Quantifier elimination for constraint logic programming

  • Authors:

  • Thomas Sturm

  • Affiliations:

  • FMI, Universität Passau, Passau, Germany

  • Venue:
  • CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
  • Year:
  • 2005

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Abstract

We present an extension of constraint logic programming, where the admissible constraints are arbitrary first-order formulas over various domains: real numbers with ordering, linear constraints over p-adic numbers, complex numbers, linear constraints over the integers with ordering and congruences (parametric Presburger Arithmetic), quantified propositional calculus (parametric qsat), term algebras. Our arithmetic is always exact. For ℝ are ℂ there are no restrictions on the polynomial degree of admissible constraints. Constraint solving is realized by effective quantifier elimination. We have implemented our methods in our system clp(rl). A number of computation examples with clp(rl) are given in order to illustrate the conceptual generalizations provided by our approach and to demonstrate its feasibility.