Paper Info
Title
Reduction strategies for left-linear term rewriting systems
Abstract
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.
Year
DOI
Venue
2005
10.1007/11601548_13
Processes, Terms and Cycles
Keywords
Field
DocType
approximated external reduction,left-linear term,leftmost-outermost reduction,nv approximation,computable normalizing strategy,reduction strategy,approximated decidable,decidable normalizing strategy,needed reduction,normalizing strategy,decidable approximation
Linear approximation,Reduction strategy,Discrete mathematics,Combinatory logic,Approximations of π,Orthogonality,Decidability,Critical pair,Rewriting,Mathematics
Conference
Volume
ISSN
ISBN
3838
0302-9743
3-540-30911-X
Citations 
PageRank 
References 
1
0.36
14
Authors
1
Name
Order
Citations
PageRank
Yoshihito Toyama153349.60