Question

modified once more. After removing the recursions, and writing a code for infix expression :
it also contains precedence checking, and no recursive grammar and no start Non terminal and also an error message.

%{
#include<stdio.h>
%}

%token ALPHA NUMBER PLUS MINUS MUL DIV LPAR RPAR

%%

expr : expr PLUS term     { printf("its an infix expression");  }
     | expr MINUS term    
     | term 
     ; 

term : term MUL factor
     | term DIV factor
     | factor
     ;


factor : LPAR expr RPAR 
       | NUMBER 
       | ALPHA
       ;
%%
main()
{
yyparse();
}

int yyerror (char *s)
{

    printf("Not an infix expression");
}

is this okay now ?

Answer 1

No it isn’t. Apart from all the conflicts, it doesn’t define any operator precedence. There are plenty of correct examples of LR expression grammars available on the Internet.

EDIT: Unary minus goes in the missing primary rule. From factor it usually goes like this:

factor: primary
    | primary '^' factor // exponentiation, note right-recursion for right-associativitity, or use %prec
    ;

primary: '(' expr ')'
    | '-' primary // unary minus; note recursion, to allow any number of them
    | NUMBER
    | IDENTIFIER
    ;