Is Extension Complexity a Fundamental Software Metric?

The concepts of implementation and extension complexities were developed in connection with an object oriented reengineering of a legacy CAD system [KA97]. These concepts consider a software system as an implementation of a number of different algorithms. Ideally, an algorithm in an object oriented (O-O) system is implemented by a single method that only processes data in its own object. Such an algorithm is desirable because it cannot cause coupling between different objects. It is possible to design and test the method that implements such an algorithm without knowing anything about the other object types (classes). The costs of implementing and testing such an algorithm are therefore usually modest. Higher implementation and testing costs may be expected in algorithms that process data in a number of objects belonging to different object types. The reason is that the implementers must have the data structures of these different object types in their mind while implementing the algorithm. Furthermore, an algorithm involving different object types will typically employ a number of different methods in these different object types. The implementers must therefore also consider all of these different methods during the implementation. It may therefore be assumed that the cognitive load on the mind of the implementers is generally higher with algorithms involving a number of different object types. The costs of implementing and testing an algorithm are therefore assumed to be related to the number of different object types involved. In order to express this the following definitions were introduced: