Results 1 
4 of
4
Algebraic Approaches to Graph Transformation, Part I: Basic Concepts and Double Pushout Approach
 HANDBOOK OF GRAPH GRAMMARS AND COMPUTING BY GRAPH TRANSFORMATION, VOLUME 1: FOUNDATIONS
, 1996
"... ..."
A 2Categorical Presentation of Term Graph Rewriting
 CATEGORY THEORY AND COMPUTER SCIENCE, VOLUME 1290 OF LNCS
, 1997
"... It is wellknown that a term rewriting system can be faithfully described by a cartesian 2category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2categorical presentation for term graph rewriting. Building on a re ..."
Abstract

Cited by 34 (17 self)
 Add to MetaCart
It is wellknown that a term rewriting system can be faithfully described by a cartesian 2category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2categorical presentation for term graph rewriting. Building on a result presented in [8], which shows that term graphs over a given signature are in onetoone correspondence with arrows of a gsmonoidal category freely generated from the signature, we associate with a term graph rewriting system a gsmonoidal 2category, and show that cells faithfully represent its rewriting sequences. We exploit the categorical framework to relate term graph rewriting and term rewriting, since gsmonoidal (2)categories can be regarded as "weak" cartesian (2)categories, where certain (2)naturality axioms have been dropped.
(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 ..."
Abstract

Cited by 20 (6 self)
 Add to MetaCart
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...
Unlimp  Uniqueness as a Leitmotiv for Implementation
, 1992
"... . When evaluation in functional programming languages is explained using calculus and/or term rewriting systems, expressions and function definitions are often defined as terms, that is as trees. Similarly, the collection of all terms is defined as a forest, that is a directed, acyclic graph where ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
. When evaluation in functional programming languages is explained using calculus and/or term rewriting systems, expressions and function definitions are often defined as terms, that is as trees. Similarly, the collection of all terms is defined as a forest, that is a directed, acyclic graph where every vertex has at most one incoming edge. Concrete implementations usually drop the last restriction (and sometimes acyclicity as well), i.e. many terms can share a common subterm, meaning that different paths of subterm edges reach the same vertex in the graph. Any vertex in such a graph represents a term. A term is represented uniquely in such a graph if there are no two different vertices representing it. Such a representation can be established by using hashconsing for the creation of heap objects. We investigate the consequences of adopting uniqueness in this sense as a leitmotiv for implementation (called Unlimp), i.e. not allowing any two different vertices in a graph to represent ...