On the adequacy of graph rewriting for simulating term rewriting

Kennaway, Richard; Klop, Jan Willem; Sleep, M. R.; Vries, F. J. de

doi:10.1145/177492.177577

Cited by 60 publications

(58 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Closer to the soundness result of Section 3 are the adequacy results relating term graph rewriting and rational term rewriting proposed in [21] and [8]. In fact, possibly cyclic finite term graphs can be considered as an alternative finite representation of rational terms, where also "horizontal sharing" is allowed.…”

Section: Discussion and Future Workmentioning

confidence: 87%

“…In fact, possibly cyclic finite term graphs can be considered as an alternative finite representation of rational terms, where also "horizontal sharing" is allowed. In [21], the notion of adequacy between rewriting systems is introduced, which is essentially equivalent to soundness plus a form of partial completeness. 6 In the same paper, it is presented an adequacy result between term graph rewriting and rational term rewriting defined using [22]; however, the result is restricted to the case of systems with at most one collapsing rules, or modulo hypercollapsing towers.…”

Section: Discussion and Future Workmentioning

confidence: 99%

“…A set of redexes # of a rational term t is rational if the associated marked term t~ is rational [21]. A parallel reduction t ~ s is rational if so is ~.…”

Section: For Each I < W S~ < Si+x; Ie {Si}imentioning

confidence: 99%

“…LFrom a computational viewpoint, rational terms are clearly a very interesting subclass of infnite terms, because they have a finitary representation; usually, however, this is not unique. Infinitary extensions of Term Rewriting have been considered by various authors during the last decade [12,11,15,16,7,20,21,22,9,8]. Most of those contributions are concerned with the study of the rewriting relation induced by a set of finite term rules on infinite terms, presenting results about the existence of normal forms (possibly reachable after w steps), confluence and so on.…”

Section: Introductionmentioning

confidence: 99%

“…Most of those contributions are concerned with the study of the rewriting relation induced by a set of finite term rules on infinite terms, presenting results about the existence of normal forms (possibly reachable after w steps), confluence and so on. Only a few of them, namely [20,21,8], focus on the subclass of rational terms, regarded essentially as the semantics of some finite but possibly cyclic structures (term graphs or #-terms).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Rational term rewriting

Corradini

Gadducci²

1998

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

Section: Discussion and Future Workmentioning

confidence: 87%

Section: Discussion and Future Workmentioning

confidence: 99%

“…A set of redexes # of a rational term t is rational if the associated marked term t~ is rational [21]. A parallel reduction t ~ s is rational if so is ~.…”

Section: For Each I < W S~ < Si+x; Ie {Si}imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Rational term rewriting

Corradini

Gadducci²

1998

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

Lambda Calculus with Explicit Recursion

Ariola

1997

Information and Computation

View full text Add to dashboard Cite

This paper is concerned with the study of A-calculus with explicit recursion, namely of cyclic A-graphs. The starting point is to treat a A-graph as a system of recursion equations involving A-terms and to manipulate such systems in an unrestricted manner, using equational logic, just as is possible for first-order term rewriting. Surprisingly, now the confluence property breaks down in an essential way. Confluence can be restored by introducing a restraining mechanism on the substitution operation. This leads to a family of A-graph calculi, which can be seen as an extension of the family of ;\a-calculi (A-calculi with explicit substitution). While the Ila-calculi treat the let-construct as a first-class citizen, our calculi support the letrec, a feature that is essential to reason about time and space behavior of functional languages and also about compilation and optimizations of programs.

show abstract

Bisimilarity in Term Graph Rewriting

Ariola

Klop

Plump

2000

Information and Computation

View full text Add to dashboard Cite

We p resent a survey of conuence properties of (acyclic) term graph rewriting. Results and counterexamples are given for dierent kinds of term graph rewriting: besides plain applications of rewrite rules, extensions with the operations of collapsing and copying, and with both operations together are considered. Collapsing and copying together constitute bisimilarity of term graphs. We establish sucient conditions for|and counterexamples to|conuence, conuence modulo bisimilarity and the Church-Rosser property modulo bisimilarity. M o reover, we address rewriting modulo bisimilarity, that is, rewriting of bisimilarity classes of term graphs.

show abstract

On the adequacy of graph rewriting for simulating term rewriting

Cited by 60 publications

References 8 publications

Rational term rewriting

Rational term rewriting

Lambda Calculus with Explicit Recursion

Bisimilarity in Term Graph Rewriting

Contact Info

Product

Resources

About