Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
Sequentiality in orthogonal term rewriting systems
Journal of Symbolic Computation
NV-sequentiality: a decidable condition for call-by-need computations in term-rewriting systems
SIAM Journal on Computing
The functional strategy and transitive term rewriting systems
Term graph rewriting
Bounded, strongly sequential and forward-branching term rewriting systems
Journal of Symbolic Computation
Call by need computations to root-stable form
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Term rewriting and all that
Sequentiality, monadic second-order logic and tree automata
Information and Computation
Advanced topics in term rewriting
Advanced topics in term rewriting
Computing in Systems Described by Equations
Computing in Systems Described by Equations
Decidable Approximations of Term Rewriting Systems
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Strong Sequentiality of Left-Linear Overlapping Rewrite Systems
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
Decidable call-by-need computations in term rewriting
Information and Computation
Correct and optimal implementations of recursion in a simple programming language
Journal of Computer and System Sciences
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Reduction strategies and acyclicity
Rewriting Computation and Proof
Hi-index | 0.00 |
Huet and Lévy (1979) showed that needed reduction is a normalizing strategy for orthogonal (i.e., left-linear and non-overlapping) term rewriting systems. In order to obtain a decidable needed reduction strategy, they proposed the notion of strongly sequential approximation. Extending their seminal work, several better decidable approximations of left-linear term rewriting systems, for example, NV approximation, shallow approximation, growing approximation, etc., have been investigated in the literature. In all of these works, orthogonality is required to guarantee approximated decidable needed reductions are actually normalizing strategies. This paper extends these decidable normalizing strategies to left-linear overlapping term rewriting systems. The key idea is the balanced weak Church-Rosser property. We prove that approximated external reduction is a computable normalizing strategy for the class of left-linear term rewriting systems in which every critical pair can be joined with root balanced reductions. This class includes all weakly orthogonal left-normal systems, for example, combinatory logic CL with the overlapping rules pred ·(succ ·x) →x and succ ·(pred ·x) →x, for which leftmost-outermost reduction is a computable normalizing strategy.