this paper we describe a new, categorical approach to normalization in typed -

Computer algebra systems typically drop some degenerate cases when evaluating expressions, e.g., x=x becomes 1 dropping the case x = 0. We claim that it is feasible in practice to compute also the degenerate cases yielding guarded expressions. We work over real closed fields but our ideas about handling guarded expression can be easily transferred to other situations. Using formulas as guards provides a powerful tool for heuristically reducing the combinatorial explosion of cases: equivalent, redundant, tautological, and contradictive cases can be detected by simplification and quantifier elimination. Our approach allows to simplify the expressions on the basis of simplification knowledge on the logical side. The method described in this paper is implemented in the reduce package guardian, which is freely available on the www. 2 1. INTRODUCTION 1 Introduction It is meanwhile a well-known fact that evaluations obtained with the interactive use of computer algebra systems (cas) are n...

Nous reprenons ici un exemple de contrôle développé par Yves Ledru du L.S.R de Grenoble [Ledru 98]. Cet exemple a déjà fait l’objet d’un nombre d’articles important lors du congrès:“Approches Formelles dans l’Assistance au Développement de Logiciels ” qui a eu lieu à Grenoble en janvier 2000 [AFADL’2000]. Ainsi, diverses techniques ont été illustrées sur ce même exemple.