Example of
constructing follow sets
first sets:
Grammar:
e
e'
e'
t
t'
t'
f
f
f
→
→
→
→
→
→
→
→
→
t e'
+ t e'
𝜀
f t'
* f t'
𝜀
(e)
x
y
Non-terminal
first set
e
{ ‘y’, ‘x’, ‘(’ }
e'
{ 𝜀, ‘+’ }
t
{ ‘y’, ‘x’, ‘(’ }
t'
{ 𝜀, ‘*’ }
f
{ ‘y’, ‘x’, ‘(’ }
follow sets:
Non-terminal
follow set
e
{$}
e'
t
t'
f
first sets:
Grammar:
e
e'
e'
t
t'
t'
f
f
f
→
→
→
→
→
→
→
→
→
t e'
+ t e'
𝜀
f t'
* f t'
𝜀
(e)
x
y
Non-terminal
first set
e
{ ‘y’, ‘x’, ‘(’ }
e'
{ 𝜀, ‘+’ }
t
{ ‘y’, ‘x’, ‘(’ }
t'
{ 𝜀, ‘*’ }
f
{ ‘y’, ‘x’, ‘(’ }
follow sets:
Non-terminal
follow set
e
{ $, ‘)’ }
e'
t
t'
f
first sets:
Grammar:
e
e'
e'
t
t'
t'
f
f
f
→
→
→
→
→
→
→
→
→
t e'
+ t e'
𝜀
f t'
* f t'
𝜀
(e)
x
y
Non-terminal
first set
e
{ ‘y’, ‘x’, ‘(’ }
e'
{ 𝜀, ‘+’ }
t
{ ‘y’, ‘x’, ‘(’ }
t'
{ 𝜀, ‘*’ }
f
{ ‘y’, ‘x’, ‘(’ }
follow sets:
Non-terminal
follow set
e
{ $, ‘)’ }
e'
{ $, ‘)’ }
t
t'
f
first sets:
Grammar:
e
e'
e'
t
t'
t'
f
f
f
→
→
→
→
→
→
→
→
→
t e'
+ t e'
𝜀
f t'
* f t'
𝜀
(e)
x
y
Non-terminal
first set
e
{ ‘y’, ‘x’, ‘(’ }
e'
{ 𝜀, ‘+’ }
t
{ ‘y’, ‘x’, ‘(’ }
t'
{ 𝜀, ‘*’ }
f
{ ‘y’, ‘x’, ‘(’ }
follow sets:
Non-terminal
follow set
e
{ $, ‘)’ }
e'
{ $, ‘)’ }
t
{ ‘+’ }
t'
f
first sets:
Grammar:
e
e'
e'
t
t'
t'
f
f
f
→
→
→
→
→
→
→
→
→
t e'
+ t e'
𝜀
f t'
* f t'
𝜀
(e)
x
y
Non-terminal
first set
e
{ ‘y’, ‘x’, ‘(’ }
e'
{ 𝜀, ‘+’ }
t
{ ‘y’, ‘x’, ‘(’ }
t'
{ 𝜀, ‘*’ }
f
{ ‘y’, ‘x’, ‘(’ }
follow sets:
Non-terminal
follow set
e
{ $, ‘)’ }
e'
{ $, ‘)’ }
t
{ ‘+’, $, ‘)’ }
t'
f
first sets:
Grammar:
e
e'
e'
t
t'
t'
f
f
f
→
→
→
→
→
→
→
→
→
t e'
+ t e'
𝜀
f t'
* f t'
𝜀
(e)
x
y
Non-terminal
first set
e
{ ‘y’, ‘x’, ‘(’ }
e'
{ 𝜀, ‘+’ }
t
{ ‘y’, ‘x’, ‘(’ }
t'
{ 𝜀, ‘*’ }
f
{ ‘y’, ‘x’, ‘(’ }
follow sets:
Non-terminal
follow set
e
{ $, ‘)’ }
e'
{ $, ‘)’ }
t
{ ‘+’, $, ‘)’ }
t'
{ ‘+’, $, ‘)’ }
f
first sets:
Grammar:
e
e'
e'
t
t'
t'
f
f
f
→
→
→
→
→
→
→
→
→
t e'
+ t e'
𝜀
f t'
* f t'
𝜀
(e)
x
y
Non-terminal
first set
e
{ ‘y’, ‘x’, ‘(’ }
e'
{ 𝜀, ‘+’ }
t
{ ‘y’, ‘x’, ‘(’ }
t'
{ 𝜀, ‘*’ }
f
{ ‘y’, ‘x’, ‘(’ }
follow sets:
Non-terminal
follow set
e
{ $, ‘)’ }
e'
{ $, ‘)’ }
t
{ ‘+’, $, ‘)’ }
t'
{ ‘+’, $, ‘)’ }
f
{ ‘*’ }
first sets:
Grammar:
e
e'
e'
t
t'
t'
f
f
f
→
→
→
→
→
→
→
→
→
t e'
+ t e'
𝜀
f t'
* f t'
𝜀
(e)
x
y
Non-terminal
first set
e
{ ‘y’, ‘x’, ‘(’ }
e'
{ 𝜀, ‘+’ }
t
{ ‘y’, ‘x’, ‘(’ }
t'
{ 𝜀, ‘*’ }
f
{ ‘y’, ‘x’, ‘(’ }
follow sets:
Non-terminal
follow set
e
{ $, ‘)’ }
e'
{ $, ‘)’ }
t
{ ‘+’, $, ‘)’ }
t'
{ ‘+’, $, ‘)’ }
f
{ ‘*’, ‘+’, $, ‘)’ }