Download e-book for kindle: Analysis and Correctness of Algebraic Graph and Model by Ulrike Golas

By Ulrike Golas

ISBN-10: 3834814938

ISBN-13: 9783834814937

Graph and version modifications play a principal 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 ameliorations. Ulrike Golas extends this thought for extra refined functions just like the specification of syntax, semantics, and version adjustments of advanced versions. according to M-adhesive transformation platforms, version modifications are effectively analyzed concerning syntactical correctness, completeness, practical habit, and semantical simulation and correctness. The built 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 retaining the semantics.

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Download e-book for iPad: Analysis and Correctness of Algebraic Graph and Model by Ulrike Golas

Graph and version differences play a crucial function for visible modeling and model-driven software program improvement. in the final decade, a mathematical thought of algebraic graph and version ameliorations has been constructed for modeling, research, and to teach the correctness of differences. Ulrike Golas extends this thought for extra subtle purposes just like the specification of syntax, semantics, and version differences of complicated types.

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

Sample text

7. If C has intersections of M1 -subobjects this means that given ci : Ci → D ∈ M1 with i ∈ I for some index set I the corresponding diagram has a limit (C, (ci : C → Ci )i∈I , c : C → D) in C with ci ◦ ci = c and c, ci ∈ M1 for all i ∈ I. Let M denote the class of all M1 -functor transformations. Given f : A → D ∈ M , by assumption we can construct component-wise the initial pushout (1x ) over f (x) in C for all x ∈ X, with b0 (x), c0 (x) ∈ M1 . B0 (x) a0 (x) C0 (x) b0 (x) (1)x c0 (x) A(x) f (x) D(x) C0 (x) c0 (x) D(x) (2) ci (x) di (x) Ci (x) B a C b (3) c A f D Define (C, (ci : C → Ci )i∈I , c : C → D) as the limit in [X, C] of all those ci : Ci → D ∈ M such that for all x ∈ X there exists a di (x) : C0 (x) → Ci (X) ∈ M1 with ci (x) ◦ di (x) = c0 (x) (2), which defines the index set I.

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. b 5. Since C\X ∼ = ComCat(idC : C → C, X : B A 1 → C, {1}), idC preserves pushouts, and a f X(M2 ) = X({id1 }) = {idX } ⊆ Isos this a c follows from Item 3.

This is obvious. -6. This follows directly from Item 1, because all these categories are instantiations of general comma categories. 7. Pushouts and pullbacks over M-morphisms as well as the induced morphisms are constructed point-wise in the functor category, thus the effective pushout property is directly induced. 3 Algebraic High-Level Petri Nets Algebraic high-level (AHL) nets combine algebraic specifications with Petri nets [PER95] to allow the modeling of data, data flow, and data changes within the net.

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Analysis and Correctness of Algebraic Graph and Model Transformations by Ulrike Golas


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