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

Authors:
Thi-Bich-Hanh Dao;Khalil Djelloul
Affiliations:
LIFO, Orléans, France;LIF, Parc scientifique et technologique de Luminy, Marseille, France
Venue:
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
Year:
2006

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Abstract

We describe in this paper a general algorithm for solving first-order constraints 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. It transforms a first-order formula ϕ, which can possibly contain free variables, into a disjunction φ of solved formulas which is equivalent in T, without new free variables and such that φ is either $\mathit{true}$ or $\mathit{false}$ or a formula having at least one free variable and being equivalent neither to $\mathit{true}$ nor to $\mathit{false}$ in T.