Fatal error: start symbol does not derive any sentence

Question

Iam trying to develop a program for a calculator using lex and yacc. I keeping getting the following error:

calc.y: warning: 5 nonterminals useless in grammar [-Wother]
calc.y: warning: 8 rules useless in grammar [-Wother]
calc.y:8.1: fatal error: start symbol I does not derive any sentence
 I : E '\n' {printf("%d\n",$1);}

I looked at similiar problems but they had infinite recursions but this one doesn't have .

calc.l

%{
#include"y.tab.h"
%}

digits [0-9]*

%%
{digits} {return DIGITS}
%%

int yywrap()
{
} 

calc.y

%{
    #include<stdio.h>   
%}

%token DIGITS

%%
I : E '\n' {printf("%d\n",$1);}
  ;
E : E '+' F {$$ = $1 + $3;}
  | E '-' F {$$ = $1 - $3;}
  ;
F : F '*' G {$$ = $1 * $3;}
  | F '/' G {$$ = $1 / $3;}
G :'('E')' 
  | DIGITS 
  ;
%%

int main()
{
    yyparse();
}
int yyerror()
{
}

Answer 1

I don't know yacc, but:

• To build an I, you need an E:

  I : E '\n'
  

• To build an E, you need an E:

  E : E '+' F
    | E '-' F
  

Since there is no way to build an E if you don't already have one (and in the beginning you don't have anything), there is no way to build an I either.

Or looking at it from the other side: E is infinitely recursive because it always refers back to itself.

---

If we start with the lexer, we get DIGITS first.

DIGITS can be used to build a G.

But there's nothing we can do with a G because the only rules that use it (F '*' G and F '/' G) also require an F to proceed, and we don't have an F. So we're stuck.