The explanation of the design patterns by the symmetry concepts

Abstract

The aim of this paper is to establish a connection between software engineering and other science disciplines, such as mathematics, physics, and alike, with the intent to use the knowledge from these disciplines to create a new software system which will be more stable and sustainable than existing systems. In that sense, this paper formally explains the design patterns through the concepts of symmetry; symmetry transformations and symmetry groups. We give the formal definition of design patterns and explain when and how the design patterns are occurring. Therefore, we have made the formal basis to create stable and sustainable software systems, based on symmetry concepts, which will be both changeable but also immune to change. We have defined the theorems that connect concepts of symmetry and class diagrams and pointed out the cases when classes make a symmetry transformation and when a set of classes make the symmetry and no-symmetry group. Finally, we have given an example to show the process of making design patterns by using the symmetry concepts.