Multilevel Typed Graph Transformations

Abstract

Multilevel modeling extends traditional modeling techniques with a potentially unlimited number of abstraction levels. Multilevel models can be formally represented by multilevel typed graphs whose manipulation and transformation are carried out by multilevel typed graph transformation rules. These rules are cospans of three graphs and two inclusion graph homomorphisms where the three graphs are multilevel typed over a common typing chain. In this paper, we show that typed graph transformations can be appropriately generalized to multilevel typed graph transformations improving preciseness, flexibility and reusability of transformation rules. We identify type compatibility conditions, for rules and their matches, formulated as equations and inequations, respectively, between composed partial typing morphisms. These conditions are crucial presuppositions for the application of a rule for a match—based on a pushout and a final pullback complement construction for the underlying graphs in the category —to always provide a well-defined canonical result in the multilevel typed setting. Moreover, to formalize and analyze multilevel typing as well as to prove the necessary results, in a systematic way, we introduce the category of typing chains and typing chain morphisms.

Adrian Rutle

Professor

Rutle is professor in software engineering with a wide experience in research, education and supervision in modelling and simulation for virtual prototyping, digital fabrication, robotics, workflow modelling, eHealth, etc. Rutle’s main interest is applying abstraction results from the field of model-driven software engineering to practical domains and has expertise in the development of modelling frameworks and domain-specific modelling languages.

Uwe Wolter

Professor

Uwe E. Wolter is associate professor at the University of Bergen, Norway. He received his PhD degree in 1989 from the Technical University Magdeburg, Germany. He was awarded with the Medal of Honour from the East-German Society of Mathematics for the best PhD thesis of the year. He held positions at Humboldt-University Berlin and Technical University Berlin before joining the Department of Informatics at the University of Bergen in 2000.