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In the late 1960s and early 1970s, the concepts of graph transformation and graph grammars started to become of interest in picture processing and computer science. The main idea was to generalize well-known rewriting techniques from strings and trees to graphs, leading to graph transformations and graph grammars. In particular, the concepts of algebraic graph transformation gained considerable importance in the early years and have done so even more in the last decade. Today, algebraic graph transformation techniques are playing a central role in theoretical computer science, as well as in several applied areas, such as software engineering, concurrent and distributed systems, and visual modeling techniques and model transformations.
The aim of this book is to present the fundamentals of algebraic graph transformation techniques for the purposes of teaching, research, and development, with respect to the following aspects:
1. Fundamentals in the sense of an introduction with a detailed motivation to algebraic graph transformation, including the main constructions and results, as well as their generalization to high-level replacement systems, with a wide range of applications in computer science and related areas.
2. Fundamentals in the sense of mathematical theories, which are the basis for precise definitions, constructions, and results, and for the implementation of algebraic graph transformation in a tool environment called AGG.
3. Fundamentals in the sense of the integration of data types and process specification techniques, where the concepts of algebraic data types are integrated with graph rewriting, leading to the concept of typed attributed graph transformation.
In accordance with these aims, the book is organized in four parts:
Introduction to Graph Transformation Systems, where graph transformations based on classical graphs are introduced and the main constructions and results are motivated in detail.
Adhesive High-Level Replacement Categories and Systems, where the theory is presented in a categorical framework with applications to a large variety of high-level structures, especially transformation systems for various kinds of graphs and Petri nets.
Typed Attributed Graph Transformation Systems, where the concepts of typed attributed graphs are carefully introduced and the main results are obtained as instantiations of Part II.
Case Study on Model Transformation, and Tool Support by AGG, where the concepts of typed attributed graph transformation are applied in a separate case study to visual model transformation, and it is shown how the theory is implemented in the AGG tool.
The book is organized in such a way that the reader can switch, after the introduction in Part I, immediately to Part III however, the concepts and results in both of these parts are instantiations of the categorical theory presented in Part II.
The material of this book is based on a theory of algebraic graph transformation developed at the Technical University of Berlin in cooperation with several international partners in the EU projects COMPUGRAPH, GETGRATS, APPLIGRAPH and SEGRAVIS. This material can also be seen as being in the tradition of algebraic specification techniques, described in the EATCS series of Monographs in Theoretical Computer Science.
Introduction 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 TAGT 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
Appendices
A Short Introduction to Category Theory
A Short Introduction to Signatures and Algebras
Detailed Proofs