Linear software models: Equivalence of modularity matrix to its modularity lattice

摘要

Modularity is an important feature to solve the composition problem of software systems from subsystems. Recently it has been shown that Software systems' Modularity Matrices linking structors to functionals can be put in almost block-diagonal form, where blocks reveal higher-level software modules. An alternative formalization has been independently proposed using Conceptual Lattices linking attributes to objects. But, are these independent formalizations related? This paper shows the equivalence of Modularity Matrices to their respective Modularity Lattices. Both formalizations support the simplest form of software composition, i.e. linear composition, expressed as an addition of independent components. This equivalence has both theoretical and practical advantages. These are illustrated by comparison of both representations for a series of case studies.