Analysis and Correctness of Algebraic Graph and Model by Ulrike Golas

By Ulrike Golas

Graph and version ameliorations play a important position for visible modeling and model-driven software program improvement. in the final decade, a mathematical conception of algebraic graph and version modifications has been constructed for modeling, research, and to teach the correctness of adjustments. Ulrike Golas extends this concept for extra subtle purposes just like the specification of syntax, semantics, and version ameliorations of complicated types. in accordance with M-adhesive transformation structures, version differences are effectively analyzed concerning syntactical correctness, completeness, sensible 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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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. In general, an AHL net denotes a net based on a specification SP in combination with an SP-algebra A, in contrast a net without a specific algebra is called a schema.

Proof 1. 1, pushouts over M-morphisms in the general comma category are constructed component-wise in the underlying categories. The induced morphism is constructed from the induced morphisms in the underlying components. Since also pullbacks over M-morphisms are constructed component-wise, the effective pushout property of the categories (Cj , Mj ) implies this property in (G, M). 2. This is obvious. -6. This follows directly from Item 1, because all these categories are instantiations of general comma categories.

This framework allowed a rich theory of transformations for all HLR categories, but the HLR properties were difficult and lengthy to verify for each category. 1 Introduction to M-Adhesive Categories Adhesive categories were introduced in [LS04] as a categorical framework for deriving process congruences from reaction rules. They require a certain compatibility of pushouts and pullbacks, called the van Kampen property, for pushouts along monomorphisms in the considered category. Later, they were extended to quasiadhesive categories in [JLS07] where the van Kampen property has to hold only for pushouts along regular monomorphisms.

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