Program to calculate First and Follow sets of given grammar



Before proceeding, it is highly recommended to be familiar with the basics in Syntax Analysis, LL(1) parsing and the rules of calculating First and Follow sets of a grammar.

  1. Introduction to Syntax Analysis
  2. Why First and Follow?
  3. FIRST Set in Syntax Analysis
  4. FOLLOW Set in Syntax Analysis

Assuming the reader is familiar with the basics discussed above, let’s start discussing how to implement the C program to calculate the first and follow of given grammar.

Example :



Input :
E  -> TR
R  -> +T R| #
T  -> F Y
Y  -> *F Y | #
F  -> (E) | i


Output :
 First(E)= { (, i, }
 First(R)= { +, #, }
 First(T)= { (, i, }
 First(Y)= { *, #, }
 First(F)= { (, i, }

-----------------------------------------------

 Follow(E) = { $, ),  }
 Follow(R) = { $, ),  }
 Follow(T) = { +, $, ),  }
 Follow(Y) = { +, $, ),  }
 Follow(F) = { *, +, $, ),  }

The functions follow and followfirst are both involved in the calculation of the Follow Set of a given Non-Terminal. The follow set of the start symbol will always contain “$”. Now the calculation of Follow falls under three broad cases :

  • If a Non-Terminal on the R.H.S. of any production is followed immediately by a Terminal then it can immediately be included in the Follow set of that Non-Terminal.
  • If a Non-Terminal on the R.H.S. of any production is followed immediately by a Non-Terminal, then the First Set of that new Non-Terminal gets included on the follow set of our original Non-Terminal. In case encountered an epsilon i.e. ” # ” then, move on to the next symbol in the production.
    Note : “#” is never included in the Follow set of any Non-Terminal.
  • If reached the end of a production while calculating follow, then the Follow set of that non-teminal will include the Follow set of the Non-Terminal on the L.H.S. of that production. This can easily be implemented by recursion.

Assumptions :

  1. Epsilon is represented by ‘#’.
  2. Productions are of the form A=B, where ‘A’ is a single Non-Terminal and ‘B’ can be any combination of Terminals and Non- Terminals.
  3. L.H.S. of the first production rule is the start symbol.
  4. Grammer is not left recursive.
  5. Each production of a non terminal is entered on a different line.
  6. Only Upper Case letters are Non-Terminals and everything else is a terminal.
  7. Do not use ‘!’ or ‘$’ as they are reserved for special purposes.

Explanation :
Store the grammar on a 2D character array production. findfirst function is for calculating the first of any non terminal. Calculation of first falls under two broad cases :

  • If the first symbol in the R.H.S of the production is a Terminal then it can directly be included in the first set.
  • If the first symbol in the R.H.S of the production is a Non-Terminal then call the findfirst function again on that Non-Terminal. To handle these cases like Recursion is the best possible solution. Here again, if the First of the new Non-Terminal contains an epsilon then we have to move to the next symbol of the original production which can again be a Terminal or a Non-Terminal.

Note : For the second case it is very easy to fall prey to an INFINITE LOOP even if the code looks perfect. So it is important to keep track of all the function calls at all times and never call the same function again.

Below is the implementation :

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// C program to calculate the First and
// Follow sets of a given grammar
#include<stdio.h>
#include<ctype.h>
#include<string.h>
  
// Functions to calculate Follow
void followfirst(char, int, int);
void follow(char c);
  
// Function to calculate First
void findfirst(char, int, int);
  
int count, n = 0;
  
// Stores the final result 
// of the First Sets
char calc_first[10][100];
  
// Stores the final result
// of the Follow Sets
char calc_follow[10][100];
int m = 0;
  
// Stores the production rules
char production[10][10];
char f[10], first[10];
int k;
char ck;
int e;
  
int main(int argc, char **argv)
{
    int jm = 0;
    int km = 0;
    int i, choice;
    char c, ch;
    count = 8;
      
    // The Input grammar
    strcpy(production[0], "E=TR");
    strcpy(production[1], "R=+TR");
    strcpy(production[2], "R=#");
    strcpy(production[3], "T=FY");
    strcpy(production[4], "Y=*FY");
    strcpy(production[5], "Y=#");
    strcpy(production[6], "F=(E)");
    strcpy(production[7], "F=i");
      
    int kay;
    char done[count];
    int ptr = -1;
      
    // Initializing the calc_first array
    for(k = 0; k < count; k++) {
        for(kay = 0; kay < 100; kay++) {
            calc_first[k][kay] = '!';
        }
    }
    int point1 = 0, point2, xxx;
      
    for(k = 0; k < count; k++)
    {
        c = production[k][0];
        point2 = 0;
        xxx = 0;
          
        // Checking if First of c has
        // already been calculated
        for(kay = 0; kay <= ptr; kay++)
            if(c == done[kay])
                xxx = 1;
                  
        if (xxx == 1)
            continue;
          
        // Function call    
        findfirst(c, 0, 0);
        ptr += 1;
          
        // Adding c to the calculated list
        done[ptr] = c;
        printf("\n First(%c) = { ", c);
        calc_first[point1][point2++] = c;
          
        // Printing the First Sets of the grammar
        for(i = 0 + jm; i < n; i++) {
            int lark = 0, chk = 0;
              
            for(lark = 0; lark < point2; lark++) {
                  
                if (first[i] == calc_first[point1][lark])
                {
                    chk = 1;
                    break;
                }
            }
            if(chk == 0)
            {
                printf("%c, ", first[i]);
                calc_first[point1][point2++] = first[i];
            }
        }
        printf("}\n");
        jm = n;
        point1++;
    }
    printf("\n");
    printf("-----------------------------------------------\n\n");
    char donee[count];
    ptr = -1;
      
    // Initializing the calc_follow array
    for(k = 0; k < count; k++) {
        for(kay = 0; kay < 100; kay++) {
            calc_follow[k][kay] = '!';
        }
    }
    point1 = 0;
    int land = 0;
    for(e = 0; e < count; e++)
    {
        ck = production[e][0];
        point2 = 0;
        xxx = 0;
          
        // Checking if Follow of ck
        // has alredy been calculated
        for(kay = 0; kay <= ptr; kay++)
            if(ck == donee[kay])
                xxx = 1;
                  
        if (xxx == 1)
            continue;
        land += 1;
          
        // Function call
        follow(ck);
        ptr += 1;
          
        // Adding ck to the calculated list
        donee[ptr] = ck;
        printf(" Follow(%c) = { ", ck);
        calc_follow[point1][point2++] = ck;
          
        // Printing the Follow Sets of the grammar
        for(i = 0 + km; i < m; i++) {
            int lark = 0, chk = 0;
            for(lark = 0; lark < point2; lark++) 
            {
                if (f[i] == calc_follow[point1][lark])
                {
                    chk = 1;
                    break;
                }
            }
            if(chk == 0)
            {
                printf("%c, ", f[i]);
                calc_follow[point1][point2++] = f[i];
            }
        }
        printf(" }\n\n");
        km = m;
        point1++; 
    }
}
  
void follow(char c)
{
    int i, j;
      
    // Adding "$" to the follow
    // set of the start symbol
    if(production[0][0] == c) {
        f[m++] = '$';
    }
    for(i = 0; i < 10; i++)
    {
        for(j = 2;j < 10; j++)
        {
            if(production[i][j] == c)
            {
                if(production[i][j+1] != '\0')
                {
                    // Calculate the first of the next
                    // Non-Terminal in the production
                    followfirst(production[i][j+1], i, (j+2));
                }
                  
                if(production[i][j+1]=='\0' && c!=production[i][0])
                {
                    // Calculate the follow of the Non-Terminal
                    // in the L.H.S. of the production
                    follow(production[i][0]);
                }
            
        }
    }
}
  
void findfirst(char c, int q1, int q2)
{
    int j;
      
    // The case where we 
    // encounter a Terminal
    if(!(isupper(c))) {
        first[n++] = c;
    }
    for(j = 0; j < count; j++)
    {
        if(production[j][0] == c)
        {
            if(production[j][2] == '#')
            {
                if(production[q1][q2] == '\0')
                    first[n++] = '#';
                else if(production[q1][q2] != '\0' 
                          && (q1 != 0 || q2 != 0))
                {
                    // Recursion to calculate First of New
                    // Non-Terminal we encounter after epsilon
                    findfirst(production[q1][q2], q1, (q2+1));
                }
                else
                    first[n++] = '#';
            }
            else if(!isupper(production[j][2]))
            {
                first[n++] = production[j][2];
            }
            else 
            {
                // Recursion to calculate First of
                // New Non-Terminal we encounter 
                // at the beginning
                findfirst(production[j][2], j, 3);
            }
        }
    
}
  
void followfirst(char c, int c1, int c2)
{
    int k;
      
    // The case where we encounter
    // a Terminal
    if(!(isupper(c)))
        f[m++] = c;
    else
    {
        int i = 0, j = 1;
        for(i = 0; i < count; i++)
        {
            if(calc_first[i][0] == c)
                break;
        }
          
        //Including the First set of the
        // Non-Terminal in the Follow of
        // the original query
        while(calc_first[i][j] != '!')
        {
            if(calc_first[i][j] != '#'
            {
                f[m++] = calc_first[i][j];
            }
            else
            {
                if(production[c1][c2] == '\0')
                {
                    // Case where we reach the
                    // end of a production
                    follow(production[c1][0]);
                }
                else
                {
                    // Recursion to the next symbol
                    // in case we encounter a "#"
                    followfirst(production[c1][c2], c1, c2+1);
                }
            }
            j++;
        }
    }
}

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Output :

 First(E)= { (, i, }
 First(R)= { +, #, }
 First(T)= { (, i, }
 First(Y)= { *, #, }
 First(F)= { (, i, }

-----------------------------------------------

 Follow(E) = { $, ),  }
 Follow(R) = { $, ),  }
 Follow(T) = { +, $, ),  }
 Follow(Y) = { +, $, ),  }
 Follow(F) = { *, +, $, ),  }



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