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Topic: Graph rewriting

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	SURVEYS OF REWRITING
		Term graph rewriting is concerned with the representation of functional expressions as graphs, and the evaluation of these expressions by rule-based graph transformation.
		This paper is a survey of (acyclic) term graph rewriting, where emphasis is given to the relations between term and term graph rewriting.
		Rewriting is a general paradigm for expressing computations in various logics, and we focus here on rewriting techniques in equational logic.
	rewriting.loria.fr /surveys.html (797 words)

	Rewriting - Wikipedia, the free encyclopedia
		What is considered are rewrite systems (also rewriting systems, or term rewriting systems, though the latter term may imply a more specific system), which in its most basic form, consist of a set of terms, plus relations on how to transform these terms.
		Rewriting systems then do not provide an algorithm for changing one term to another, but a set of possible substitutions that could be applied.
		There are rewriting systems which do not have normal forms: a very simple one is the rewriting system on two terms a and b with a → b, b → a.
	en.wikipedia.org /wiki/Rewriting (714 words)

	Term Graph Rewriting (Site not responding. Last check: 2007-10-25)
		For this algebraic characterisation, an extension to the algebraic approach to (graph) rewriting was necessary, yielding a Fibred Approach, also described in more detail in [Kahl-1997b].
		Kinship of fibred rewriting steps with double-pushout rewriting steps is obvious; the main differences are that horizontal morphisms may belong to a different category than vertical morphisms, and that the host object is now the result of a universal construction, thus overcoming the traditional necessity of gluing conditions.
		Close inspection of the above rewriting step reveals that sharing is preserved as far as possible, and that the copying of what Wadsworth called ``non-abstractable parts'' already takes places in the construction of the host object, the middle graph of the lower row.
	www.cas.mcmaster.ca /~kahl/tgr.html (273 words)

	5.3 Graph Rewriting (Site not responding. Last check: 2007-10-25)
		The plan-rewriting rules in PbR are an extension of traditional graph rewriting rules.
		Nevertheless, there are several techniques that can transfer from graph rewriting into Planning by Rewriting, particularly for fully-specified rules.
		25] defines an abstract machine for graph isomorphism and studies a set of conditions under which traditional graph rewriting can be performed efficiently.
	www.cs.cmu.edu /afs/cs/project/jair/pub/volume15/ambite01a-html/node30.html (126 words)

	[No title]
		Graph rewriting is a comprehensive framework where the transformation of a variety of different structures can be modelled and studied in an uniform way.
		In particular, Term Graph rewriting refers to techniques and theories for representing terms and term rewrite rules as graphs and graph rewrite rules.
		Term Graph rewriting offers a model of computation which is closer to real implementations of functional and logic programming paradigms than pure term rewriting, but which avoids unnecessary machine detail.
	www.dcs.st-and.ac.uk /~sal/Rewriting/367 (640 words)

	Term Graph Rewriting - Plump (ResearchIndex) (Site not responding. Last check: 2007-10-25)
		Abstract: Term graph rewriting is concerned with the representation of functional expressions as graphs, and the evaluation of these expressions by rule-based graph transformation.
		16 term graph rewriting is adequate for rational parallel term..
		8 Admissible graph rewriting and narrowing (context) - Echahed, Janodet - 1998 ACM DBLP
	citeseer.ist.psu.edu /plump98term.html (1475 words)

	Re: Note on graph vs. term reduction
		For graph reduction of the lambda calculus, the original reference is %A Wadsworth, C. %T Semantics and pragmatics of the lambda calculus %R D.Phil.
		For graph rewriting implementation of functional languages, see: %A Peyton-Jones, S.L. %T The Implementation of Functional Languages %I Prentice-Hall %D 1987 For the optimality properties of combinator graph reduction, there is a series of three papers by Staples (which actually prove it for regular term graph rewrite systems, of which combinatory logic is an example).
		These conferences are concerned with graph rewriting in general, not just the particular application to functional language implementation.
	www.cis.upenn.edu /~bcpierce/types/archives/1990/msg00006.html (760 words)

	Graph rewriting - Definition, explanation
		During the application of graph rewriting to a graph, subgraphs are replaced according to the rules of a rewrite system.
		Sometimes graph grammar is used as a synonym for graph rewriting system, especially in context of formal languages.
		There are several approaches to graph rewriting, one of them is the algebraic approach, which is based upon category theory.
	www.calsky.com /lexikon/en/txt/g/gr/graph_rewriting.php (356 words)

	Congruences for Contextual Graph-Rewriting (Site not responding. Last check: 2007-10-25)
		We introduce a comprehensive operational semantic theory of graph rewriting.
		Consequently, graph rewriting systems are associated with canonical labelled transition systems, on which bisimulation equivalence is a congruence with respect to arbitrary graph contexts (cospans of graphs).
		As a consequence, we both generalise and shed light on rewriting via borrowed contexts due to Ehrig and König.
	www.brics.dk /BRICS/RS/04/11/index.html (118 words)

	Graph rewriting - Wikipedia, the free encyclopedia
		During the application of graph rewriting to a graph, subgraphs are replaced according to the rules of a rewrite system.
		Sometimes graph grammar is used as a synonym for graph rewriting system, especially in context of formal languages.
		In contrast a graph rewriting rule of the SPO approach is a single morphism in the category labeled multigraphs with partial graph morphisms as arrows:
	en.wikipedia.org /wiki/Graph_rewriting (366 words)

	Re: Note on graph vs. term reduction (Site not responding. Last check: 2007-10-25)
		In this case, one generally cannot map a graph to a finite term; possibly infinite tress are the natural substitute.
		The MITRE papers "A correctness proof for combinator reduction with cycles", (to appear, Jan 1990 TOPLAS) and "Redex capturing in term graph rewriting" (Tech Report M89-36, July 89, submitted for publication) contain results on implementing term rewriting systems with cyclic graph rewriting rules.
		The second paper formalizes a notion of convergence for infinite tree rewritings sequences, and proves a general result comparing cyclic graph rewriting to tree rewriting sequences.
	www.seas.upenn.edu /~sweirich/types/archive/1990/msg00010.html (178 words)

	Abstract of: Equational term graph rewriting (Site not responding. Last check: 2007-10-25)
		It is shown how Equational Logic induces a notion of copying and substitution on term graphs, or systems of recursion equations, and also suggests the introduction of hidden or nameless nodes in a term graph.
		The general framework of term graphs with copying is compared with the more restricted copying facilities embodied in the μ-rule, and translations are given between term graphs and μ-expressions.
		Next, orthogonal term graph rewrite systems, also in the presence of copying and hidden nodes, are shown to be confluent.
	db.cwi.nl /rapporten/abstract.php?abstractnr=525 (167 words)

	Graph Rewriting (Site not responding. Last check: 2007-10-25)
		The idea is that the objects discovered in an image are placed in a graph data structure with links between objects based on their spatial relationship to each other (e.g.
		Identifying the higher level structure in the document can then be done by rewriting the graph: e.g.
		This project is to develop a working graph rewriter and associated algorithms to experiment with these ideas.
	www.cs.bham.ac.uk /~aps/teaching/projects/XML/projlist/projN287.html (165 words)

	JOT: Journal of Object Technology - Constraint Validation in Model Compilers, L. Lengyel, T. Levendovszky, H. Charaf
		Applying a graph rewriting rule means finding an isomorphic occurrence (match) of LHS in the graph to which the rule is being applied (host graph), and replacing this subgraph with RHS.
		A direct corollary of this is that an OCL expression in LHS is a precondition to the rewriting rule, and an OCL expression in RHS is a postcondition to the rewriting rule.
		The rewriting process uses matches found by the matching process and the compiled binary to validate the constraints on the matched parts of the host graph.
	www.jot.fm /issues/issue_2006_05/article3 (6711 words)

	GETGRATS Home Page
		The aim of the project is to develop a General Theory of Graph Transformation Systems (GTS) by solidifying the use of mathematics in their study and regarding them as the objects of discourse and interest.
		The group has experience concerning the language theoretic aspects of node-based graph rewriting systems, their use as models of computation, and the use of graph transformations in databases.
		In the area of graph transformations current research activities include structuring, analysis, and semantics, and the application of graph transformation techniques for the specification of parallel and distributed systems.
	www.di.unipi.it /~andrea/GETGRATS (2148 words)

	2.2 Rewriting
		Plan rewriting in PbR is related to term and graph rewriting.
		Graph rewriting, akin to term rewriting, refers to the process of replacing a subgraph of a given graph, when some conditions are satisfied, by another subgraph.
		The main drawback of general graph rewriting is its complexity.
	www.cs.cmu.edu /afs/cs.cmu.edu/project/jair/pub/volume15/ambite01a-html/node8.html (354 words)

	EPSRC Grant GR/H41300: Final Report (Site not responding. Last check: 2007-10-25)
		The aim of the project was to explore the usefulness of graph rewriting as an implementation technique for multi-paradigm languages focussing mainly, but not exclusively, on declarative programming styles.
		The model was implemented using a graph rewriting system in which graph terms represented both processes and the names, or channels, used for communication.
		The theoretical basis of the language can be described as multiset rewriting of graph terms but an alternative view is to see certain terms as process descriptors, while other terms represent messages sent to those processes.
	www2.cmp.uea.ac.uk /~jrwg/MultiPar/finalrep.html (1774 words)

	HANDBOOK OF GRAPH GRAMMARS AND COMPUTING BY GRAPH TRANSFORMATION
		Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction.
		The area of graph grammars and graph transformations generalizes formal language theory based on strings and the theory of term rewriting based on trees.
		Volume 1 of the indispensable Handbook of Graph Grammars and Computing by Graph Transformations includes a state-of-the-art presentation of the foundations of all the basic approaches to rule-based graph specification and transformation: algebraic approach, logic approach, node-based rewriting, (hyper)edge-based rewriting, programmed graph rewriting, and 2-structures.
	www.worldscibooks.com /compsci/3303.html (348 words)

	Term Rewriting vs. Functional Programming
		For term rewriting, some people are advocating the rho (rewriting) calculus [3], which differs from the lambda calculus in that it makes pattern matching explicit.
		Given a term rewriting system and a term, inferencing a normal form of the term is comparable to the execution of a functional program.
		When studying first order rewriting system people often try to use confluent systems, which are independent of the tree traversal order in their result.
	www.codecomments.com /message589315.html (2404 words)

	Cover Pages: Graph Exchange Language (GXL)
		The structure of graphs exchanged by GXL streams is given by a schema denoted as UML class diagrams which in turn can be exchanged by graphs represented as GXL document.
		GXL originates in the GRAph eXchange format, GraX (University of Koblenz, DE) for exchanging typed, attributed, ordered directed graphs (TGraphs), combined with the Tuple Attribute Language, TA (University of Waterloo, CA) and the graph format of the PROGRES graph rewriting system (University Bw München, DE).
		The maximum common XML data submodel for all existing graph transformation systems could be adopted instead, agreeing upon those features (elements and attributes) considered to be essential and leaving out additional features which, although important for particular applications, are not essential from the point of view of software exchange within the graph transformation community.
	xml.coverpages.org /gxl.html (763 words)

	Term Graph Rewriting (Site not responding. Last check: 2007-10-25)
		Term graph rewriting is concerned with the representation of expressions as graphs, and the evaluation of these expressions by rule-based graph transformation.
		Term graph rewriting reflects the properties of real implementations of term rewriting based on shared structures, and has applications in functional and logic programming and in automated reasoning.
		Besides efficiency, term graph rewriting differs from conventional term rewriting in properties like termination and confluence.
	www.ii.uib.no /~pinar/seminar/plump.html (143 words)

	Corrections and Updates to Graph Rewriting, 1990
		Graph grammars, even context-free, are difficult to parse as we have seen.
		Linear time graph recognition algorithms based on graph rewriting systems are constructed effectively for sets of graphs that are both definable in MSOL and of bounded tree-width ([ACPS]).
		Classes of functions on graphs evaluable in polynomial time on graphs generated by context-free graph grammars are defined in [BPT, CM, HR], by extending the idea of compatibility introduced in [21, 26, 50, 66] for graph properties.
	www.labri.fr /perso/courcell/CorrectHDBK90.html (1703 words)

	FOTS - University of Antwerp
		The aim of this workshop is to bring together a number of researchers interested in the use of graph rewriting for refactoring.
		Topics of interest: the use of graph transformation and related techniques for the formalization of refactoring, and for the development of refactoring tools.
		In [1] an attempt to model refactorings at the source code level is presented, and in [2] distributed graph transformations are used to maintain consistency between the code and the model while refactorings are carried out.
	www.fots.ua.ac.be /graphtransfo_refactoring (913 words)

	TERMGRAPH 2002
		Using graphs rather than strings or trees allows to share common subexpressions, which improves the efficiency of computations in space and time.
		Research in term graph rewriting ranges from theoretical questions to practical implementation issues.
		The aim of this workshop is to bring together researchers working in these different domains and to foster their interaction, to provide a forum for presenting new ideas and work in progress, and to enable newcomers to learn about current activities in term graph rewriting.
	www-users.cs.york.ac.uk /~det/Termgraph_2002/cfp.html (240 words)

	Graph Drawing by Graph Rewriting
		Graph rewriting combines Turing completeness and a visual view of graphs, which allows graph drawing algorithms to be developed quickly.
		It already had implicit graph theoretical operations, allowing operations such as finding the shortest path between two nodes, or finding all the neigbours of a node.
		The missing features were geometric operations such as placing a node at a particular position, finding the screen location of a node, or the length of an arc.
	www.cs.kent.ac.uk /people/staff/pjr/gdgr/main.html (163 words)

	Computer Science: Publication: A Graph Rewriting Visual Language for Database Programming
		It uses a graph rewriting paradigm as a basis for a fully visual, computationally complete language.
		The graphs it rewrites represent the schema and instances of a database.
		The unique graph rewriting method used by Spider has syntactic and semantic simplicity.
	www.cs.ukc.ac.uk /pubs/1997/503/index.html (236 words)

	Chemistry, Graph Tranformation and Programming Languages \| Lambda the Ultimate
		The hope is to generalize the notion of synthetic organic chemistry to graph grammars, and create a stronger underlying formalism that would allow us to make useful tools and think of new problems and applications that can be solved by thinking of them in a “chemical” fashion.
		What I think I mean, is that by having a flexible graph rewriting system that you can show "chemistry" is just an instance of; it would be convienent for people to explore the use of graph transformation in what they study.
		Now while chemical graph rewrite rules might be used to easily characterise the effect of a single ion upon a single graph structure held in a fixed orientation, as the complexity of the interacting components increases the interactions of even only two graph structures (two interacting molecules) becomes inordinately complex.
	lambda-the-ultimate.org /node/view/645 (2895 words)

	[No title] (Site not responding. Last check: 2007-10-25)
		Call for Papers 3rd International Workshop on Term Graph Rewriting TERMGRAPH 2006 1 April 2006, Vienna, Austria A satellite event of ETAPS 2006 http://www.dcs.kcl.ac.uk/events/TERMGRAPH2006/ Term graph rewriting is concerned with the representation of functional expressions as graphs and the evaluation of these expressions by rule-based graph transformation.
		The advantage of using graphs rather than strings or trees is that common subexpressions can be shared, which improves the efficiency of computations in space and time.
		This includes (but is not limited to): Theory of first-order and higher-order term graph rewriting; Graph rewriting in lambda calculus (sharing graphs, interaction nets, optimality); Applications in functional, logic and functional-logic programming; Applications in automated reasoning and symbolic computation; Implementation issues; System descriptions.
	plc.inf.elte.hu /felhivasok/termgraph2006.txt (285 words)

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