Type-consistency problems for queries in object-oriented databases

Method invocation mechanism is one of the essential features in object-oriented programming languages. This mechanism contributes to data encapsulation and code reuse, but there is a risk of run-time type errors. In the case of object-oriented databases (OODBs), a run-time error causes rollback. Therefore, it is desirable to ensure that a given OODB schema is consistent, i.e., no run-time type error occurs during the execution of queries under any database instance of the OODB schema. This paper discusses the computational complexity of type-consistency problems. As a model of OODB schemas, we adopt update schemas introduced by Hull et al., which have all of the basic features of OODBs such as class hierarchy, inheritance, complex objects, and so on. For some subclasses of update schemas, the complexity of a type-consistency problem is presented. Importantly, it turns out that non-flatness of the class hierarchy, nontermination of queries, and update operations in queries each make the problem difficult.