With regard to a set of trees as described in Raw Material, we can define
a new binary operator. Unlike the cons operator, this one is not
required to associate an element of the set with every possible pair
of elements. For very many pairs of operands we will have nothing to
say about its result. In fact, we require nothing of it beyond
a few simple properties to be described presently.
Because this is the only other operator than cons, there is no
need to have a special notation for it, so it will be denoted by empty
space. The tree associated by the operator with a pair of trees x
and y, if any, will be expressed in the infix notation
x y. For convenience, the operator is regarded as
being right associative, so that a b c can be
written for a (b c).