This chapter presents an introduction to the theoretical foundations of abstract data types. In particular, an algebraic treatment is given of abstract data types defined by equational theories. We then extend this approach to include objects with dynamic state changes. We start this chapter with a discussion of the notion of types and reflect on how types affect object-oriented programming. At the end of the chapter, a distinction is made between a syntactic, semantic and operational interpretation of types.
The notion of data abstraction gives rise to a wealth of possibly interesting assignments.
For example, one may think of exploring
including proof-theoretical aspects with respect to invariance properties, as outlined in chapter refinement.
Another interesting area of investigation is
In particular, do we need modules when we have classes, and how may they be integrated with classes with respect to visibility and protection?