Fundamental Theory for Typed Attributed Graphs and Graph Transformation based on Adhesive HLR Categories

The concept of typed attributed graphs and graph transformation is most significant for modeling and meta modeling in software engineering and visual languages, but up to now there is no adequate theory for this important branch of graph transformation. In this article we give a new formalization of typed attributed graphs, which allows node and edge attribution. The first main result shows that the corresponding category is isomorphic to the category of algebras over a specific kind of attributed graph structure signature. This allows to prove the second main result showing that the category of typed attributed graphs is an instance of "adhesive HLR categories". This new concept combines adhesive categories introduced by Lack and Sobocinski with the well-known approach of high-level replacement (HLR) systems using a new simplified version of HLR conditions. As a consequence we obtain a rigorous approach to typed attributed graph transformation providing as fundamental results the Local Church-Rosser, Parallelism, Concurrency, Embedding and Extension Theorem and a Local Confluence Theorem known as Critical Pair Lemma in the literature.

[1]  Hartmut Ehrig,et al.  Parallelism and concurrency in high-level replacement systems , 1991, Mathematical Structures in Computer Science.

[2]  Reiko Heckel,et al.  Confluence of Typed Attributed Graph Transformation Systems , 2002, ICGT.

[3]  Hartmut Ehrig,et al.  Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation , 2006, Fundam. Informaticae.

[4]  Hartmut Ehrig,et al.  A Generic Component Framework for System Modeling , 2002, FASE.

[5]  Martin Grogbse-Rhode,et al.  Semantic Integration of Heterogeneous Software Specifications (Monographs in Theoretical Computer Science) , 2004 .

[6]  Roswitha Bardohl,et al.  A visual environment for visual languages , 2002, Sci. Comput. Program..

[7]  Hartmut Ehrig,et al.  Fundamental Theory for Typed Attributed Graph Transformation , 2004, ICGT.

[8]  Hartmut Ehrig,et al.  Adhesive High-Level Replacement Categories and Systems , 2004, ICGT.

[9]  Detlef Plump,et al.  Towards Graph Programs for Graph Algorithms , 2004, ICGT.

[10]  Hartmut Ehrig,et al.  Handbook of graph grammars and computing by graph transformation: vol. 3: concurrency, parallelism, and distribution , 1999 .

[11]  Hartmut Ehrig,et al.  Theory of Constraints and Application Conditions: From Graphs to High-Level Structures , 2004, Fundam. Informaticae.

[12]  Hartmut Ehrig,et al.  Fundamentals of Algebraic Specification 1 , 1985, EATCS Monographs on Theoretical Computer Science.

[13]  Hartmut Ehrig,et al.  Introduction to the Algebraic Theory of Graph Grammars (A Survey) , 1978, Graph-Grammars and Their Application to Computer Science and Biology.