Solving first-order constraints in the theory of the evaluated trees

Authors:
Thi-Bich-Hanh Dao;Khalil Djelloul
Affiliations:
Laboratoire d'Informatique Fondamentale d'Orléans, France;Faculty of Computer Science, University of Ulm, Germany
Venue:
CSCLP'06 Proceedings of the constraint solving and contraint logic programming 11th annual ERCIM international conference on Recent advances in constraints
Year:
2006

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Abstract

We present in this paper a first-order extension of the solver of Prolog III, by giving not only a decision procedure, but a full first-order constraint solver in the theory T of the evaluated trees, which is a combination of the theory of finite or infinite trees and the theory of the rational numbers with addition, subtraction and a linear dense order relation. The solver is given in the form of 28 rewriting rules which transform any first-order formula ϕ into an equivalent disjunction φ of simple formulas in which the solutions of the free variables are expressed in a clear and explicit way. The correctness of our algorithm implies the completeness of a first-order theory built on the model of Prolog III.