Mathematica as a Rewrite Language

Bruno Buchberger 

In: Proceedings of the 2nd Fuji International Workshop on Functional and Logic
Programming), November 1-4, 1996, Shonan Village Center, (T. Ida, A. Ohori, M. Takeichi
eds.), World Scientific, Singapore - New Jersey - London - Hongkong, 1996, pp. 1-13.

(ISBN 9810229232. Copyright: World Scientific


ABSTRACT:

We desribe a part of Mathematics as a rewrite sublanguage of predicate logic with the 
additional construct of sequence variables. Starting from this view, we explain why
Mathematica is a good starting point for the design and implementation of a new mathematical
software system, Theorema, that provides a common frame for computer-support of all phases
in the process of "doing mathematics" including proving, programming, and computing. As 
examples, we describe the implementation of funtors  and the implementation of a simple
induction prover in Mathematica.