Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond

There is a hidden intrigue in the title. CT is one of the most abstract mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a recent trend in software development, industrially supported by standards, tools, and the status of a new "silver bullet". Surprisingly, categorical patterns turn out to be directly applicable to mathematical modeling of structures appearing in everyday MDE practice. Model merging, transformation, synchronization, and other important model management scenarios can be seen as executions of categorical specifications. Moreover, the paper aims to elucidate a claim that relationships between CT and MDE are more complex and richer than is normally assumed for "applied mathematics". CT provides a toolbox of design patterns and structural principles of real practical value for MDE. We will present examples of how an elementary categorical arrangement of a model management scenario reveals deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

The Meaning of UML Models

The Unified Modelling Language (UML) is intended to express complex ideas in an intuitive and easily understood way. It is important because it is widely used in software engineering and other disciplines. Although an official definition document exists, there is much debate over the precise meaning of UML models. ¶ In response, the academic community have put forward many different proposals for formalising UML, but it is not at all obvious how to decide between them. Indeed, given that UML practitioners are inclined to reject formalisms as non-intuitive, it is not even obvious that the definition should be “formal” at all. Rather than searching for yet another formalisation of UML, our main aim is to determine what would constitute a good definition of UML. ¶ The first chapter sets the UML definition problem in a broad context, relating it to work in logic and the philosophy of science. ..

On modeling, mathematics, category theory and RM-ODP

Abstract. RM-ODP is about modeling, and mathematics is one of the oldest, and deserved, modeling disciplines. Experience accumulated in mathematics in general, and some of machineries developed, may well turn out to be relevant for arranging/organizing / formalizing the concepts managed in RM-ODP. Especially promising here is mathematical category theory that is nothing but a discipline and framework for structure engineering considered in an abstract and precise way.