Rules are an important pattern in data mining, but existing approaches are limited to conjunctions of binary literals, fixed measures and counting based algorithms. Rules can be much more diverse, useful and interesting! This work introduces and solves the Generalised Rule Mining (GRM) problem, which abstracts rule mining, removes restrictions on the semantics of rules and redefines rule mining by functions on vectors. This also lends to an interesting geometric interpretation for rule mining. The GRM framework and algorithm allow new methods that are not possible with existing algorithms, can speed up existing methods and separate rule semantics from algorithmic considerations. The GRM algorithm scales linearly in the number of rules found and provides orders of magnitude speed up over fast candidate generation type approaches (in cases where these can be applied).