Splicing in Modified BNF Syntax

The primary extension used is the following:

[[O]]

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

O_1 | ... | O_l

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

(O_{i_1}... O_{i_j}) 1<= j

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)

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