By Ulrike Golas
Graph and version ameliorations play a valuable function for visible modeling and model-driven software program improvement. in the final decade, a mathematical conception of algebraic graph and version alterations has been built for modeling, research, and to teach the correctness of differences. Ulrike Golas extends this thought for extra refined purposes just like the specification of syntax, semantics, and version changes of complicated versions. according to M-adhesive transformation platforms, version alterations are effectively analyzed relating to syntactical correctness, completeness, useful habit, and semantical simulation and correctness. The constructed equipment and effects are utilized to the non-trivial challenge of the specification of syntax and operational semantics for UML statecharts and a version transformation from statecharts to Petri nets keeping the semantics.
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Additional info for Analysis and Correctness of Algebraic Graph and Model Transformations
The comma category (F, (M1 × M2 ) ∩ M orF ), with F = ComCat(F, G; I), where F : C → X preserves pushouts along M1 -morphisms and G : D → X preserves pullbacks along M2 -morphisms, 4. the product category (C × D, M1 × M2 ), 5. the slice category (C\X, M1 ∩ M orC\X ), 6. the coslice category (X\C, M1 ∩ M orX\C ), 7. the functor category ([X, C], M1 -functor transformations). Proof For the general comma category, it is easy to show that M is a class of monomorphisms closed under isomorphisms, composition, and decomposition since this holds for all components Mj .
During the model transformation process, the intermediate models are typed over AT G. This type graph may contain not only AT GS and AT GT , but also additional types and relations which are needed for the transformation process only. The resulting model MT is automatically typed over AT G. If it is not already typed over AT GT , a restriction is used as the last step of the transformation to obtain a valid target model [EEPT06]. 3 Model Transformation Based on Graph Transformation AT GS AT GT AT G typeMS MS 15 typeMT M1 ...
It might be expected that, at least in the category Sets, every pushout is a van Kampen square. Unfortunately, this is not true, but at least pushouts along monomorphisms are van Kampen squares in Sets and several other categories. For an M-adhesive category, we consider a category C together with a morphism class M of monomorphisms. We require pushouts along Mmorphisms to be M-van Kampen squares, along with some rather technical conditions for the morphism class M which are needed to ensure compatibility of M with pushouts and pullbacks.
Analysis and Correctness of Algebraic Graph and Model Transformations by Ulrike Golas