Then come some examlples from the paper. After the examples, comes the algorithm proper. If you want to execute this theory as a prolog program, it should be quite easy to do. After the algorithm, I give a screen-capture of it working on some examples. This relation defines type type correct checking algorithm.
Any situation is a type correct with the empty type.
This determines if something is an elment of a set. If X is the first element of the list, then it is an element.