Empty string in an ambiguous grammar?

Question

I'm a bit confused by the role of the empty string in this ambiguous grammar:

A' -> A
A -> if A B
A -> null
B -> [empty string]
B -> else S

So what does B -> empty string mean/do? Does that mean B could transition to A? And "if", "else", and "null are terminals, then what is the empty string?

Answer 1

In a grammar when a rule transitions to the empty string, that means that the symbol just disappears. For example, here is a possible derivation:

A'
A
if A B
if null B
if null

Notice that on the last line, B is replaced by the empty string -- nothing. It goes away. (We could have instead decided to replace B by else S.)

Answer 2

You can eliminate B by substituting all its expansions wherever it appears, giving the equivalent grammar

A' -> A
A -> if A
A -> if A else S
A -> null