The primary extension used is the following:
An expression of this form appears whenever a list of elements is to be spliced into a larger structure and the elements can appear in any order. The symbol O represents a description of the syntax of some number of syntactic elements to be spliced; that description must be of the form
where each O_i can be of the form S or of the form S* or of the form S^1.
The expression [[O]] means that a list of the form
is spliced into the enclosing expression, such that if n != m and 1<= n,m<= j, then either O_{i_n}!= O_{i_m} or O_{i_n} = O_{i_m} = Q_k, where for some 1<= k <= n, O_k is of the form Q_k*.
Furthermore, for each O_{i_n} that is of the form Q_k^1, that element is required to appear somewhere in the list to be spliced.
For example, the expression
(x [[A | B* | C]] y)
means that at most one A, any number of B’s, and
at most one C can occur in any order.
It is a description of any of these:
(x y)
(x B A C y)
(x A B B B B B C y)
(x C B A B B B y)
but not any of these:
(x B B A A C C y)
(x C B C y)
In the first case, both A and C appear too often,
and in the second case C appears too often.
The notation [[O_1 | O_2 | ...]]^+ adds the additional restriction that at least one item from among the possible choices must be used. For example:
(x [[A | B* | C]]^+ y)
means that at most one A, any number of B’s, and
at most one C can occur in any order, but that in any case at least
one of these options must be selected.
It is a description of any of these:
(x B y)
(x B A C y)
(x A B B B B B C y)
(x C B A B B B y)
but not any of these:
(x y)
(x B B A A C C y)
(x C B C y)
In the first case, no item was used;
in the second case, both A and C appear too often;
and in the third case C appears too often.
Also, the expression:
(x [[A^1 | B^1 | C]] y)
can generate exactly these and no others:
(x A B C y)
(x A C B y)
(x A B y)
(x B A C y)
(x B C A y)
(x B A y)
(x C A B y)
(x C B A y)