Modularization Metrics: Assessing Package Organization in Legacy Large Object-Oriented Software

There exist many large object-oriented software systems consisting of several thousands of classes that are organized into several hundreds of packages. In such software systems, classes cannot be considered as units for software modularization. In such context, packages are not simply classes containers, but they also play the role of modules: a package should focus to provide well identified services to the rest of the software system. Therefore, understanding and assessing package organization is primordial for software maintenance tasks. Although there exist a lot of works proposing metrics for the quality of a single class and/or the quality of inter-class relationships, there exist few works dealing with some aspects for the quality of package organization and relationship. We believe that additional investigations are required for assessing package modularity aspects. The goal of this paper is to provide a complementary set of metrics that assess some modularity principles for packages in large legacy object-oriented software: Information-Hiding, Changeability and Reusability principles. Our metrics are defined with respect to object-oriented dependencies that are caused by inheritance and method call. We validate our metrics theoretically through a careful study of the mathematical properties of each metric.