User Evaluator Simplifier

Solving sophisticated mathematical problems often requires algebraic algorithms and theorems. However, there are no environments integrating theorem provers and computer algebra systems which consistently provide the inference capabilities of the rst and the powerful arithmetic of the latter systems. As an example for such a mechanized mathematics environment we describe a prototype implementation of an interface between Isabelle and Maple. It is achieved by extending the simpliier of Isabelle through the introduction of a new class of simpliication rules called evaluation rules in order to make selected operations of Maple available, and without any modiication to the computer algebra system. Addition-aly, we specify syntax translations for the concrete syntax of Maple which enables the communication between both systems illustrated by some examples that can be solved by theorems and algorithms. 1 Introduction Problem solving in mathematics often requires the application of both procedural algebraic knowledge (algorithms) and deductive knowledge (theorems). The advantages of combining both strategies have been recognized by both communities: symbolic computation and analytical reasoning. Some of these advantages concern the introduction of mathematical theories and arithmetics, in particular real numbers, into provers, as well as providing logical languages and justiications to symbolic calculators. Two aspects must be further investigated: (i) the problem of combining algorithms and theorems in one single system, (ii) the heterogeneous integration of several packages. On the one hand classical computer algebra systems (CAS), for example Maple Char et al. 92] or Mathemat-ica Wolfram 91], usually ooer a straightforward programming language with ad-hoc implementations of rewriting. One of the most promising approaches towards introducing theorem proving into CAS is an extension of Analyt-ica Clarke & Zhao 94], a Mathematica package to prove