This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. It contains an introduction to classical graphs. Basic and advanced results are first shown for an abstract form of replacement systems and are then instantiated to several forms of graph and Petri net transformation systems. The book develops typed attributed graph transformation and contains a practical case study.

Zusammenfassung

Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory.

Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool environment. Finally the appendix covers the basics of category theory, signatures and algebras.

The book addresses both research scientists and graduate students in computer science, mathematics and engineering.

Inhalt
to Graph Transformation Systems.- General Introduction.- Graphs, Typed Graphs, and the Gluing Construction.- Graph Transformation Systems.- Adhesive High-Level Replacement Categories and Systems.- Adhesive High-Level Replacement Categories.- Adhesive High-Level Replacement Systems.- Embedding and Local Confluence.- Constraints and Application Conditions.- Typed Attributed Graph Transformation Systems.- Typed Attributed Graphs.- Typed Attributed Graph Transformation Systems.- Embedding and Local Confluence for Typed AGT Systems.- Adhesive HLR Categories for Typed Attributed Graphs.- Constraints, Application Conditions and Termination for Typed AGT Systems.- Typed Attributed Graph Transformation with Inheritance.- Case Study on Model Transformation, and Tool Support by AGG.- Case Study on Model Transformation.- Implementation of Typed Attributed Graph Transformation by AGG.