Get Analysis and Correctness of Algebraic Graph and Model PDF

By Ulrike Golas

Graph and version differences play a significant position for visible modeling and model-driven software program improvement. in the final decade, a mathematical idea of algebraic graph and version variations has been built for modeling, research, and to teach the correctness of adjustments. Ulrike Golas extends this idea for extra refined functions just like the specification of syntax, semantics, and version variations of complicated versions. in line with M-adhesive transformation platforms, version alterations are effectively analyzed concerning syntactical correctness, completeness, practical 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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In [RK09], an approach based on nested graph predicates is introduced which define a relationship between rules and matches. While nesting extends the expressiveness of these transformations, it is quite complicated to write and understand these predicates and it seems to be difficult to relate or integrate them to the theoretical results for graph transformation. In [BFH87], the theory of amalgamation for the double-pushout approach has been developed on a set-theoretical basis for pairs of standard graph rules without application conditions.

If the inclusion functor reflects binary coproducts I A this is obvious. Otherwise, if we have an initial iB object I, given A, B ∈ C we can construct the pushout over iA : I → A, iB : I → B, which exists A +I B B because iA , iB ∈ M or due to general pushouts. In this case, the pushout object is also the coproduct of A and B, because for any object in comparison to the coproduct the morphisms agree via iA and iB on I, and the constructed pushout induces also the coproduct morphism. 3. This follows directly from Item 1, since the comma category is an instantiation of general comma categories.

3. Since comma categories are an instantiation of general comma categories, this follows directly from Item 1. The initial pushout of f = (f1 , f2 ) : D (A1 , A2 , (opA i )) → (D1 , D2 , (opi )) ∈ M1 ×M2 is the component-wise initial −1 ◦ opA pushout in C and D, with B = (B1 , B2 , opB i = G(b2 ) i ◦ F (b1 )) and C −1 D C = (C1 , C2 , opi = G(c1 ) ◦ opi ◦ F (c1 )). C 4. D (M2 ) ⊆ {id1 } = Isos this follows from Item 3. The initial pushout (3) over a morphism (f1 , f2 ) : (A1 , A2 ) → (D1 , D2 ) ∈ M1 × M2 is the component-wise product of the initial pushouts over f1 in C and f2 in D.

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