实验：FIRST & FOLLOW 集合计算

输入文法，自动计算所有非终结符的 FIRST 和 FOLLOW 集合。

Non-Terminal	FIRST	FOLLOW
E	{ (, id }	{ $, ) }
E'	{ +, ε }	{ $, ) }
T	{ (, id }	{ +, $, ) }
T'	{ *, ε }	{ +, $, ) }
F	{ (, id }	{ *, +, $, ) }

Terminals: +, *, (, ), id

Calculation Process (Derivation)

FIRST Set Derivation

E': Added { + }
E' -> ... + ... (First(+) ⊆ First(E'))
E': Added { ε }
E' -> ε
T': Added { * }
T' -> ... * ... (First(*) ⊆ First(T'))
T': Added { ε }
T' -> ε
F: Added { ( }
F -> ... ( ... (First(() ⊆ First(F))
F: Added { id }
F -> ... id ... (First(id) ⊆ First(F))
T: Added { (, id }
T -> ... F ... (First(F) ⊆ First(T))
E: Added { (, id }
E -> ... T ... (First(T) ⊆ First(E))

FOLLOW Set Derivation

E: Added { $ }
Start Symbol
T: Added { + }
E -> ... T E' ... (First(E') ⊆ Follow(T))
T: Added { $ }
E -> ... T ... (Follow(E) ⊆ Follow(T))
E': Added { $ }
E -> ... E' ... (Follow(E) ⊆ Follow(E'))
F: Added { * }
T -> ... F T' ... (First(T') ⊆ Follow(F))
F: Added { +, $ }
T -> ... F ... (Follow(T) ⊆ Follow(F))
T': Added { +, $ }
T -> ... T' ... (Follow(T) ⊆ Follow(T'))
E: Added { ) }
F -> ... E ) ... (First()) ⊆ Follow(E))
T: Added { ) }
E -> ... T ... (Follow(E) ⊆ Follow(T))
E': Added { ) }
E -> ... E' ... (Follow(E) ⊆ Follow(E'))
F: Added { ) }
T -> ... F ... (Follow(T) ⊆ Follow(F))
T': Added { ) }
T -> ... T' ... (Follow(T) ⊆ Follow(T'))