A formal model for object bases

Abstract

We introduce FMOB: a formal model for Objectbases. The term "Objectbase" represents better the widely used "object­ oriented database". FMOB consists of ( 1) objects (classes and their instances) with extended encapsulation capabilities, (2) second-order objects (respectively 2-classes and 2-instances) for supporting the structural relations specialization, as­sociation, aggregation and grouping. Every 2-object encapsulates a two-level-hierarchy ( t-1-h) of objects formally defined. The inheritance notion is generalized and replaced by the link concept, which allows, in a uniform way, the proper reusabil­ity of data, methods and other object-properties across one or more 2-object of the above type. (3) FMOB also supports complex objects through an appropriate composition of 2-objects. The model is based on a universal algebra of words and appropriate extensions. Every building block of the objectbase has its corresponding algebra. The algebra of abstract words is functionally complete. The modified greedy algorithm optimizes all linear objective functions over the search (or branching) greedoid defined on the underlying digraph of a second order-object.