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By Ulrike Golas

Graph and version variations play a significant function for visible modeling and model-driven software program improvement. in the final decade, a mathematical idea of algebraic graph and version modifications has been built for modeling, research, and to teach the correctness of changes. Ulrike Golas extends this idea for extra subtle functions just like the specification of syntax, semantics, and version ameliorations of advanced types. in keeping with M-adhesive transformation structures, version variations are effectively analyzed concerning syntactical correctness, completeness, useful 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 protecting the semantics.

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7. If C has binary coproducts, the coproduct of two functors A, B : X → C in [X, C] is the component-wise coproduct functor A + B with A + B(x) = 3 M-Adhesive Transformation Systems 30 A(x)+B(x) for an object x ∈ X and A+B(h) = A(h)+B(h) for a morphism h ∈ X. 2 Epi–M Factorization For Epi–M factorizations, we obtain the same results as for E –M pair factorizations by replacing the class of morphism pairs E by the class of all epimorphisms and M by M. We do not explicitely state these results here, but they can be easily deduced from the results in the following.

This is obvious. 3. This follows directly from Item 1, since any comma category is an instantiation of a general comma categories. For morphisms f = (f1 , f2 ) and g = (g1 , g2 ) in F we construct the component-wise pair factorizations ((e1 , e1 ), m1 ) of f1 , g1 with (e1 , e1 ) ∈ E1 and m1 ∈ M1 , and ((e2 , e2 ), m2 ) of f2 , g2 with (e2 , e2 ) ∈ E2 and m2 ∈ M2 . This leads to morphisms e = (e1 , e2 ), e = (e1 , e2 ), and m = (m1 , m2 ) in F, and an E –M pair factorization with (e, e ) ∈ E and m ∈ M .

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.

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