By Ulrike Golas
Graph and version differences play a relevant position for visible modeling and model-driven software program improvement. in the final decade, a mathematical thought of algebraic graph and version differences has been built for modeling, research, and to teach the correctness of changes. Ulrike Golas extends this concept for extra subtle functions just like the specification of syntax, semantics, and version variations of complicated types. in response to M-adhesive transformation platforms, version variations are effectively analyzed concerning 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 holding the semantics.
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Additional info for Analysis and Correctness of Algebraic Graph and Model Transformations
E. d ∈ G. 2. 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 .
In this section, we show that diﬀerent versions of AHL schemas, nets, and systems are M-adhesive categories [Pra07, Pra08]. 18 (AHL schema) An AHL schema over an algebraic speciﬁcation SP , where SP = (SIG, E, X) has additional variables X and SIG = (S, OP ), is given by AC = (P, T, pre, post, cond, type) with sets P of places and T of transitions, pre, post : T → (TSIG (X) ⊗ P )⊕ as pre- and post-domain functions, cond : T → Pf in (Eqns(SIG, X)) assigning to each t ∈ T a ﬁnite set cond(t) of equations over SIG and X, and type : P → S a type function.
There is a clear correspondence between meta-models and type graphs, where classes correspond to node types, associations to edge types, the conformity of a model to the meta-model corresponds to the existence of a typing morphism into the type graph, and OCL constraints correspond to graph constraints. To simplify the modeling of graph transformations, type graphs have been extended with node type inheritance [LBE+ 07]. Such a type graph with inheritance can be ﬂattened leading to an equivalent ﬂattened system, which can be analyzed using the standard results for graph transformation.