Database abstractions

Aggregation is introduced as an abstraction which is important in conceptualizing the real world. Aggregation transforms a relationship between objects into a higher-level object. A new data type, called aggregate, is developed which, under certain criteria of “well-definedness,” specifies aggregation abstractions. Relational databases defined as collections of aggregates are structured as a hierarchy of n-ary relations. To maintain well-definedness, update operations on such databases must preserve two invariants. Well-defined relations are distinct from relations in third normal form. It is shown that these notions are complementary and both are important in database design. A top-down methodology for database design is described which separates decisions concerning aggregate structure from decisions concerning key identification. It is suggested that aggregate types, and other types which support real-world abstractions without introducing implementation detail, should be incorporated into programming languages.