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One of the early insights into the meaning of objects and classes was the recognition that objects are best understood as fixed points, while classes can be interpreted as the generators of these fixed points. Later came the realization that the types of objects and classes were also related to fixed points and their generators.
Language features that provide support for automatically creating these fixed points, especially when defining subclasses, seem to provide extra expressiveness. When dealing with systems of objects, automatic support for mutual recursion and subclasses seems to provide the power of virtual types, for example, but with provable static type safety.
In this talk I will discuss the role of fixed points in object-oriented languages and contrast the power of languages which provide automatic support for these fixed points with those that force the programmer to attempt to manually construct these fixed points.
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