| Point 3 of the ADT definition says that for each access to the data structure there must be an operation defined. The above access examples seem to contradict this requirement. Is this really true?
| Let's look again at the two possibilities for representing imaginary numbers. Let's stick to the real part. In the first version, x equals c[0]. In the second version, x equals c.r. In both cases x equals ``something''. It is this ``something'' which differs from the actual data structure used. But in both cases the performed operation ``equal'' has the same meaning to declare x to be equal to the real part of the complex number c: both cases archieve the same semantics.
| If you think of more complex operations the impact of decoupling data structures from operations becomes even more clear. For example the addition of two complex numbers requires you to perform an addition for each part. Consequently, you must access the value of each part which is different for each version. By providing an operation ``add'' you can encapsulate these details from its actual use. In an application context you simply ``add two complex numbers'' regardless of how this functionality is actually archieved.
| Once you have created an ADT for complex numbers, say Complex, you can use it in the same way like well-known data types such as integers.