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Logic program semantics for programming with equations

  • Joxan Jaffar
  • Peter J. Stuckey
Session 3b: Theory And Semantics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 225)

Abstract

We consider logic programming-like systems which are based on solving equations in a given structure as opposed to obtaining unifiers. While such systems are elegant from an operational point of view, a logical interpretation of the programs is not always apparent. In this paper, we restrict ourselves to the class of structures ℜ satisfying the eliminable variable property: we can construct an explicit definition, in the form of one system of equations, of the set of solutions to any ℜ-solvable system of equations. Correspondingly, we consider only the class of equality theories E such that every E-unifiable system of equations has an E-mgu. We then state three properties which provide basic relationships between E and ℜ. We prove that their satisfaction establishes an equivalence between a program considered as an equation solving engine (with respect to a structure) and the program considered as a logic program (with respect to a corresponding equality theory). A logical basis for these programs is thus given.

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6. References

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    A. Colmerauer, "Equations and Inequations on Finite and Infinite Trees", Proc. 2nd. Int. Conf. on Fifth Generation Computer Systems, Tokyo, pp 85–99, November 1984.Google Scholar
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    J. Jaffar, J-L. Lassez and M.J. Maher, "A Logical Foundation for PROLOG II", Technical Report 44, Dept. of Computer Science, Monash University, December 1984. [Revised November 1985]Google Scholar
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    J. Jaffar, J-L. Lassez and M.J. Maher, "A Logic Programming Language Scheme", in Logic Programming: Relations, Functions and Equations, D. DeGroot and G. Lindstrom (Eds), Prentice-Hall, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Joxan Jaffar
    • 1
  • Peter J. Stuckey
    • 1
  1. 1.Department of Computer ScienceMonash UniversityVictoriaAustralia

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