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ContextSensitive Rewriting Strategies
, 1997
"... Contextsensitive rewriting is a simple restriction of rewriting which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is (explicitly or automatically) specified on the arguments of symbols of the signature and inductively ..."
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Cited by 43 (30 self)
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Contextsensitive rewriting is a simple restriction of rewriting which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is (explicitly or automatically) specified on the arguments of symbols of the signature and inductively extended to arbitrary positions of terms built from those symbols. Termination is not only preserved but usually improved and several methods have been developed to formally prove it. In this paper, we investigate the definition, properties, and use of contextsensitive rewriting strategies, i.e., particular, fixed sequences of contextsensitive rewriting steps. We study how to define them in order to obtain efficient computations and to ensure that contextsensitive computations terminate whenever possible. We give conditions enabling the use of these strategies for rootnormalization, normalization, and infinitary normalization. We show that this theory is suitable for formalizing ...
Rational Term Rewriting
, 1998
"... . Rational terms (possibly infinite terms with finitely many subterms) can be represented in a finite way via terms, that is, terms over a signature extended with selfinstantiation operators. For example, f ! = f(f(f(: : :))) can be represented as x :f(x) (or also as x :f(f(x)), f(x :f(x)), ..."
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Cited by 22 (12 self)
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. Rational terms (possibly infinite terms with finitely many subterms) can be represented in a finite way via terms, that is, terms over a signature extended with selfinstantiation operators. For example, f ! = f(f(f(: : :))) can be represented as x :f(x) (or also as x :f(f(x)), f(x :f(x)), . . . ). Now, if we reduce a term t to s via a rewriting rule using standard notions of the theory of Term Rewriting Systems, how are the rational terms corresponding to t and to s related? We answer to this question in a satisfactory way, resorting to the definition of infinite parallel rewriting proposed in [7]. We also provide a simple, algebraic description of term rewriting through a variation of Meseguer's Rewriting Logic formalism. 1 Introduction Rational terms are possibly infinite terms with a finite set of subterms. They show up in a natural way in Theoretical Computer Science whenever some finite cyclic structures are of concern (for example data flow diagrams, cyclic te...
(Cyclic) Term Graph Rewriting is adequate for Rational Parallel Term Rewriting
 CGH
, 1997
"... Acyclic Term Graphs are able to represent terms with sharing, and the relationship between Term Graph Rewriting (TGR) and Term Rewrtiting (TR) is now well understood [BvEG + 87, HP91]. During the last years, some researchers considered the extension of TGR to possibly cyclic term graphs, which ..."
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Cited by 20 (6 self)
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Acyclic Term Graphs are able to represent terms with sharing, and the relationship between Term Graph Rewriting (TGR) and Term Rewrtiting (TR) is now well understood [BvEG + 87, HP91]. During the last years, some researchers considered the extension of TGR to possibly cyclic term graphs, which can represent possibly infinite, rational terms. In [KKSdV94] the authors formalize the classical relationship between TGR and TR as an "adequate mapping" between rewriting systems, and extend it by proving that unraveling is an adequate mapping from cyclic TGR to rational, infinitary term rewriting: In fact, a single graph reduction may correspond to an infinite sequence of term reductions. Using the same notions, we propose a different adequacy result, showing that unraveling is an adequate mapping from cyclic TGR to rational parallel term rewriting, where at each reduction infinitely many rules can be applied in parallel. We also argue that our adequacy result is more natural...
A rewriting calculus for cyclic higherorder term graphs
 in &quot;2nd International Workshop on Term Graph Rewriting  TERMGRAPH’2004
, 2004
"... graphs ..."
Computing by Graph Transformation  A Survey and Annotated Bibliography
, 1996
"... this paper as candidates to represent the processes in a concurrent system or, more exactly, as representatives of equivalent views on the processes. The main results give sufficient conditions for existence and uniqueness of canonical derivations. ..."
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Cited by 13 (0 self)
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this paper as candidates to represent the processes in a concurrent system or, more exactly, as representatives of equivalent views on the processes. The main results give sufficient conditions for existence and uniqueness of canonical derivations.
Rewriting On Cyclic Structures: Equivalence Between The Operational And The Categorical Description
, 1999
"... . We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut for the case of circular redexes, fo ..."
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Cited by 12 (6 self)
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. We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework allows us to model in a concise way also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures, and to relate term graph rewriting to other rewriting formalisms. R'esum'e. Nous pr'esentons une formulation cat'egorique de la r'e'ecriture des graphes cycliques des termes, bas'ee sur une variante de 2theorie alg'ebrique. Nous prouvons que cette pr'esentation est 'equivalente `a la d'efinition op'erationnelle propos'ee par Barendregt et d'autres auteurs, mais pas dons le cas des radicaux circulaires, pour lesquels nous proposons (et justifions formellem...
Rewriting on Cyclic Structures
 EXTENDED ABSTRACT IN FIXED POINTS IN COMPUTER SCIENCE, SATELLITE WORKSHOP OF MFCS'98
, 1998
"... We present a categorical formulation of the rewriting of possibly cyclic term graphs, and the proof that this presentation is equivalent to the wellaccepted operational definition proposed in [3]  but for the case of circular redexes, for which we propose (and justify formally) a different treatm ..."
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Cited by 4 (3 self)
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We present a categorical formulation of the rewriting of possibly cyclic term graphs, and the proof that this presentation is equivalent to the wellaccepted operational definition proposed in [3]  but for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework, based on suitable 2categories, allows to model also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures. Furthermore, it can be used for defining various extensions of term graph rewriting, and for relating it to other rewriting formalisms.
Computing by Graph Transformation II (COMPUGRAPH II)
"... This report gives an overview over the ongoing activities of the ESPRIT Basic Research Working Group "Computing by Graph Transformation" started on March 1st, 1989. Its second phase COMPUGRAPH II began on October 1st, 1992 and lasts to March 31st, 1996. The main aim of the COMPUGRAPH ..."
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This report gives an overview over the ongoing activities of the ESPRIT Basic Research Working Group "Computing by Graph Transformation" started on March 1st, 1989. Its second phase COMPUGRAPH II began on October 1st, 1992 and lasts to March 31st, 1996. The main aim of the COMPUGRAPH project is to demonstrate the potential of graph transformation as a uniform framework for the development of modern software systems. The research activities therefore cover the whole spectrum from theoretical investigations to practical software engineering applications. This is reflected in the following research areas according to which the work in the COMPUGRAPH project has been organized:
Memoïzation for Term (Hypergraph) Rewriting (Extended Abstract)
"... ) Introduction Memoization is an optimization technique for implementing functional programming languages: The result of a function application is stored in a table, in order to be looked up later on if the function is reapplied to equal arguments. Redundant reevaluation of functions is avoided i ..."
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) Introduction Memoization is an optimization technique for implementing functional programming languages: The result of a function application is stored in a table, in order to be looked up later on if the function is reapplied to equal arguments. Redundant reevaluation of functions is avoided in this way, providing a sideeffectfree notion of memory. Commonly, memoization has been considered for the rather restricted classes of rewrite rules allowed in functional languages, and its semantics has been defined on the implementation level, usually depending on the evaluation strategy employed. In this paper, we generalize memoization considerably: ffl We consider two general classes of rules: convergent, and orthogonal rewrite systems. ffl We define its semantics by a simple modification of the evaluation rules. ffl Our results do not suppose a particular evaluation strategy. The present paper goes beyond earlier work described in [Hof92]: Full memoization is extended to converge...