While many advances towards effective anomaly detection techniques targeting specific applications have been made in recent years, little work has been done to develop application-agnostic approaches to the subject. In this article, we present such an approach, in which anomaly detection methods are treated as formal, structured objects. We consider a general class of methods, with an emphasis on methods that utilize structural properties of the data they operate on. For this class of methods, we develop a decomposition into sub-methods-simple, restricted objects, which may be reasoned about independently and combined to form methods. As we show, this formalism enables the construction of software that facilitates formulating, implementing, evaluating, as well as algorithmically finding and calibrating anomaly detection methods.