2.0 Using Types and Modes

Only recently have I begun to realize that the problem is not merely one of technical mastery or the competent application of the rules ... but that there is actually something else which is guiding these rules. It actually involves a different level of mastery. It’s quite a different process to do it right; and every single act that you do can be done in that sense well or badly. But even assuming that you have got the technical part clear, the creation of this quality is a much more complicated process of the most utterly absorbing and fascinating dimensions. It is in fact a major creative or artistic act – every single little thing you do – ...

– Christopher Alexander

(from Patterns of Software by Richard Gabriel)

In this chapter we look at the key notion of type and its generalization mode. We show that every FriCAS object has a type that determines what you can do with the object. In particular, we explain how to use types to call specific functions from particular parts of the library and how types and modes can be used to create new objects from old. We also look at Record and Union types and the special type Any. Finally, we give you an idea of how FriCAS manipulates types and modes internally to resolve ambiguities.