Subtyping and application of context-free classes

Object-oriented systems are usually not designed from scratch but constructed using frameworks or class libraries. This construction should lead to correct systems provided the reused classes are locally correct. Therefore knowledge about the features that a certain class provides is often not enough. It is additionally necessary to know the correct semantics of classes, i.e. information on how to use these features. Especially, we have to mind the sequences of method calls that are acceptable by an object. Using regular languages for the description of these sequences works fine for some classes but is not adequate for others, e.g. for stacks, buffers, queues or lists etc. In this paper we present a more general approach for the specification of the dynamic behavior of objects using context-free grammars. We investigate questions of correctness in subtyping and application of such classes. We define sufficient conditions for class systems such that local correctness in subtyping and application implies global correctness of the system