Information Preserving Bidirectional Model Transformations

Within model-driven software development, model transformation has become a key activity. It refers to a variety of operations modifying a model for various purposes such as analysis, optimization, and code generation. Most of these transformations need to be bidirectional to e.g. report analysis results, or keep coherence between models. In several application-oriented papers it has been shown that triple graph grammars are a promising approach to bidirectional model transformations. But up to now, there is no formal result showing under which condition corresponding forward and backward transformations are inverse to each other in the sense of information preservation. This problem is solved in this paper based on general results for the theory of algebraic graph transformations. The results are illustrated by a transformation of class models to relational data base models which has become a quasistandard example for model transformation.