RELATIVE COMPLETENESS AND SPECIFICATION OF ABSTRACT DATA TYPES.

Completeness is a fundamental concept in the theory of abstract data type specification. In this paper, the concepts of relative completeness and base completeness are proposed. The correspondence between relative completeness and computational equivalence and that between base completeness and behavioral equivalence have been shown. It is proved that every base specification has a unique maximal consistent extension and the initial model of the maximal extension is precisely the final model of the original specification in the sense of the final algebra approach. These results reveal the relationship between the initial algebra and final algebra approaches.