Explicit representation of terms defined by counter examples
Journal of Automated Reasoning
Journal of Logic Programming
Foundations of deductive databases and logic programming
Equational problems anddisunification
Journal of Symbolic Computation
Communications of the ACM
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Term rewriting and all that
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
A decision procedure for term algebras with queues
ACM Transactions on Computational Logic (TOCL)
Independence of Negative Constraints
TAPSOFT '89/CAAP '89 Proceedings of the International Joint Conference on Theory and Practice of Software Development, Volume 1: Advanced Seminar on Foundations of Innovative Software Development I and Colloquium on Trees in Algebra and Programming
Incremental Algorithms for Constraint Solving and Entailment over Rational Trees
Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science
Solving Disequations in Equational Theories
Proceedings of the 9th International Conference on Automated Deduction
An Improved Lower Bound for the Elementary Theories of Trees
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Essentials of Constraint Programming
Essentials of Constraint Programming
Essentials of Constraint Programming
Essentials of Constraint Programming
Proceedings of the 2006 ACM symposium on Applied computing
Theory and Practice of Logic Programming
Automatic Implication Checking for CHR Constraints
Electronic Notes in Theoretical Computer Science (ENTCS)
Parallelizing union-find in constraint handling rules using confluence analysis
ICLP'05 Proceedings of the 21st international conference on Logic Programming
A Full First-Order Constraint Solver for Decomposable Theories
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
From exponential to almost linear decomposability of finite or infinite trees
Proceedings of the 2009 ACM symposium on Applied Computing
A full first-order constraint solver for decomposable theories
Annals of Mathematics and Artificial Intelligence
A complete axiomatization of strict equality
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
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We present in this paper a first-order axiomatization of an extended theory T of finite or infinite trees, built on a signature containing an infinite set of function symbols and a relation finite(t), which enables to distinguish between finite and infinite trees. We show that T has at least one model and prove its completeness by giving not only a decision procedure, but a full first-order constraint solver that gives clear and explicit solutions for any first-order constraint satisfaction problem in T. The solver is given in the form of 16 rewriting rules that transform any first-order constraint ϕ into an equivalent disjunction φ of simple formulas such that φ is either the formula true or the formula false or a formula having at least one free variable, being equivalent neither to true nor to false and where the solutions of the free variables are expressed in a clear and explicit way. The correctness of our rules implies the completeness of T. We also describe an implementation of our algorithm in CHR (Constraint Handling Rules) and compare the performance with an implementation in C++ and that of a recent decision procedure for decomposable theories.