A Proposal to Study Type Systems for Computer Algebra

It is widely recognized that programming languages should offer features to help structure programs. To achieve this goal, languages like Ada, Modula-2, objectoriented languages, and functional languages have been developed. The structuring techniques available so far (like modules, classes, parametric polymorphism) are still not enough or not appropriate for some application areas. In symbolic computation, in particular computer algebra, several problems occur that are difficult to handle with any existing programming language. Indeed, nearly all available computer algebra systems suffer from the fact that the underlying programming language imposes too many restrictions. We propose to develop a language that combines the essential features from functional languages, object-oriented languages, and computer algebra systems in a semantically clean manner. Although intended for use in symbolic computation, this language should prove interesting as a general purpose programming language. ..