Formalization of Architecture-Centric Model Mapping Using Category Theory

Model transformation is touted to play a key role in model-driven development. The mapping relations between models are the foundation and basis for the transformation. On the basis of software architecture, this paper tries to provide a precise semantics for both components structuring and models mapping by using category theory. Morphism composition is used to trace the interconnections and mapping relations between component-based models, while consistency between the sorts /operations of component models at different abstract levels is maintained by functors. Category theory supports the diagrammatic representation of component model that visualizes the relationships between components and the structural features, which can be used to strengthen the understandability and traceability of model transformation. The formalization enables users to check whether the mapping relations satisfy some desired properties and also is suitable to automatic software development, and thus can make an effective support to model-driven software development.

[1]  José Luiz Fiadeiro,et al.  A mathematical toolbox for the software architect , 1996, Proceedings of the 8th International Workshop on Software Specification and Design.

[2]  Mark J. Gerken,et al.  Specification of Software Architecture , 2000, Int. J. Softw. Eng. Knowl. Eng..

[3]  HailpernB.,et al.  Model-driven development , 2006 .

[4]  Carl Kesselman,et al.  Generalized communicators in the Message Passing Interface , 1996, Proceedings. Second MPI Developer's Conference.

[5]  Steve M. Easterbrook,et al.  Management of evolving specifications using category theory , 1998, Proceedings 13th IEEE International Conference on Automated Software Engineering (Cat. No.98EX239).

[6]  Xiao Yang,et al.  MDA-based Modeling and Transformation Approach for WEB Applications , 2006, Sixth International Conference on Intelligent Systems Design and Applications.

[7]  Virginia Torczon,et al.  On the Convergence of Pattern Search Algorithms , 1997, SIAM J. Optim..

[8]  Horst Herrlich,et al.  Abstract and concrete categories , 1990 .

[9]  Neeraj Suri,et al.  An approach to specify and test component-based dependable software , 2002, 7th IEEE International Symposium on High Assurance Systems Engineering, 2002. Proceedings..

[10]  Anneke Kleppe,et al.  MDA explained - the Model Driven Architecture: practice and promise , 2003, Addison Wesley object technology series.

[11]  Jean-Louis Sourrouille,et al.  Model mapping using formalism extensions , 2005, IEEE Software.

[12]  Krzysztof Czarnecki,et al.  Feature-based survey of model transformation approaches , 2006, IBM Syst. J..

[13]  Jiang Guo,et al.  Using category theory to model software component dependencies , 2002, Proceedings Ninth Annual IEEE International Conference and Workshop on the Engineering of Computer-Based Systems.

[14]  Peri L. Tarr,et al.  Model-driven development : The good , the bad , and the ugly & , 2006 .

[15]  Tamara G. Kolda,et al.  Asynchronous Parallel Pattern Search for Nonlinear Optimization , 2001, SIAM J. Sci. Comput..

[16]  Chandler Davis.  THEORY OF POSITIVE LINEAR DEPENDENCE. , 1954 .

[17]  David L. Levine,et al.  Users guide to the PGAPack parallel genetic algorithm library , 1995 .

[18]  Virginia Torczon,et al.  PDS: Direct Search Methods for Unconstrained Optimization on Either Sequential or Parallel Machines , 1992 .