Results 11 
15 of
15
From Trees to Graphs: Defining the Semantics of Diagram Languages with Graph Transformation
 ICALP Satellite Workshops, Proceedings in Informatics
, 2000
"... In order to define the semantics of diagram languages, new techniques may be developed following the established approaches of denotational, operational, or algebraic semantics of programming languages. Due to the multidimensional nature of diagrams (as opposed to the linear structure of progra ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
In order to define the semantics of diagram languages, new techniques may be developed following the established approaches of denotational, operational, or algebraic semantics of programming languages. Due to the multidimensional nature of diagrams (as opposed to the linear structure of programs), these new approaches should be based on graphs (rather than trees or terms) and graph transformation could provide the underlying technology. In this paper, we try to substantiate this claim by reviewing some of the most important approaches to semantics and discussing their applicability to diagram languages. Keywords diagram languages, semantics, graph transformation 1 Introduction The most important means for communication is the use of language. The language can be a natural one  like in humanhuman communication  or an artificial one  as in humancomputer or computercomputer communication. In general, in the case of speaking, writing, or reading, the symbols in the la...
Van Kampen diagrams are bicolimits in Span
"... In adhesive categories, pushouts along monomorphisms are Van Kampen (vk) squares, a special case of a more general notion called vkdiagram. Other examples of vkdiagrams include coproducts in extensive categories and strict initial objects. Extensive and adhesive categories characterise useful ex ..."
Abstract
 Add to MetaCart
In adhesive categories, pushouts along monomorphisms are Van Kampen (vk) squares, a special case of a more general notion called vkdiagram. Other examples of vkdiagrams include coproducts in extensive categories and strict initial objects. Extensive and adhesive categories characterise useful exactness properties of, respectively, coproducts and pushouts along monos and have found several applications in theoretical computer science. We show that the property of being vk is actually universal, not in C but in the bicategory of spans Span C. This theorem of pure category theory sheds light on the nature of spans and suggests promising generalisations of the theory of adhesive categories.
Van Kampen colimits as bicolimits in Span
"... The exactness properties of coproducts in extensive categories and pushouts along monos in adhesive categories have found various applications in theoretical computer science, e.g. in program semantics, data type theory and rewriting. We show that these properties can be understood as a single unive ..."
Abstract
 Add to MetaCart
The exactness properties of coproducts in extensive categories and pushouts along monos in adhesive categories have found various applications in theoretical computer science, e.g. in program semantics, data type theory and rewriting. We show that these properties can be understood as a single universal property in the associated bicategory of spans. To this end, we first provide a general notion of Van Kampen cocone that specialises to the above colimits. The main result states that Van Kampen cocones can be characterised as exactly those diagrams in C that induce bicolimit diagrams in the bicategory of spans Span C, provided that C has pullbacks and enough colimits.
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 ..."
Abstract
 Add to MetaCart
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.