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Lazy rewriting on eager machinery
 ACM Transactions on Programming Languages and Systems
, 2000
"... The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives a ..."
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Cited by 23 (1 self)
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The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behaviour of a term rewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting. 1
Reduction strategies for leftlinear term rewriting systems
 Processes, Terms and Cycles: Steps on the Road to Infinity:Essays Dedicated to Jan Willem Klop on the Occasion of His 60th Birthday, volume 3838 of Lecture Notes in Computer Science
, 2005
"... Abstract. Huet and Lévy (1979) showed that needed reduction is a normalizing strategy for orthogonal (i.e., leftlinear and nonoverlapping) term rewriting systems. In order to obtain a decidable needed reduction strategy, they proposed the notion of strongly sequential approximation. Extending the ..."
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Abstract. Huet and Lévy (1979) showed that needed reduction is a normalizing strategy for orthogonal (i.e., leftlinear and nonoverlapping) 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 leftlinear 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 leftlinear overlapping term rewriting systems. The key idea is the balanced weak ChurchRosser property. We prove that approximated external reduction is a computable normalizing strategy for the class of leftlinear term rewriting systems in which every critical pair can be joined with root balanced reductions. This class includes all weakly orthogonal leftnormal systems, for example, combinatory logic CL with the overlapping rules pred · (succ · x) → x and succ · (pred · x) → x, for which leftmostoutermost reduction is a computable normalizing strategy. 1
Efficient simulation of forwardbranching systems with constructor systems
 Journal of Symbolic Computation
, 1989
"... Strongly sequential constructor systems admit a very efficient algorithm to compute normal forms. Thatte found a transformation that allows us to simulate any orthogonal system with a constructor system. Unfortunately, this transformation does not generally preserve strong sequentiality. On the othe ..."
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Strongly sequential constructor systems admit a very efficient algorithm to compute normal forms. Thatte found a transformation that allows us to simulate any orthogonal system with a constructor system. Unfortunately, this transformation does not generally preserve strong sequentiality. On the other hand, the class of forwardbranching systems contains the class of strongly sequential constructor systems. Moreover, it admits a reduction algorithm similar to the reduction algorithm of the strongly sequential constructor class, but less efficient on the entire class of forwardbranching systems. In this article, we present a new transformation which transforms any forwardbranching system into a strongly sequential constructor system. The size of the system increases only modestly over that of the original one in many practical situation. We give an algorithm for this transformation and we prove its correctness and completeness. The new system is then proved to be equivalent to the input system, with respect to the behavior and the semantics. We then give a new transformation algorithm which increases the size of the system only linearly.
Leftincompatible Term Rewriting Systems and Functional Strategy
"... This paper extends leftincompatible term rewriting systems defined by Toyama et.al.[17]. It is also shown that the functional strategy is normalizing in the class, where the functional strategy is the reduction strategy that finds index by some rule selection method and topdown and lefttoright l ..."
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This paper extends leftincompatible term rewriting systems defined by Toyama et.al.[17]. It is also shown that the functional strategy is normalizing in the class, where the functional strategy is the reduction strategy that finds index by some rule selection method and topdown and lefttoright lazy pattern matching method. 1
Categories and Subject Descriptors: D.3.4 [Programming Languages]: Processors—compilers;
"... The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behavior of a termrewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as ..."
Abstract
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The article introduces a novel notion of lazy rewriting. By annotating argument positions as lazy, redundant rewrite steps are avoided, and the termination behavior of a termrewriting system can be improved. Some transformations of rewrite rules enable an implementation using the same primitives as an implementation of eager rewriting.