Analysis and Correctness of Algebraic Graph and Model Transformations

von: Ulrike Golas

Vieweg+Teubner (GWV), 2011

ISBN: 9783834899347 , 226 Seiten

Format: PDF, OL

Kopierschutz: Wasserzeichen

Windows PC,Mac OSX Apple iPad, Android Tablet PC's Online-Lesen für: Windows PC,Mac OSX,Linux

Preis: 96,29 EUR

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Mehr zum Inhalt

Analysis and Correctness of Algebraic Graph and Model Transformations


 

Foreword

6

Abstract

7

Zusammenfassung

9

Contents

11

List of Figures

14

1 Introduction

16

2 Introduction to Graph and Model Transformation, and Related Work

22

2.1 Model Transformation

22

2.2 Graph Transformation

24

2.3 Model Transformation Based on Graph Transformation

29

3 M-Adhesive Transformation Systems

34

3.1 Graphs, Typed Graphs, and Typed Attributed Graphs

35

3.2 M-Adhesive Categories

37

3.2.1 Introduction to M-Adhesive Categories

37

3.2.2 Construction of M-Adhesive Categories

41

3.2.3 Preservation of Additional Properties via Constructions

43

3.2.3.1 Binary Coproducts

43

3.2.3.2 Epi–M Factorization

45

3.2.3.3 E'–M' Pair Factorization

45

3.2.3.4 Initial Pushouts

49

3.3 Algebraic High-Level Petri Nets

55

3.4 Transformations in M-Adhesive Systems

61

3.4.1 Conditions and Constraints over Objects

62

3.4.2 Rules and Transformations

64

3.4.3 Main Analysis Results in M-Adhesive Transformation Systems

66

3.4.3.1 Local Church-Rosser and Parallelism Theorem

66

3.4.3.2 Concurrency Theorem

68

3.4.3.3 Embedding and Extension Theorem

70

3.4.3.4 Critical Pairs and Local Confluence Theorem

72

4 Amalgamated Transformations

76

4.1 Foundations and Analysis of Amalgamated Transformations

76

4.1.1 Kernel, Multi, and Complement Rules

77

4.1.2 Amalgamated Rules and Transformations

84

4.1.3 Parallel Independence of Amalgamated Transformations

96

4.1.4 Other Results for Amalgamated Transformations

102

4.1.5 Interaction Schemes and Maximal Matchings

103

4.1.6 Main Results for Amalgamated Transformations Based on Maximal Matchings

106

4.2 Operational Semantics Using Amalgamation

108

4.2.1 Semantics for Elementary Nets

108

4.2.2 Syntax of Statecharts

113

4.2.3 Semantics for Statecharts

119

5 Model Transformation Based on Triple Graph Transformation

130

5.1 Introduction to Triple Graph Transformation

130

5.1.1 The Category of Triple Graphs

131

5.1.2 Triple Graph Transformation

132

5.2 Triple Graph Transformation with Application Conditions

134

5.2.1 S-and T -Consistent Application Conditions

135

5.2.2 Composition and Decomposition of Triple Transformations

146

5.3 Model Transformation SC2PN from Statecharts to Petri Nets

151

6 Analysis, Correctness, and Construction of Model Transformations

168

6.1 Syntactical Correctness

169

6.2 Termination and Functional Behavior

171

6.2.1 Termination

171

6.2.2 Termination of Statecharts Semantics

172

6.2.3 Functional Behavior

174

6.3 Semantical Simulation and Correctness

176

6.3.1 Simulation of Petri Nets

178

6.3.2 Semantical Correctness of the Model Transformation SC2PN

180

6.4 On-the-Fly Construction of Model Transformations

188

7 Conclusion and Future Work

196

7.1 Theoretical Contributions

196

7.2 Relevance for Model-Driven Software Development

198

7.3 Case Studies

200

7.4 Tool Support

201

7.5 Future Work

203

Appendix

205

A Categorical Results

206

A.1 Proofs for Construction of M-Adhesive Categories

206

A.2 Proofs for Generalized AHL Schemas as an M-Adhesive Category

208

A.3 Proofs for AHL Systems as an M-adhesive Category

210

A.3.1 The Category of Markings

210

A.3.2 From Nets to Net Systems

214

A.4 Proofs for Amalgamated Transformations

216

Bibliography

224

Index

236