google Scholar
  2. [2]
    A. Colmerauer. PROLOG II: Manuel de Reference et Modele Theorique. Technical report, GIA-Faculte de Sciences de Luminy, March 1982.Google Scholar
  3. [3]
    A. Colmerauer. An Introduction to Prolog III. CACM, 28(4):412–418, 1990.Google Scholar
  4. [4]
    Y. Deville and P. Van Hentenryck. An Efficient Arc-Consistency Algorithm for a Class of CSP Problems. Technical Report CS-90-36, CS Department, Brown University, 1990.Google Scholar
  5. [5]
    M. Dincbas, H. Simonis, and P. Van Hentenryck. Extending Equation Solving and Constraint Handling in Logic Programming. In MCC, editor, Colloquium on Resolution of Equations in Algebraic Structures (CREAS), Texas, May 1987.Google Scholar
  6. [6]
    M. Dincbas, P. Van Hentenryck, H. Simonis, A. Aggoun, T. Graf, and F. Berthier. The Constraint Logic Programming Language CHIP. In FGCS-88, Tokyo, Japan, 1988.Google Scholar
  7. [7]
    J. Jaffar and J-L. Lassez. Constraint Logic Programming. In POPL-87, Munich, FRG, 1987.Google Scholar
  8. [8]
    J. Jaffar and S. Michaylov. Methodology and Implementation of a CLP System. In ICLP-87, Melbourne, Australia, May 1987.Google Scholar
  9. [9]
    A.K. Mackworth. Consistency in Networks of Relations. AI Journal, 8(1):99–118, 1977.Google Scholar
  10. [10]
    R. Mohr and T.C. Henderson. Arc and Path Consistency Revisited. AI Journal, 28:225–233, 1986.Google Scholar
  11. [11]
    L. Naish. Negation and Control in Prolog. PhD thesis, University of Melbourne, Australia, 1985.Google Scholar
  12. [12]
    W. Older and A. Vellino. Extending Prolog with Constraint Arithmetics on Real Intervals. In Canadian Conference on Computer & Electrical Engineering, Ottawa, 1990.Google Scholar
  13. [13]
    G.D. Plotkin. A Structural Approach to Operational Semantics. Technical Report DAIMI FN-19, CS Department, University of Aarhus, 1981.Google Scholar
  14. [14]
    V.A. Saraswat. Concurrent Constraint Programming Languages. PhD thesis, Carnegie-Mellon University, 1989.Google Scholar
  15. [15]
    P. Van Hentenryck. A Framework for Consistency Techniques in Logic Programming. In IJCAI-87, Milan, Italy, August 1987.Google Scholar
  16. [16]
    P. Van Hentenryck. Constraint Satisfaction in Logic Programming. Logic Programming Series, The MIT Press, Cambridge, MA, 1989.Google Scholar
  17. [17]
    P. Van Hentenryck and Y. Deville. A new Logical Connective and its Application to Constraint Logic Programming. Technical Report CS-90-24, CS Department, Brown University, 1990.Google Scholar
  18. [18]
    P. Voda. The Constraint Language Trilogy: Semantics and Computations. Technical report, Complete Logic Systems, North Vancouver, BC, Canada, 1988.Google Scholar
  19. [19]
    C. Walinsky. CLP(Σ*). In ICLP-89, Lisbon, Portugal, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Pascal van Hentenryck
    • 1
  • Yves Deville
    • 2
  1. 1.Brown UniversityProvidence
  2. 2.University of NamurNamurBelgium

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