Overloading and Inheritance

This paper reports on some recent investigations aimed at separating and clarifying a number of concepts that frequently appear in object-based and object-oriented languages. Concepts considered include are over-loading, encapsulation, the message paradigm, and a limited form of inheritance. We also introduce formulations of the concepts of overload-systems and coercion-systems, and we present a treatment of (+, ×)-recursive classes and the definition of primitive recursive functions over such classes.