context-free-grammarparse-tree

How is this parse tree generated?

I was reading https://www.cs.odu.edu/~zeil/cs390/f16/Public/cfg/index.html and came across this example grammar:

Expr -> Expr + Term  
Expr -> Expr - Term  
Expr -> Term  
Term -> Term * Factor  
Term -> Term/Factor  
Factor -> (Expr)  
Factor -> id

Using this grammar, the following parse tree is given for the string "a - b - c":

parse tree

My question is, how are the Factor non-terminals being produced from Term non-terminals? I don't see how this is done in the grammar. To me it would seem that the grammar needs an extra production rule like Term -> Factor.

Solution

  • Absolutely correct. The grammar is missing the production Term ⇒ Factor, as can be seen in the parse tree.