Abstract

A method schema is a simple programming formalism for object-oriented databases with features such as classes, methods, inheritance, name overloading, and late binding. An important problem is to check whether a given method schema can lead to an inconsistency in some interpretation. This consistency question is shown to be undecidable in general. Decidability is obtained for monadic and/or recursion-free method schemas. In particular, consistency of monadic method schemas is shown to be decidable in O(nc 3 ) time, where n is the size of the method definitions and c is the size of the class hierarchy; also, it is logspace-complete in PTIME, even for monadic, recursion-free schemas. Method signature covariance is shown to simplify the computational complexity of key decidable cases. For example: one coded method in the context of base methods with covariant signatures can be tested for consistency in O(n+c) time for the monadic case (without covariance this problem is in O(nc 2 ) t...

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