Inheritance of Rewrite Rule Structures Applied to Symbolic Computation

This paper defines and presents a method of inheritance for structures that are defined by rewrite rules. This method is natural in the sense that it can be easily and cleanly implemented in rewrite rules themselves. This framework of inheritance is not that of classical Object-Oriented Programming. It is shown that this inheritance has particular application to structures implemented in rewrite rules and, more generally, to symbolic computation. The treatment is practical, and examples are presented in Mathematica for concreteness. 1 Introduction An algebraic specification is a way of describing an abstract data type in an implementation independent way. Throughout this paper, an implementation of an algebraic specification or an abstract structure in terms of a system of rewrite rules will be called a symbolic specification. So a symbolic specification is a set of rewrite rules describing how to manipulate symbols in keeping with some algebraic specification or abstract structure..