An Algebraic Formalization of the GoF Design Patterns

TL;DR

This paper introduces an algebraic, graph-based formal approach using category theory to specify and analyze GoF design patterns, enabling pattern composition, nested submodels, and cross-diagram synchronization.

Contribution

It presents a novel algebraic formalization method for design patterns that supports pattern composition, nested submodels, and inter-pattern synchronization across multiple diagrams.

Findings

Enables formal specification of patterns with category theory

Supports nested submodels and pattern composition

Allows cross-diagram pattern synchronization

Abstract

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.