1. WELCOME TO A
JOURNEY TO
CS419
Dr. Hussien Sharaf
Computer Science Department
dr.sharaf@from-masr.com

2. FIRST

1.
2.
3.
Let X be a grammar symbol (a terminal or nonterminal or
), then the FIRST(X) can be computed by the following rules:
If X is terminal, then FIRST(X) is {X}.
If X → is a production, then add to FIRST(X).
If X is nontermianl and X → Y1 Y2 …… Yk is a production, then
place a in FIRST(X) if for some i, a is in FIRST(Yi), and is in
all of FIRST(Y1), ……., FIRST(Yi-1); that is, Y1 …...Yi-1 → . If is
in FIRST(Yj) for all j = 1, 2, ……., k, then add to FIRST(X).
For example ,everything in FIRST(Y1) is surely in FIRST(X). If
Y1 doesn’t derive , then we add nothing more to
FIRST(X), but if Y1 → , then we add FIRST(Y2) and so on.
Ali
Hussien
Dr. Hussien M. Sharaf
First(Ali)
Ali
2

3. FIRST SET EXAMPLE
Consider the following grammar:
E → TQ
Q → +TQ |
T → FR
R → *FR |
F → (E) | id
Then,
FIRST(E) = FIRST(T) = FIRST(F) = {(, id}.
FIRST(Q) = {+, }
FIRST(R) = {*, }

Dr. Hussien M. Sharaf
3

4. FOLLOW
To compute FOLLOW(A) for all nonterminals A, then
apply the following rules until nothing can be added to
any FOLLOW set:
1. Place $ in FOLLOW(S), where S is the start symbol and
$ is the input right endmarker.
i.e. $ ∈ FOLLOW(S)
2. If there is a production A → αBβ, then everything in
FIRST(β) except for is placed in FOLLOW(B).

i.e. (FIRST(β) ~
) ⊆ FOLLOW(B)
Ali Plays
Dr. Hussien M. Sharaf
Follow of Ali
Plays
4

5. FOLLOW
If there is a production A → αB, or [a production A
→ αBβ where FIRST(β) contains (i.e β → )], then
everything in FOLLOW(A) is in FOLLOW(B).
i.e. FOLLOW(A) ⊆ FOLLOW(B)
3.
Ali Plays
Dr. Hussien M. Sharaf
Follow of Ali
Plays
5

6. FOLLOW SET EXAMPLE
Consider again the previous grammar:
E → TQ
Q → +TQ |
First (‘)’) ⊆
T → FR
Follow(E) because
F → (E)
R → *FR |
E is the start
F → (E) | id
symbol
Then,
First(Q) ⊆ Follow(T)
Because 1. E → TQ
FOLLOW(E) = FOLLOW(Q) = { ) , $ }.
FOLLOW(T) = FOLLOW(R) ={ +, ), $ }
Follow(E) ⊆
Follow(T)
FOLLOW(F) = {*, +, ), $}

Because 2. Q →
Dr. Hussien M. Sharaf
First(Q) ⊆
Follow(T)
Because E → TQ
6

7. FOLLOW SET EXAMPLE
Consider again the previous grammar:
E → TQ
Q → +TQ |
T → FR
R → *FR |
F → (E) | id
FOLLOW(E) = FOLLOW(Q) = { ) , $ }.
FOLLOW(T) = FOLLOW(R) ={ +, ), $ }
FOLLOW(F) = { * , + , ) , $ }

First(R) ⊆ Follow(F)
Because T→ FR
Dr. Hussien M. Sharaf
First(R) ⊆ Follow(F)
Because 1. T→ FR
Follow(T) ⊆ Follow(F)
Because 2. R →
7

8. EXAMPLE 1
[ Alfred V. Aho, Compilers Principles, Techniques, and
Tools, 1986, Addison-Wesley, page 188]
Construct the parsing table for the following grammar:
1. E
TQ
2. Q
+TQ |
3. T → FR
4. R
5. F
E
Q
Dr. Hussien M. Sharaf
T
R
F
First Set
{(, id}
{+, }
{(, id}
{*, }
{(, id}
*FR |
(E) | id
Follow set
{$, )}
{$, )}
{+, ), $ }
{+, ), $}
{*, +, ), $}
8

9. EXAMPLE 1 (CONT.)
The parsing table for the previous grammar is:
1. E
TQ
2. Q
+TQ |
3. T → FR
id
E E
+
(
E
Q
id
Dr. Hussien M. Sharaf
$
TQ
Q
Q
R
R
T → FR
R
F
*FR |
(E) | id
)
+TQ
T → FR
R
F
*
TQ
Q
T
4. R
5. F
R
*FR
F
(E)
9

10. FIRST AND FOLLOW EXAMPLE
S →A
 A → BC | DBC
 B → bB ΄|
 B ΄→ bB΄|
 C →c|
 D →a|d
FIRST(S) = { a, b, c, d,
FIRST(A) = { a, b, c, d,
FIRST(B) = { b, }
FIRST(B ΄) = { b, }
FIRST(C) = { c, }
FIRST(D) = { a, d }

Dr. Hussien M. Sharaf
}
}
FOLLOW(S) = { $ }
FOLLOW(A) = { $ }
FOLLOW(B) = { c, $ }
FOLLOW(B ΄) ={ c, $ }
FOLLOW(C) = { $ }
FOLLOW(D) = { b, c, $ }
10

11. EXAMPLE 2 PAGE 156
The parsing table for the following grammar is:
1. S
If_Stat | other
2. If_Stat
if(Exp) S Else_part
if
S
If_Stat
S
3. Else_part
If_Stat S
other
4. Exp
else
else S |
true | false
true
false
$
other
If_Stat
if(exp) S
Else_part
Else_part
Exp
Dr. Hussien M. Sharaf
Else_part
else S
Else_part
exp
true
exp
false
11

12. EXAMPLE 3
The parsing table for the following grammar is:
1. E
TQ
6. R
*FR
2.
3.
4.
5.
+TQ
-TQ
7. R
8. R
9. F
10.F
/FR
Q
Q
Q
T
FR
+
-
*
/
E
Q
(
)
1
2
3
F
Dr. Hussien M. Sharaf
8
6
7
4
5
8
9
$
1
5
8
id
4
T
R
(E)
id
8
10
12

13. THANK YOU