Program to calculate First and Follow sets of given grammar

05 Nov, 2021
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. 
Introduction to Syntax AnalysisWhy First and Follow?FIRST Set in Syntax AnalysisFOLLOW Set in Syntax Analysis
Introduction to Syntax Analysis
Why First and Follow?
FIRST Set in Syntax Analysis
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-terminal 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 :  
Epsilon is represented by ‘#’.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.L.H.S. of the first production rule is the start symbol.Grammar is not left recursive.Each production of a non-terminal is entered on a different line.Only Upper Case letters are Non-Terminals and everything else is a terminal.Do not use ‘!’ or ‘$’ as they are reserved for special purposes.
Epsilon is represented by ‘#’.
Productions are of the form A=B, where ‘A’ is a single Non-Terminal and ‘B’ can be any combination of Terminals and Non- Terminals.
L.H.S. of the first production rule is the start symbol.
Grammar is not left recursive.
Each production of a non-terminal is entered on a different line.
Only Upper Case letters are Non-Terminals and everything else is a terminal.
Do not use ‘!’ or ‘$’ 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 :  
C
// 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 Followvoid followfirst(char, int, int);void follow(char c); // Function to calculate Firstvoid findfirst(char, int, int); int count, n = 0; // Stores the final result// of the First Setschar calc_first[10][100]; // Stores the final result// of the Follow Setschar calc_follow[10][100];int m = 0; // Stores the production ruleschar 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 already 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++;        }    }}
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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