An efficient method for checking object-oriented database schema correctness

Inheritance is introduced in object-oriented systems to enhance code reuse and create more compact and readable software. Powerful object models adopt multiple inheritance, allowing a type (or class) definition to inherit from more than one supertype. Unfortunately in applying this powerful modeling mechanism, inheritance conflicts may be generated, which arise when the same property or operation is defined in more than one supertype. Inheritance conflicts identification and resolution is the key issue of this article. In strongly typed object-oriented systems the resolution of inheritance conflicts depends on the compatibility of the types of the conflicting definitions. In case of incompatible types, a contradiction arises. This article focuses an object-oriented databases (ODBs), providing a method aimed at supporting the designer in the construction of correct ODB schemas. The first necessary condition for schema correctness is the absence of contradictions. A second cause of schema incorrectness is due to the presence of structurally recursive types that, when defined within certain hierarchical patterns, cause the nontermination of the inheritance process. In the article, after the formal definition of a correct schema, two graph-theoretic methods aimed at verifying ODB schema correctness are analyzed. Although the brst method is intuitive but inefficient, the second allows schema correctness to be checked in polynomial time, in the size of the schema. The results of this study are included in the implementation of Mosaico, an environment for ODB application design.