By Ulrike Golas

ISBN-10: 3834814938

ISBN-13: 9783834814937

Graph and version changes play a valuable function for visible modeling and model-driven software program improvement. in the final decade, a mathematical thought of algebraic graph and version adjustments has been built for modeling, research, and to teach the correctness of adjustments. Ulrike Golas extends this concept for extra refined purposes just like the specification of syntax, semantics, and version alterations of complicated versions. in keeping with M-adhesive transformation platforms, version differences are effectively analyzed relating to syntactical correctness, completeness, practical habit, and semantical simulation and correctness. The built 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 protecting the semantics.

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In the slice category, the X coproduct of (A, a ) and (B, b ) is the object (A + B, [a , b ]) which consists of the coproduct A + B in C together with the morphism [a , b ] : A + B → X induced by a and b . 6. If C has general pushouts, given two objects (A, a ) b X A and (B, b ) in X\C we construct the pushout over a a and b in C. The coproduct of (A, a ) and (B, b ) a is the pushout object A +X B together with the A +X B B b coslice morphism b ◦ a = a ◦ b . For any object (C, c ) in comparison to the coproduct, the coslice morphism c ensures that the morphisms agree via a and b in X such that the pushout also induces the coproduct morphism.

In the slice category, the X coproduct of (A, a ) and (B, b ) is the object (A + B, [a , b ]) which consists of the coproduct A + B in C together with the morphism [a , b ] : A + B → X induced by a and b . 6. If C has general pushouts, given two objects (A, a ) b X A and (B, b ) in X\C we construct the pushout over a a and b in C. The coproduct of (A, a ) and (B, b ) a is the pushout object A +X B together with the A +X B B b coslice morphism b ◦ a = a ◦ b . For any object (C, c ) in comparison to the coproduct, the coslice morphism c ensures that the morphisms agree via a and b in X such that the pushout also induces the coproduct morphism.

1 Binary Coproducts In most cases, binary coproducts can be constructed in the underlying categories, with some compatibility requirements for the preservation of binary coproducts. Note that we do not have to analyze the compatibility of binary coproducts with M, as done in [PEL08], since this is a general result in M-adhesive categories as shown in Rem. 9. 12 If the M-adhesive categories (C, M1 ), (D, M2 ), and (Cj , Mj ) for j ∈ J have binary coproducts then also the following M-adhesive categories have binary coproducts: 1.

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