Class-based versus object-based: a denotational comparison

In object-oriented programming one distinguishes two kinds of languages. Class-based languages are centered around the concept of classes as descriptions of objects. In object-based languages the concept of a class is substituted by constructs for the creation of individual objects. Usually, the object-based languages attract interest because of their "simplicity". This paper contains a thorough denotational analysis which reveals that simplicity is quickly lost if one tackles verification issues. This is due to what is sometimes called "recursion through the store". By providing a denotational semantics for a simple class-based and a simple object-based language it is shown that the denotational semantics of the object-based language needs much more advanced domain theoretic machinery than the class based one. The gap becomes even wider when we define concepts of specification and appropriate verification rules.