Analysis and Correctness of Algebraic Graph and Model Transformations [electronic resource] /
Golas, Ulrike.author.
Graph and model transformations play a central role for visual modeling and model-driven software development. Within the last decade, a mathematical theory of algebraic graph and model transformations has been developed for modeling, analysis, and to show the correctness of transformations. Ulrike Golas extends this theory for more sophisticated applications like the specification of syntax, semantics, and model transformations of complex models. Based on M-adhesive transformation systems, model transformations are successfully analyzed regarding syntactical correctness, completeness, functional behavior, and semantical simulation and correctness. The developed methods and results are applied to the non-trivial problem of the specification of syntax and operational semantics for UML statecharts and a model transformation from statecharts to Petri nets preserving the semantics.
Description based upon print version of record.
Foreword; Abstract; Zusammenfassung; Contents; List of Figures; 1 Introduction; 2 Introduction to Graph and Model Transformation, and Related Work; 2.1 Model Transformation; 2.2 Graph Transformation; 2.3 Model Transformation Based on Graph Transformation; 3 M-Adhesive Transformation Systems; 3.1 Graphs, Typed Graphs, and Typed Attributed Graphs; 3.2 M-Adhesive Categories; 3.2.1 Introduction to M-Adhesive Categories; 3.2.2 Construction of M-Adhesive Categories; 3.2.3 Preservation of Additional Properties via Constructions; 3.2.3.1 Binary Coproducts; 3.2.3.2 Epi-M Factorization
3.2.3.3 E'-M' Pair Factorization3.2.3.4 Initial Pushouts; 3.3 Algebraic High-Level Petri Nets; 3.4 Transformations in M-Adhesive Systems; 3.4.1 Conditions and Constraints over Objects; 3.4.2 Rules and Transformations; 3.4.3 Main Analysis Results in M-Adhesive Transformation Systems; 3.4.3.1 Local Church-Rosser and Parallelism Theorem; 3.4.3.2 Concurrency Theorem; 3.4.3.3 Embedding and Extension Theorem; 3.4.3.4 Critical Pairs and Local Confluence Theorem; 4 Amalgamated Transformations; 4.1 Foundations and Analysis of Amalgamated Transformations; 4.1.1 Kernel, Multi, and Complement Rules
4.1.2 Amalgamated Rules and Transformations4.1.3 Parallel Independence of Amalgamated Transformations; 4.1.4 Other Results for Amalgamated Transformations; 4.1.5 Interaction Schemes and Maximal Matchings; 4.1.6 Main Results for Amalgamated Transformations Based on Maximal Matchings; 4.2 Operational Semantics Using Amalgamation; 4.2.1 Semantics for Elementary Nets; 4.2.2 Syntax of Statecharts; 4.2.3 Semantics for Statecharts; 5 Model Transformation Based on Triple Graph Transformation; 5.1 Introduction to Triple Graph Transformation; 5.1.1 The Category of Triple Graphs
5.1.2 Triple Graph Transformation5.2 Triple Graph Transformation with Application Conditions; 5.2.1 S-and T -Consistent Application Conditions; 5.2.2 Composition and Decomposition of Triple Transformations; 5.3 Model Transformation SC2PN from Statecharts to Petri Nets; 6 Analysis, Correctness, and Construction of Model Transformations; 6.1 Syntactical Correctness; 6.2 Termination and Functional Behavior; 6.2.1 Termination; 6.2.2 Termination of Statecharts Semantics; 6.2.3 Functional Behavior; 6.3 Semantical Simulation and Correctness; 6.3.1 Simulation of Petri Nets
6.3.2 Semantical Correctness of the Model Transformation SC2PN6.4 On-the-Fly Construction of Model Transformations; 7 Conclusion and Future Work; 7.1 Theoretical Contributions; 7.2 Relevance for Model-Driven Software Development; 7.3 Case Studies; 7.4 Tool Support; 7.5 Future Work; Appendix; A Categorical Results; A.1 Proofs for Construction of M-Adhesive Categories; A.2 Proofs for Generalized AHL Schemas as an M-Adhesive Category; A.3 Proofs for AHL Systems as an M-adhesive Category; A.3.1 The Category of Markings; A.3.2 From Nets to Net Systems; A.4 Proofs for Amalgamated Transformations
Bibliography
Includes bibliographical references and author index.
Graph and model transformations play a central role for visual modeling and model-driven software development. Within the last decade, a mathematical theory of algebraic graph and model transformations has been developed for modeling, analysis, and to show the correctness of transformations. Ulrike Golas extends this theory for more sophisticated applications like the specification of syntax, semantics, and model transformations of complex models. Based on M-adhesive transformation systems, model transformations are successfully analyzed regarding syntactical correctness, completeness, functional behavior, and semantical simulation and correctness. The developed methods and results are applied to the non-trivial problem of the specification of syntax and operational semantics for UML statecharts and a model transformation from statecharts to Petri nets preserving the semantics.
Computers.
Computer science.
Theory of Computation.
Computer Science, general.