A class abstraction for a hierarchical type system

In object oriented database languages and in languages supporting the semantic data model the construct used to collect sets of homogeneous entities is usually enriched with the possibility of imposing a set-inclusion relation among different collections. We call "class" such a data structure characterized by its ability of collecting values and of being in a containment relation with other classes. In many languages the class notion is not realized by a first class data type but is defined in some special way and the definition of a class is overloaded with constraints, and tightly linked to the definition of types. In this paper we embed in a strongly typed language with type inclusion a basic, but powerful, notion of a class data type which is just a first class data type orthogonal to the other notions of the language. In this context we study one of the most problematic issues in class data types, migration of objects from superclasses to subclasses.