By Ulrike Golas

Graph and version alterations play a imperative 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 constructed for modeling, research, and to teach the correctness of alterations. Ulrike Golas extends this concept for extra refined functions just like the specification of syntax, semantics, and version ameliorations of complicated versions. in response to M-adhesive transformation platforms, version modifications are effectively analyzed concerning syntactical correctness, completeness, sensible habit, and semantical simulation and correctness. The constructed tools 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 conserving the semantics.

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**Additional resources for Analysis and Correctness of Algebraic Graph and Model Transformations**

**Example text**

In this chapter, only a short overview over the used notions and categorical terms is given. We expect the reader to be familiar with category theory, see [EEPT06] for an overview, and, for example, [Mac71, AHS90] for more thorough introductions. Moreover, only a short outline of the theory of Madhesive transformation systems is given here. For the entire theory with all deﬁnitions, theorems, proofs, and examples see [EEPT06, EP06, PE07]. U. 1 Graphs, Typed Graphs, and Typed Attributed Graphs Graphs and graph-like structures are the main basis for (visual) models.

T. such a veriﬁcation speciﬁcation V SP if A ∈ T SP implies that A ∈ V SP . Minimal gluings of transformation patterns are analyzed to ensure the correctness. This approach works well for the analysis of syntactical correctness, but is diﬃcult to adopt for semantical correctness. 3 M-Adhesive Transformation Systems M-adhesive categories constitute a powerful framework for the deﬁnition of transformations. The double–pushout approach, which is based on categorical constructions, is a suitable description of transformations leading to a great number of results as the Local Church-Rosser, Parallelism, Concurrency, Embedding, Extension, and Local Conﬂuence Theorems.

26 3 M-Adhesive Transformation Systems As shown in [EHL10a], if f g A B C D (C, M) has binary coproducts then these are compat(6) (7) ible with M, which means B + C idC +g B + D that f, g ∈ M implies f + A + C f +idC B + C g ∈ M: For f : A → B, g : C → D, pushout (6) with f ∈ M implies that f + idC ∈ M and pushout (7) with g ∈ M implies that idB + g ∈ M. Thus, also f + g = (f + id) ◦ (id + g) ∈ M by composition of M-morphisms. 2 Construction of M-Adhesive Categories M-adhesive categories are closed under diﬀerent categorical constructions.