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 S consists of a graph GSβ and a set of
constraints CSβ declared over GSβ, 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