  This document reports on the use of an algebraic, visual, formal approach to
the specification of patterns for the formalization of the GoF design patterns.
The approach is based on graphs, morphisms and operations from category theory
and exploits triple graphs to annotate model elements with pattern roles. Being
based on category theory, the approach can be applied to formalize patterns in
different domains. Novel in our proposal is the possibility of describing
(nested) variable submodels, inter-pattern synchronization across several
diagrams (e.g. class and sequence diagrams for UML design patterns), pattern
composition, and conflict analysis.
