The type checks that require information only about the top level of the expression tree will be called surface types.

Types that check a complete expression tree (probably recursively) will be called nested types.

Most of the system types are surface types since these are encoded in the top node of the expression tree. Thus

Both return true regardless of the types of the components of the set in the first case, and regardless of the types of the terms of the sum in the second.

The following types are examples of surface types:

The type 'constant', on the other hand, will completely scan an expression to determine whether or not it is composed of any nonconstant parts. Hence it is a nested type. The following types are examples of nested types: