A formal approach to designing a class-subclass structure using a partial-order on the functions

We present a formal method for designing the class structure based on a partial order on the functions, which is derived from the use-relationship between the functions and the various data items. We can regard this method as an initial step in building a theory of refactoring and design-patterns. Our method can identify the functions which should be factored into subfunctions, including their desired signatures and a reduced use-complexity, in order to simplify the class-subclass structure. A similar remark holds for the decomposition or consolidation of data items as well. We illustrate our method with several examples.