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A BiCategorical Axiomatisation of Concurrent Graph Rewriting
, 1999
"... In this paper the concurrent semantics of doublepushout (DPO) graph rewriting, which is classically defined in terms of shiftequivalence classes of graph derivations, is axiomatised via the construction of a free monoidal bicategory. In contrast to a previous attempt based on 2categories, the us ..."
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Cited by 18 (10 self)
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In this paper the concurrent semantics of doublepushout (DPO) graph rewriting, which is classically defined in terms of shiftequivalence classes of graph derivations, is axiomatised via the construction of a free monoidal bicategory. In contrast to a previous attempt based on 2categories, the use of bicategories allows to define rewriting on concrete graphs. Thus, the problem of composition of isomorphism classes of rewriting sequences is avoided. Moreover, as a first step towards the recovery of the full expressive power of the formalism via a purely algebraic description, the concept of disconnected rules is introduced, i.e., rules whose interface graphs are made of disconnected nodes and edges only. It is proved that, under reasonable assumptions, rewriting via disconnected rules enjoys similar concurrency properties like in the classical approach.
Some Algebraic Laws for Spans (and Their Connections With MultiRelations)
 Proceedings of RelMiS 2001, Workshop on Relational Methods in Software. Electronic Notes in Theoretical Computer Science, n.44 v.3, Elsevier Science (2001
, 2001
"... This paper investigates some basic algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions, analyzing the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets. O ..."
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Cited by 9 (3 self)
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This paper investigates some basic algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions, analyzing the monoidal structures induced over both spans and cospans by the cartesian product and disjoint union of sets. Our results nd analogous counterparts in (and are partly inspired by) the theory of relational algebras, thus our paper also shed some light on the relationship between (co)spans and the categories of (multi)relations and of equivalence relations. And, since (co)spans yields an intuitive presentation in terms of dynamical system with input and output interfaces, our results introduce an expressive, twofold algebra that can serve as a specication formalism for rewriting systems and for composing software modules and open programs. Key words: Spans, multirelations, monoidal categories, system specications. Introduction The use of spans [1,6] (and of the dual notion of cospans) have been...
Infinitary term graph rewriting is simple, sound and complete
, 2012
"... Based on a simple metric and a simple partial order on term graphs, we develop two infinitary calculi of term graph rewriting. We show that, similarly to infinitary term rewriting, the partial order formalisation yields a conservative extension of the metric formalisation of the calculus. By showing ..."
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Cited by 3 (3 self)
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Based on a simple metric and a simple partial order on term graphs, we develop two infinitary calculi of term graph rewriting. We show that, similarly to infinitary term rewriting, the partial order formalisation yields a conservative extension of the metric formalisation of the calculus. By showing that the resulting calculi simulate the corresponding wellestablished infinitary calculi of term rewriting in a sound and complete manner, we argue for the appropriateness of our approach to capture the notion of infinitary term graph rewriting.
Modeling Pointer Redirection as Cyclic Termgraph Rewriting
 TERMGRAPH 2006 PRELIMINARY VERSION
, 2006
"... We tackle the problem of datastructure rewriting including global and local pointer redirections. Each basic rewrite step may perform three kinds of actions: (i) Local redirection, the aim of which is to redirect specific pointers determined by means of a pattern; (ii) Replacement, that may add new ..."
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Cited by 3 (3 self)
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We tackle the problem of datastructure rewriting including global and local pointer redirections. Each basic rewrite step may perform three kinds of actions: (i) Local redirection, the aim of which is to redirect specific pointers determined by means of a pattern; (ii) Replacement, that may add new information to datastructures; (iii) Global redirection, which is aimed at redirecting all pointers targeting a node towards another one. We define a new framework, following the doublepushout approach, where graph rewrite rules may mix these three kinds of actions in a row. We define first the category of graphs we consider and then we define rewrite rules as pairs of graph homomorphisms of the form L ← K → R. In our setting, graph K is not arbitrary, it is used to encode pointer redirection. Furthermore, pushouts do not always exist and complement pushouts, when they exist, are not unique. Despite these concerns, our definition of rewriting steps is such that a rewrite rule can always be fired, once a matching is found.
Appligraph: Applications of Graph Transformation  Fourth Annual Progress Report
, 2001
"... This report summarizes the activities in the fourth year of the ESPRIT Working Group APPLIGRAPH, covering the period from April 1, 2000, to March 31, 2001. The principal objective of this Working Group is to promote applied graph transformation as a rulebased framework for the specication and devel ..."
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Cited by 1 (0 self)
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This report summarizes the activities in the fourth year of the ESPRIT Working Group APPLIGRAPH, covering the period from April 1, 2000, to March 31, 2001. The principal objective of this Working Group is to promote applied graph transformation as a rulebased framework for the specication and development of systems, languages, and tools and to improve the awareness of its industrial relevance
Modular Implementation of Programming Languages and a PartialOrder Approach to Infinitary Rewriting
, 2012
"... In this dissertation we investigate two independent areas of research. In the first part, we develop techniques for implementing programming languages in a modular fashion. Within this problem domain, we focus on operations on typed abstract syntax trees with the goal of developing a framework that ..."
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In this dissertation we investigate two independent areas of research. In the first part, we develop techniques for implementing programming languages in a modular fashion. Within this problem domain, we focus on operations on typed abstract syntax trees with the goal of developing a framework that facilitates the definition, manipulation and composition of such operations. The result of our work is a comprehensive combinator library that provides these facilities. What sets our approach apart is the use of recursion schemes derived from tree automata in order to implement operations on abstract syntax trees. The second part is concerned with infinitary rewriting, a field that studies transfinite rewrite sequences. We extend the established theory of infinitary rewriting in two ways: (1) a novel approach to convergence in infinitary rewriting that replaces convergence in a metric space with the limit inferior in a partially ordered set; (2) extending infinitary term rewriting to infinitary term graph rewriting. We show correspondences between the established calculi based on metric convergence and the newly developed calculi based on partial orders. Moreover, we show the advantages of our partial order approach in terms of better confluence and normalisation properties of infinitary term rewriting as well as in terms of better completeness This dissertation is a collection of nine research papers pertaining to two independent areas of research.
ATermGraphSyntax for Algebras over Multisets ⋆
"... Abstract. Earlier papers argued that term graphs play for the specification of relationbased algebras the same role that standard terms play for total algebras. The present contribution enforces the claim by showing that term graphs are a sound and complete representation for multiset algebras, i.e ..."
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Abstract. Earlier papers argued that term graphs play for the specification of relationbased algebras the same role that standard terms play for total algebras. The present contribution enforces the claim by showing that term graphs are a sound and complete representation for multiset algebras, i.e., algebras whose operators are interpreted over multisets. 1
www.elsevier.com/locate/entcs A Note on an OldFashioned Algebra for (Disconnected) Graphs
"... Graphs with interfaces are a simple and intuitive tool for allowing a graph G to interact with the environment, by equipping it with two morphisms J → G, I → G. These “handles ” were used to define graphical operators, and to provide an inductive presentation of graph rewriting. A main feature of gr ..."
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Graphs with interfaces are a simple and intuitive tool for allowing a graph G to interact with the environment, by equipping it with two morphisms J → G, I → G. These “handles ” were used to define graphical operators, and to provide an inductive presentation of graph rewriting. A main feature of graphs with interfaces is their characterization as terms of a free algebra. So far, this was possible only with discrete interfaces, i.e., containing no edge. This note shows that a similar free construction can be performed also with disconnected interfaces, i.e., containing only nodes connected to at most one edge. Keywords: Algebraic presentation of graphs, disconnected graphs, DPO approach, parallel derivations.