Dice notation EBNF grammar

rpg = rpg "+" rpg1
    | rpg "-" rpg1
    | rpg1
    ;

rpg1 = rpg1 "*" rpg2
     | rpg1 "/" rpg2
     | rpg2
     ;

rpg2 = rpg2 "^" alldice
     | alldice
     ;

alldice = [loop] "d" loop
        | gdice
        ;

gdice = [loop] "d" loop "g" [loop]
      | ldice
      ;

ldice = [loop] "d" loop "l" [loop]
      | loop
      ;

loop = num
     | "(" rpg ")"
     ;

num = digit [num] ;

digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;