3. FIRST Function
32
▪ FIRST function indicates the set of terminals that begin strings derived
from a given string of grammar symbols
Rules for Finding FIRST Sets:
1. If X is a terminal, then FIRST(X) = {X}.
2. If X is a nonterminal and X→ Y1Y2 . . Yk is a production for some
k>=1, then place a in FIRST(X) if for some i, a is in FIRST(Yi), and ℇ is
in all of FIRST(Y1), . . . , FIRST(Yi-1); that is, Y1 . . . Yi-1 ⇒ ℇ. If ℇ is in
FIRST(Yj) for all j = 1, 2, . . . , k, then add ℇ to FIRST(X). For example,
everything in FIRST(Y1) is surely in FIRST(X). If Yi does not derive ℇ
then we add nothing more to FIRST(X), but if Y1 ⇒ ℇ, then we add
FIRST(Y2), and so on.
3. If X → ℇ is a production, then add ℇ to FIRST(X).
4. Continue until no more terminals or ℇ can be added to any FIRST set.
*
*
4. FOLLOW Function
34
▪ FOLLOW function indicates the set of terminals that can appear
immediately to the right of a given nonterminal in some sentential form
▪ Rules:
1. Place $ in FOLLOW(S), where S is the start symbol, and $ is the input
right end marker.
2. If there is a production A → 𝞪B𝞫, then everything in FIRST(𝞫) except ℇ
is in FOLLOW(B).
3. If there is a production A → 𝞪B, or a production A → 𝞪B𝞫, where
FIRST(𝞫) contains ℇ, then everything in FOLLOW(A) is in FOLLOW(B).
4. Continue until nothing can be added to any FOLLOW set.
5. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
6. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
Nonterminal S has 2 productions:
1. the first will be FIRST(B)
2. the first will be FIRST(C)
So need to solve these first
7. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
8. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
Nonterminal B has 2
productions, the first
begins with a and
second is ε
9. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
Nonterminal B has 2
productions, the first
begins with a and
second is ε
{ a, ε }
10. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, ε }
11. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, ε }
Nonterminal C has 2
productions, the first
begins with a and
second is ε
12. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, ε }
Nonterminal C has 2
productions, the first
begins with a and
second is ε
{ c, ε }
13. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, ε }
{ c, ε }
14. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, ε }
{ c, ε }
Nonterminal S has 2 productions:
1. the first will be FIRST(B) which is {a, ε}
Here we won’t write the ε, instead we
will use what is after nonterminal B
2. the second will be FIRST(C) which is {c,
ε} Here we won’t write the ε, instead we
will use what is after nonterminal C
15. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
Nonterminal S has 2 productions:
1. the first will be FIRST(B) which is {a, ε}
Here we won’t write the ε, instead we
will use what is after nonterminal B
2. the second will be FIRST(C) which is {c,
ε} Here we won’t write the ε, instead we
will use what is after nonterminal C
16. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
17. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
Since S is start symbol,
FOLLOW is $
{ a, ε }
{ c, ε }
18. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
Since S is start symbol,
FOLLOW is $
{ a, ε }
{ c, ε }
{ $ }
19. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
{ $ }
20. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
{ $ }
Find occurrence(s) of B in rhs:
1. What comes after it in first occurrence? b
2. What comes after it in second occurrence? Since
it is at right most in production, so
FOLLOW(nonterminal on left) = FOLLOW(B)
which again will be b
21. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
{ $ }
Find occurrence(s) of B in rhs:
1. What comes after it in first occurrence? b
2. What comes after it in second occurrence? Since
it is at right most in production, so
FOLLOW(nonterminal on left) = FOLLOW(B)
which again will be b
22. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
{ $ }
Find occurrence(s) of B in rhs:
1. What comes after it in first occurrence? b
2. What comes after it in second occurrence? Since
it is at right most in production, so
FOLLOW(nonterminal on left) = FOLLOW(B)
which again will be b
{ b }
23. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
{ $ }
{ b }
24. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
{ $ }
{ b }
Find occurrence(s) of C in rhs:
1. What comes after it in first occurrence? d
2. What comes after it in second occurrence? Since
it is at right most in production, so
FOLLOW(nonterminal on left) = FOLLOW(C)
which again will be d
25. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
{ $ }
{ b }
Find occurrence(s) of C in rhs:
1. What comes after it in first occurrence? d
2. What comes after it in second occurrence? Since
it is at right most in production, so
FOLLOW(nonterminal on left) = FOLLOW(C)
which again will be d
26. FIRST and FOLLOW Functions, Contd.
36
▪ Example 1:
Nontermina
l
First Follow
S
B
C
S → B b | C d
B → a B | ε
C → c C | ε
{ a, b, c, d }
{ a, ε }
{ c, ε }
{ $ }
{ b }
Find occurrence(s) of C in rhs:
1. What comes after it in first occurrence? d
2. What comes after it in second occurrence? Since
it is at right most in production, so
FOLLOW(nonterminal on left) = FOLLOW(C)
which again will be d
{ d }
27. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
28. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
Nonterminal E has 1
production that starts with T
and T starts with F, so do
FIRST(F)
29. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
30. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
Nonterminal F has 2
productions that starts with
( or id
31. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
Nonterminal F has 2
productions that starts with
( or id
{ (, id }
32. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
33. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
Nonterminal T’ has 2
productions that start with *
or ε
34. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
Nonterminal T’ has 2
productions that start with *
or ε
{ *, ε }
35. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
36. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
Nonterminal T has
FIRST(F)
37. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
Nonterminal T has
FIRST(F)
{ (, id }
38. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
39. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
Nonterminal E’ has 2
productions
40. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
Nonterminal E’ has 2
productions
{ +, ε }
41. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
42. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
Nonterminal E has
FIRST(T) Remember,
FIRST(T) is FIRST (F)
43. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
Nonterminal E has
FIRST(T) Remember,
FIRST(T) is FIRST (F)
{ (, id }
44. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id }
45. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id }
46. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
1. Since start symbol
FOLLOW is the $
2. Check for E in rhs, the )
is after it
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id }
47. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
1. Since start symbol
FOLLOW is the $
2. Check for E in rhs, the )
is after it
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id }
48. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
1. Since start symbol
FOLLOW is the $
2. Check for E in rhs, the )
is after it
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
49. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
50. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
Check for E’ in rhs:
1. In first occurrence it is in E
production at right most part, so it
will have FOLLOW(E) = {$, )}
2. In 2nd occurrence it is in E’
production at right most part so
will have FOLLOW(E’)
51. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
Check for E’ in rhs:
1. In first occurrence it is in E
production at right most part, so it
will have FOLLOW(E) = {$, )}
2. In 2nd occurrence it is in E’
production at right most part so
will have FOLLOW(E’)
52. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
Check for E’ in rhs:
1. In first occurrence it is in E
production at right most part, so it
will have FOLLOW(E) = {$, )}
2. In 2nd occurrence it is in E’
production at right most part so
will have FOLLOW(E’)
{ $, ) }
53. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
54. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
Check for T in rhs:
1. In first occurrence it is in E production
followed by E’, so it will have FIRST(E’) = {+,
ε}
Can’t have ε in FOLLOW, so replace E’ in the
production with empty so production
becomes E → T and since T is at right most,
we will get FOLLOW(E) = {$, )}
2. In second occurrence it is followed by E’ so
FIRST(E’) = {+, ε)} … (same as 1.)
55. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
Check for T in rhs:
1. In first occurrence it is in E production
followed by E’, so it will have FIRST(E’) = {+,
ε}
Can’t have ε in FOLLOW, so replace E’ in the
production with empty so production
becomes E → T and since T is at right most,
we will get FOLLOW(E) = {$, )}
2. In second occurrence it is followed by E’ so
FIRST(E’) = {+, ε)} … (same as 1.)
56. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
{ +, $, ) }
Check for T in rhs:
1. In first occurrence it is in E production
followed by E’, so it will have FIRST(E’) = {+,
ε}
Can’t have ε in FOLLOW, so replace E’ in the
production with empty so production
becomes E → T and since T is at right most,
we will get FOLLOW(E) = {$, )}
2. In second occurrence it is followed by E’ so
FIRST(E’) = {+, ε)} … (same as 1.)
57. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
{ +, $, ) }
58. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
Check for T’ in rhs:
1. In first occurrence it is in T production at right
most side so will be FOLLOW(T) = {+, $, )}
2. In 2nd occurrence it is in T’ production at right
most side so will be FOLLOW(T’) = {+, $, )}
{ +, $, ) }
59. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
Check for T’ in rhs:
1. In first occurrence it is in T production at right
most side so will be FOLLOW(T) = {+, $, )}
2. In 2nd occurrence it is in T’ production at right
most side so will be FOLLOW(T’) = {+, $, )}
{ +, $, ) }
60. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
Check for T’ in rhs:
1. In first occurrence it is in T production at right
most side so will be FOLLOW(T) = {+, $, )}
2. In 2nd occurrence it is in T’ production at right
most side so will be FOLLOW(T’) = {+, $, )}
{ +, $, ) }
{ +, $, ) }
61. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
{ +, $, ) }
{ +, $, ) }
62. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
{ +, $, ) }
{ +, $, ) }
Check for F in rhs:
1. In first occurrence it is in T production
followed by T’ so will be FIRST(T’) = { *, ε }
Can’t have ε, so replace T’ with empty, then F
will be at right most of T production, so will
have FOLLOW(T) = {+, $, ) }
2. In 2nd occurrence it is in T’ production – same
as 1
63. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
{ +, $, ) }
{ +, $, ) }
Check for F in rhs:
1. In first occurrence it is in T production
followed by T’ so will be FIRST(T’) = { *, ε }
Can’t have ε, so replace T’ with empty, then F
will be at right most of T production, so will
have FOLLOW(T) = {+, $, ) }
2. In 2nd occurrence it is in T’ production – same
as 1
64. FIRST and FOLLOW Functions, Contd.
36
▪ Example 2:
Nontermin
al
First Follow
E
E’
T
T’
F
E → T E’
E’ → + T E’ | ε
T → F T’
T’ →* F T’ | ε
F → ( E ) | id
{ (, id }
{ *, ε }
{ (, id }
{ +, ε }
{ (, id } { $, ) }
{ $, ) }
{ +, $, ) }
{ +, $, ) }
Check for F in rhs:
1. In first occurrence it is in T production
followed by T’ so will be FIRST(T’) = { *, ε }
Can’t have ε, so replace T’ with empty, then F
will be at right most of T production, so will
have FOLLOW(T) = {+, $, ) }
2. In 2nd occurrence it is in T’ production – same
as 1
{ *, +, $, ) }
