67 research outputs found
Cartesian institutions with evidence: Data and system modelling with diagrammatic constraints and generalized sketches
Data constraints are fundamental for practical data modelling, and a
verifiable conformance of a data instance to a safety-critical constraint
(satisfaction relation) is a corner-stone of safety assurance. Diagrammatic
constraints are important as both a theoretical concepts and a practically
convenient device. The paper shows that basic formal constraint management can
well be developed within a finitely complete category (hence the reference to
Cartesianity in the title). In the data modelling context, objects of such a
category can be thought of as graphs, while their morphisms play two roles: of
data instances and (when being additionally labelled) of constraints.
Specifically, a generalized sketch consists of a graph and a set of
constraints declared over , and appears as a pattern for typical
data schemas (in databases, XML, and UML class diagrams). Interoperability of
data modelling frameworks (and tools based on them) very much depends on the
laws regulating the transformation of satisfaction relations between data
instances and schemas when the schema graph changes: then constraints are
translated co- whereas instances contra-variantly. Investigation of this
transformation pattern is the main mathematical subject of the paperComment: 35 pages. The paper will be presented at the conference on Applied
Category Theory, ACT'2
A Diagrammatic Logic for Object-Oriented Visual Modeling
Formal generalized sketches is a graph-based specification format that borrows its main ideas from categorical and ordinary first-order logic, and adapts them to software engineering needs. In the engineering jargon, it is a modeling language design pattern that combines mathematical rigor and appealing graphical appearance. The paper presents a careful motivation and justification of the applicability of generalized sketches for formalizing practical modeling notations. We extend the sketch formalism by dependencies between predicate symbols and develop new semantic notions based on the Instances-as-typed-structures idea. We show that this new framework fits in the general patterns of the institution theory and is well amenable to algebraic manipulations. Keywords: Diagrammatic modeling; model management; generic logic; categorical logic; diagram predicate; categorical sketchpublishedVersio
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
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