The purpose of this paper is to develop a method for designing and verifying data abstractions using the functional approach. Before doing so, the existing techniques for designing and verifying procedure and data abstractions will be surveyed briefly. These techniques will then be modified and extended to verify data abstractions. By using the concept of a mathematical function, one can model the behavior of a procedure abstraction and give a more uniform and clearer meaning to the stepwise refinement and verification of procedure abstractions. The concept of a state machine is then used as a basis to specify data abstractions. Using state machine specification, a technique for expressing the design of a data abstraction is then given. A method is then developed to verify the design of a data abstraction with respect to its specifications.

The purpose of this paper is to explore the concepts and provide examples of data structures, data types and data abstractions The term data structures has been around for about 30 years; the term data type has been around for about 20 years; and the term data abstraction is a recent one and has been used for the last five years. All these terms are used widely today, and sometimes even interchangeably. After exploring the three terms, the similarities and differences between these will be pointed out and a unified way of looking at the three concepts will be presented. The clarity and precision in the presentation will be achieved by providing pictures wherever helpful, rather than through complex notations to make the reading light and easy. There are a total of 27 diagrams in the paper. The point is to get the key ideas across as easily as possible.

Current architecture for microprogrammable machines vary widely. In order to avoid the applicability of the testing technique to a particular machine example, hardware, microware and microprograms are represented in a general fashion. This representation will account for a composite of features common to a large variety of contemporary machines. Such a general description seems to be absolutely necessary, when a comparison of two microprograms executing on different machines has to be made. After defining the model, correctness and equivalence of loopfree microprograms will be defined. The testing techniques are then developed. In the Appendix are shown two examples of straight line microprograms (for simplicity), to which the developed model is applied.