On the sequential nature of unification
Journal of Logic Programming
On the Church-Rosser property for the direct sum of term rewriting systems
Journal of the ACM (JACM)
Journal of Symbolic Computation
Implementing first-order rewriting with constructor systems (Note)
Theoretical Computer Science
Unique normal forms for Lambda calculus with surjective pairing
Information and Computation
Handbook of theoretical computer science (vol. B)
A theory of using history for equational systems with applications
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Simulation of Turing machines by a regular rewrite rule
Theoretical Computer Science
Transformations and confluence for rewrite systems
Theoretical Computer Science
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Variations on the Common Subexpression Problem
Journal of the ACM (JACM)
Computing in Systems Described by Equations
Computing in Systems Described by Equations
Completeness of Hierarchical Combinations of term Rewriting Systems
Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science
Completeness of Combinations of Constructor Systems
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
Unique normal forms in term rewriting systems with repeated variables
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Complexity of finitely presented algebras
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
An improved algorithm for computing with equations
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
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Programming language interpreters, proving theorems of the form A = 2?, abstract data types, and program optimization can all be represented by a finite set of rules called a rewrite system. In this paper, we study two fundamental concepts, uniqueness of normal forms and confluence, for nonlinear systems in the absence of termination. This is a difficult topic with only a few results so far. Through a novel approach, we show that every persistent system has unique normal forms. This result is tight and a substantial generalization of previous work. In the process we derive a necessary and sufficient condition for persistence for the first time and give new classes of persistent systems. We also prove the confluence of the union (function symbols can be shared) of a nonlinear system with a left-linear system under fairly general conditions. Again persistence plays a key role in this proof. We are not aware of any confluence result that allows the same level of function symbol sharing.