The formula-tree of a simple type is an alternative tree-like representation. For this is split into primitive parts, and the formula-tree defines some kind of hierarchy over these primitive parts.

(P1):
(P2):
(P3):

Here, are called the tail-variables of the respective primitive part, while and are head-variables. The arity of a primitive part is the number of its tail-variables.

- the root of the formula-tree is the only primitive part of form (P1);
- every node of form (P2) or (P3) in the formula-tree descends from a tail-variable in another primitive part.

The following algorithm computes the formula-tree
of a type
. We use dashed lines for the edges of the formula-tree in order to
distinguish them from the edges in
the primitive parts (nodes) of the tree.

- If , i.e.
, then
.
- If , then
where

and for and we recursively define