GReTA seminar: "A Journey from Graphs to Generalized Sketches"
Channel: GReTA Seminar
Date: 2023-04-21

Speaker:

Uwe Wolter (Department of Informatics, University of Bergen, Norway)


Note: This is a joint event with the working group "Catégories supérieures, polygraphes et homotopie" at IRIF, Université Paris Cité (https://www.irif.fr/seminaires/cat/index)

Abstract:

In the talk we present the Generalized Sketch Formalism à la Makkai/Diskin as a straightforward and quite natural generalization of specification formalisms based on graphs and graph transformations.
 
We discuss why traditional Ehresmann Sketches are not fully adequate for the formalization of Software Models and argue in favor of Generalized Sketches. Ehresmann Sketches utilize only the properties commutative, limit or colimit, respectively, while we are allowed to work with arbitrary “user defined” properties in Generalized Sketches. Makkai proposed Sketch Implications as a tool to axiomatize the meaning of “user defined” properties and we elucidate that especially limit and colimit properties can be expressed by means of Sketch Implications. On the other side, we can utilize Sketch Implications as a tool to describe the structure of Software Models.
 
Compared to Graph Transformations, Sketch Transformations give us a more refined and expressive tool at hand to formalize Model Transformations. It looks like, however, that only the use of cospan transformation rules instead of the traditional span transformation rules would enable us to derive full advantage of sketches.


About the GReTA seminars:

The GReTA – Graph TRansformation Theory and Applications virtual seminar series aims to serve as a platform for the international graph rewriting community, to promote recent developments and trends in the field, and to permit a regular networking and interaction between members of this community. Seminars are held twice a month in the form of Zoom sessions (some of which will be live-streamed to YouTube). Please refer to http://www.irif.fr/~greta for further details (including information on how to register for participating in the Zoom meetings).