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Term Rewriting Systems
, 1992
"... Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstra ..."
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Cited by 613 (18 self)
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Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss
Rewrite, Rewrite, Rewrite, Rewrite, Rewrite, ...
, 1989
"... .We study properties of rewrite systems that are not necessarily terminating, but allow instead for trans#nite derivations that have a limit. In particular, we give conditions for the existence of a limit and for its uniqueness and relate the operational and algebraic semantics of in#nitary theories ..."
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Cited by 9 (1 self)
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#nitary theories. We also consider su#cient completeness of hierarchical systems. Is there no limit? Job 16:3 1. Introduction Rewrite systems are sets of directed equations used to compute by repeatedly replacing equal terms in a given formula, as long as possible. For one approach to their use in computing
Confluence of Right Ground Term Rewriting Systems is Decidable
, 2003
"... Term rewriting systems provide a versatile model of computation. An important property which allows to abstract from potential nondeterminism of parallel execution of the modelled program is confluence. In this paper we prove that confluence of a fairly large class of systems, namely right ground t ..."
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Term rewriting systems provide a versatile model of computation. An important property which allows to abstract from potential nondeterminism of parallel execution of the modelled program is confluence. In this paper we prove that confluence of a fairly large class of systems, namely right ground
Confluence of shallow rightlinear rewrite systems
 Proc. 14th CSL
, 2005
"... Abstract. We show that confluence of shallow and rightlinear term rewriting systems is decidable. This class of rewriting system is expressive enough to include nontrivial nonground rules such as commutativity, identity, and idempotence. Our proof uses the fact that this class of rewrite systems is ..."
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Cited by 11 (3 self)
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Abstract. We show that confluence of shallow and rightlinear term rewriting systems is decidable. This class of rewriting system is expressive enough to include nontrivial nonground rules such as commutativity, identity, and idempotence. Our proof uses the fact that this class of rewrite systems
Deciding fundamental properties of right(ground or variable) rewrite systems by rewrite closure
 In Intl. Joint Conf. on Automated Deduction, IJCAR, volume 3097 of LNAI
, 2004
"... Abstract. Right(ground or variable) rewrite systems (RGV systems for short)are term rewrite systems where all right hand sides of rules are restricted to be either ground or a variable. We define a minimal rewrite extension R of the rewriterelation induced by a RGV system R. This extension admits a ..."
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Cited by 5 (2 self)
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Abstract. Right(ground or variable) rewrite systems (RGV systems for short)are term rewrite systems where all right hand sides of rules are restricted to be either ground or a variable. We define a minimal rewrite extension R of the rewriterelation induced by a RGV system R. This extension admits
On the confluence of trace rewriting systems
 PROCEEDINGS OF THE 18TH CONFERENCE ON FOUNDATIONS OF SOFTWARE TECHNOLOGY AND THEORETICAL COMPUTER SCIENCE, (FSTTCS'98), CHENNAI (INDIA), NUMBER 1530 IN LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... Trace rewriting systems, i.e., rewriting systems over trace monoids, generalize both semiThue systems and vector replacement systems. In [NO88], a particular trace monoid M is constructed such that confluence is undecidable for the class of lengthreducing trace rewriting systems over M. In this pa ..."
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Cited by 2 (2 self)
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Trace rewriting systems, i.e., rewriting systems over trace monoids, generalize both semiThue systems and vector replacement systems. In [NO88], a particular trace monoid M is constructed such that confluence is undecidable for the class of lengthreducing trace rewriting systems over M
Term Graph Rewriting
, 1998
"... Term graph rewriting is concerned with the representation of functional expressions as graphs, and the evaluation of these expressions by rulebased graph transformation. Representing expressions as graphs allows to share common subexpressions, improving the efficiency of term rewriting in space ..."
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Cited by 88 (5 self)
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and time. Besides efficiency, term graph rewriting differs from term rewriting in properties like termination and confluence. This paper is a survey of (acyclic) term graph rewriting, where emphasis is given to the relations between term and term graph rewriting. We focus on soundness of term graph
Rewriting Systems
, 1999
"... reduction systems . . . . . . . . . . . . . . . . . . . . 11 1.6 Properties of arss . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Lambda calculus and combinatory logic 17 2.1 Lambda terms . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 The rewrite rules . . . . . . . . . . . . ..."
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Cited by 2 (0 self)
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. . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Rewrite strategies and confluence . . . . . . . . . . . . . . . . . 20 2.4 The power of lambda calculus . . . . . . . . . . . . . . . . . . . 22 2.5 Combinatory logic . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Term rewriting systems 29 3.1 Terms
Deciding the Confluence of Ordered Term Rewrite Systems
"... . A term rewrite system (TRS) terminates if, and only if, its rules are contained in a reduction ordering ?. In order to deal with any set of equations, including inherently nonterminating ones (like commutativity) , TRS have been generalized to ordered TRS (E; ?), where equations of E are appl ..."
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Cited by 4 (0 self)
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. A term rewrite system (TRS) terminates if, and only if, its rules are contained in a reduction ordering ?. In order to deal with any set of equations, including inherently nonterminating ones (like commutativity) , TRS have been generalized to ordered TRS (E; ?), where equations of E
Results 1  10
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41,196