Theorem Proving for the

This paper discusses the challenges of adding symbolic computation capabilities to a computer algebra system. Indeed, a simple expressions such as m × n can be evaluated to a full value when both m and n have known values. However, if one or both of them have no definite value, then most CASs treat them as symbols and a syntactic representation of some kind is returned. Most CASs do this without much regard to types and semantics of the eventual values the symbols stand for. On the other hand, without knowing the semantics of m and n, the expression m × n − n × m cannot be given a reliable meaning, nor can (a + b)× (a − b). This paper presents a light-weight approach to enhance a computer algebra system with the support of typed symbolic computations.