An Approach to Class Reasoning in Symbolic Computation

A methodology, following the object-oriented paradigm, for modeling mathematical structure by axiomatization is presented. A suitable programming language is defined in terms of its class construct and inheritance. The class construct allows for expressing also the properties of the structure represented by the class. By reasoning about the properties defined in classes (class reasoning) logical relations among the related mathematical structures can be evaluated. We show how class reasoning can be applied in order to rearrange and/or modify a hierarchy of (classes representing) mathematical structures.