Algebraic Validation of software Metrics

A method is described for the formal evaluation of a software metric and its underlying model. This is based upon the specification of the model as an algebra and its desired behaviour as an associated axiom set. If these axioms can be proved to be invariant across the model, then the model may be considered to be valid with respect to its axioms. Where an axiom cannot be shown to be invariant this implies that either the model is anomalous or that the axiom was inappropriate. This approach is applied to a design metric based upon intermodule coupling. It is argued that this method of metric validation is a general one, and one which is capable of increasing confidence in the correctness of a metric particularly during the early stages of its development when empirical data may either be sparse or unavailable. It is intended as a practical means whereby metrics workers can eliminate pathological metrics prior to embarking upon costly and time consuming empirical validation exercises. We do not intend that this method should supplant empirically based means of validation, rather that it is complementary technique.