runner% cat aritht.c
/* arith0.c: simple parser -- no output
 * grammar:
 *   P ---> E '#'
 *   E ---> T {('+'|'-') T}
 *   T ---> S {('*'|'/') S}
 *   S ---> F '^' S
 *   F ---> char | '(' E ')'
 */
#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
char next;
void E(void);
void T(void);
void S(void);
void F(void);
void error(void);
void scan(void);
void enter(char);
void leave(char);
void spaces(int);
int level = 0;

void main(void)
{
   scan();
   E();
   if (next != '#') error();
   else printf("Successful parse\n");
}

void E(void)
{
   enter('E');
   T();
   while (next == '+' || next == '-') {
      scan();
      T();
   }
   leave('E');
}

void T(void)
{
   enter('T');
   S();
   while (next == '*' || next == '/') {
      scan();
      S();
   }
   leave('T');
}
void S(void)
{
   enter('S');
   F();
   if (next == '^') {
      scan();
      S();
   }
   leave('S');
}
void F(void)
{
   enter('F');
   if (isalpha(next)) {
      scan();
   }
   else if (next == '(') {
      scan();
      E();
      if (next == ')') scan();
      else error();
   }
   else {
      error();
   }
   leave('F');
}
void scan(void)
{
   while (isspace(next = getchar()))
      ;
}
void error(void)
{
   printf("\n*** ERROR ***\n");
   exit(1);
}
void enter(char name)
{
   spaces(level++);
   printf("%c: Enter, \t", name);
   printf("Next == %c\n", next);
}
void leave(char name)
{
   spaces(--level);
   printf("%c: Leave, \t", name);
   printf("Next == %c\n", next);
}

void spaces(int local_level)
{
   while (local_level-- > 0)
      printf(" ");
}
runner% cc -o aritht aritht.c
runner% aritht
a+b#
E: Enter,       Next == a
 T: Enter,      Next == a
  S: Enter,     Next == a
   F: Enter,    Next == a
   F: Leave,    Next == +
  S: Leave,     Next == +
 T: Leave,      Next == +
 T: Enter,      Next == b
  S: Enter,     Next == b
   F: Enter,    Next == b
   F: Leave,    Next == #
  S: Leave,     Next == #
 T: Leave,      Next == #
E: Leave,       Next == #
Successful parse
runner% aritht
a*(b+c)#
E: Enter,       Next == a
 T: Enter,      Next == a
  S: Enter,     Next == a
   F: Enter,    Next == a
   F: Leave,    Next == *
  S: Leave,     Next == *
  S: Enter,     Next == (
   F: Enter,    Next == (
    E: Enter,   Next == b
     T: Enter,  Next == b
      S: Enter,         Next == b
       F: Enter,        Next == b
       F: Leave,        Next == +
      S: Leave,         Next == +
     T: Leave,  Next == +
     T: Enter,  Next == c
      S: Enter,         Next == c
       F: Enter,        Next == c
       F: Leave,        Next == )
      S: Leave,         Next == )
     T: Leave,  Next == )
    E: Leave,   Next == )
   F: Leave,    Next == #
  S: Leave,     Next == #
 T: Leave,      Next == #
E: Leave,       Next == #
Successful parse
runner% aritht
a-b-c#
E: Enter,       Next == a
 T: Enter,      Next == a
  S: Enter,     Next == a
   F: Enter,    Next == a
   F: Leave,    Next == -
  S: Leave,     Next == -
 T: Leave,      Next == -
 T: Enter,      Next == b
  S: Enter,     Next == b
   F: Enter,    Next == b
   F: Leave,    Next == -
  S: Leave,     Next == -
 T: Leave,      Next == -
 T: Enter,      Next == c
  S: Enter,     Next == c
   F: Enter,    Next == c
   F: Leave,    Next == #
  S: Leave,     Next == #
 T: Leave,      Next == #
E: Leave,       Next == #
Successful parse
runner% aritht
a^b^c#
E: Enter,       Next == a
 T: Enter,      Next == a
  S: Enter,     Next == a
   F: Enter,    Next == a
   F: Leave,    Next == ^
   S: Enter,    Next == b
    F: Enter,   Next == b
    F: Leave,   Next == ^
    S: Enter,   Next == c
     F: Enter,  Next == c
     F: Leave,  Next == #
    S: Leave,   Next == #
   S: Leave,    Next == #
  S: Leave,     Next == #
 T: Leave,      Next == #
E: Leave,       Next == #
Successful parse
runner%