Consider the following BNF grammar rules: <pop> ::= [ <bop>, <pop> ] | <bop> <bo

Question

Consider the following BNF grammar rules:

<pop>   ::=   [ <bop>, <pop> ] | <bop>

<bop>   ::=   <boop> | ( <pop> )

<boop> ::=   x | y | z

For each of the strings listed below, indicate all syntactic categories of which it is a member, if any. (“Syntactic categories” refer to the nonterminal ancestors of a string). In each case, provide a rationale for your response.

a - z

b - ( x )

c - [ y ]

d - ( [ x , y ] )

e - [ ( x ) , y ]

f - [ ( x ), [ y , x ] ]

Explanation / Answer

a. z is boop and any boop is also a bop and a pop.

b.( x ) is a bop -- and therefore also a pop

c. [ y ] is invalid -- cannot have brackets without a comma

d. ( [ x , y ] ) is a bop -- parens around a pop, and therefore also a pop

e. [(x), y] is only a pop -- brackets around a bop and a pop

f. [ (x), [y,x] ] is only a pop -- brackets around a bop and a pop

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