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Dactl: An Experimental Graph Rewriting Language
 Proc. 4th International Workshop on Graph Grammars
, 1991
"... This paper gives some examples of how computation in a number of languages may be described as graph rewriting, giving the Dactl notation for the examples shown. It goes on to present the Dactl model more formally before giving a formal definition of the syntax and semantics of the language. 2 Examp ..."
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Cited by 34 (7 self)
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This paper gives some examples of how computation in a number of languages may be described as graph rewriting, giving the Dactl notation for the examples shown. It goes on to present the Dactl model more formally before giving a formal definition of the syntax and semantics of the language. 2 Examples of Computation by Graph Rewriting
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 21 (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...
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...
Relating Graph and Term Rewriting via Böhm Models
 in Engineering, Communication and Computing 7
, 1993
"... . Dealing properly with sharing is important for expressing some of the common compiler optimizations, such as common subexpressions elimination, lifting of free expressions and removal of invariants from a loop, as sourcetosource transformations. Graph rewriting is a suitable vehicle to accommoda ..."
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Cited by 8 (4 self)
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. Dealing properly with sharing is important for expressing some of the common compiler optimizations, such as common subexpressions elimination, lifting of free expressions and removal of invariants from a loop, as sourcetosource transformations. Graph rewriting is a suitable vehicle to accommodate these concerns. In [4] we have presented a term model for graph rewriting systems (GRSs) without interfering rules, and shown the partial correctness of the aforementioned optimizations. In this paper we define a different model for GRSs, which allows us to prove total correctness of those optimizations. Differently from [4] we will discard sharing from our observations and introduce more restrictions on the rules. We will introduce the notion of Bohm tree for GRSs, and show that in a system without interfering and nonleft linear rules (orthogonal GRSs), Bohm tree equivalence defines a congruence. Total correctness then follows in a straightforward way from showing that if a program M co...
On the Adequacy of Graph Rewriting for Simulating Term Rewriting
, 1994
"... Several authors have investigated the correspondence between graph rewriting and term rewriting. Almost invariably they have considered only acyclic graphs. Yet cyclic graphs naturally arise from certain optimisations in implementing functional languages. They correspond to infinite terms, and th ..."
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Cited by 5 (1 self)
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Several authors have investigated the correspondence between graph rewriting and term rewriting. Almost invariably they have considered only acyclic graphs. Yet cyclic graphs naturally arise from certain optimisations in implementing functional languages. They correspond to infinite terms, and their reductions correspond to transfinite term reduction sequences, which have recently received detailed attention. We formalise the close correspondence between finitary cyclic graph rewriting and a restricted form of infinitary term rewriting, called rational term rewriting. This subsumes the known relation between finitary acyclic graph rewriting and finitary term rewriting.