Solving First-Order Constraints in the Theory of the Evaluated Trees

Thi-Bich-Hanh Dao (1) , Khalil Djelloul (1)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

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 firstorder 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 ' into an equivalent disjunction D 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.

Domains: Logic in Computer Science [cs.LO]

Thi-Bich-Hanh Dao, Khalil Djelloul. Solving First-Order Constraints in the Theory of the Evaluated Trees. Recent Advance in constraints. Lecture notes in computer science. Selected revised paper Csclp 2006., Apr 2007, France. pp.LNAI, Vol 4651. P 108-123. ⟨hal-00202314⟩