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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
Simulation as a correct transformation of rewrite systems
 In Proceedings of 22nd Symposium on Mathematical Foundations of Computer Science, LNCS 1295
, 1997
"... Abstract. Kamperman and Walters proposed the notion of a simulation of one rewrite system by another one, whereby each term of the simulating rewrite system is related to a term in the original rewrite system. In this paper it is shown that if such a simulation is sound and complete and preserves te ..."
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Cited by 4 (4 self)
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Abstract. Kamperman and Walters proposed the notion of a simulation of one rewrite system by another one, whereby each term of the simulating rewrite system is related to a term in the original rewrite system. In this paper it is shown that if such a simulation is sound and complete and preserves termination, then the transformation of the original into the simulating rewrite system constitutes a correct step in the compilation of the original rewrite system. That is, the normal forms of a term in the original rewrite system can then be obtained by computing the normal forms of a related term in the simulating rewrite system. 1
Unique normal forms and confluence of rewrite systems: Persistence
 In Proc. 14th IJCAI
, 1995
"... 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 sy ..."
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Cited by 3 (1 self)
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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 leftlinear 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. 1
Transformations of Reduction Systems
, 1996
"... We consider transformations of reduction systems in an abstract setting. We study some sets of correctness criteria for such transformations, adapt a notion of simulation proposed by Kamperman and Walters, and show that the resulting !simulation behaves well w.r.t. the criteria. We apply our resul ..."
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Cited by 1 (0 self)
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We consider transformations of reduction systems in an abstract setting. We study some sets of correctness criteria for such transformations, adapt a notion of simulation proposed by Kamperman and Walters, and show that the resulting !simulation behaves well w.r.t. the criteria. We apply our results in an investigation of a transformation proposed by Thatte, and prove that this transformation preserves semicompleteness for weakly persistent systems.
Correct Transformation of Rewrite Systems for Implementation Purposes
"... We propose the notion of a correct transformation of one rewrite system into another. If such a transformation is correct, then the normal forms of a term in the original rewrite system can be obtained by computing the normal forms of the interpretation of this term in the transformed rewrite system ..."
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We propose the notion of a correct transformation of one rewrite system into another. If such a transformation is correct, then the normal forms of a term in the original rewrite system can be obtained by computing the normal forms of the interpretation of this term in the transformed rewrite system. We showfor several transformations from the literature that they are correct, most notably for the notion of simulation from Kamperman and Walters. 1
Correctness Criteria for Transformations of Rewrite Systems  With An Application . . .
"... We define a lifting of the notion of transformation of term rewriting systems to arbitrary relational structures, that ties in with the simulation relations of concurrency theory. We illustrate the resulting concepts in an examination of Thatte's transformation of term rewriting systems. We ref ..."
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We define a lifting of the notion of transformation of term rewriting systems to arbitrary relational structures, that ties in with the simulation relations of concurrency theory. We illustrate the resulting concepts in an examination of Thatte's transformation of term rewriting systems. We refute an earlier claim that this transformation preserves confluence for weakly persistent systems. We conclude by proving the preservation of weak normalization, and of confluence in weakly normalizing systems and in nonoverlapping systems with linear subtemplates. 1