Category Theory Framework for Variability Models with Non-functional Requirements

In Software Product Line (SPL) engineering one uses Variability Models (VMs) as input to automated reasoners to generate optimal products according to certain Quality Attributes (QAs). Variability models, however, and more specifically those including numerical features (i.e., NVMs), do not natively support QAs, and consequently, neither do automated reasoners commonly used for variability resolution. However, those satisfiability and optimisation problems have been covered and refined in other relational models such as databases. Category Theory (CT) is an abstract mathematical theory typically used to capture the common aspects of seemingly dissimilar algebraic structures. We propose a unified relational modelling framework subsuming the structured objects of VMs and QAs and their relationships into algebraic categories. This abstraction allows a combination of automated reasoners over different domains to analyse SPLs. The solutions' optimisation can now be natively performed by a combination of automated theorem proving, hashing, balanced-trees and chasing algorithms. We validate this approach by means of the edge computing SPL tool HADAS.