Dominique Duval

Dominique Duval, Rachid Echahed

This paper introduces sketch-oriented databases, a categorical framework that encodes database paradigms as finite-limit sketches and individual databases and schemas as set-valued models. It illustrates the formalism through graph-oriented paradigms such as quivers, RDF triplestores and property graphs. It also shows how common graph features such as labels, attributes, typing, and paths, are uniformly captured by sketch constructions. Because paths play an important role in queries, we propose inference rules formalized via localizers to compute useful paths lazily; such localizers are also useful for tasks like database type conformance. Finally, the paper introduces stuttering sketches, whose aim is to facilitate modular composition and scalable model growth: stuttering sketches are finite-limit sketches in which relations are specified by a single limit instead of two nested limits, and the paper proves that finite unions of models of a stuttering sketch are pointwise colimits.

Dominique Duval, Rachid Echahed, Frederic Prost et al.

Copying, or cloning, is a basic operation used in the specification of many applications in computer science. However, when dealing with complex structures, like graphs, cloning is not a straightforward operation since a copy of a single vertex may involve (implicitly)copying many edges. Therefore, most graph transformation approaches forbid the possibility of cloning. We tackle this problem by providing a framework for graph transformations with cloning. We use attributed graphs and allow rules to change attributes. These two features (cloning/changing attributes) together give rise to a powerful formal specification approach. In order to handle different kinds of graphs and attributes, we first define the notion of attributed structures in an abstract way. Then we generalise the sesqui-pushout approach of graph transformation in the proposed general framework and give appropriate conditions under which attributed structures can be transformed. Finally, we instantiate our general framework with different examples, showing that many structures can be handled and that the proposed framework allows one to specify complex operations in a natural way.