1.将以下文法消除左递归,分析符号串 i*i+i 。
并分别求FIRST集、FOLLOW集,和SELECT集
E -> E+T | T
T -> T*F | F
F -> (E) | i
消除左递归:
E -> TE’
E’ -> +TE’ | ε
T -> FT’
T’ -> *FT’ | ε
F -> (E) | i
分析符号串 i*i+i:
first集:
FIRST(TE')={ (, i }
FIRST(+TE')={+}
FIRST(ε)={ε}
FIRST(FT')={ (, i }
FIRST(*FT')={*}
FIRST((E))={ ( }
FIRST(i)={i}
follow集:
FOLLOW(E)={ ),# }
FOLLOW(E')={ ),# }
FOLLOW(T)={+,),#}
FOLLOW(T')={+,),#}
FOLLOW(F)={*,+,),#}
select集:
SELECT(E->TE')=FIRST(TE')={ (, i }
SELECT(E'->+TE')=FIRST(+TE')={+}
SELECT(E'->ε)=FIRST(ε)-{ε}UFOLLOW(E')=FOLLOW(E')={ ),# }
SELECT(T->FT')=FIRST(FT')={ (,i }
SELECT(T'->*FT')=FIRST(*FT')={*}
SELECT(T'->ε)=FIRST(ε)-{ε}UFOLLOW(T')=FOLLOW(T')={ +,),# }
SELECT(F->(E))=FIRST((E))={ ( }
SELECT(F->i)=FIRST(i)={i}
2.P101练习7(2)(3)文法改写,并分别求FIRST集、FOLLOW集,和SELECT集
文法改写:
A->aA'
A'->ABe | ε
B->dB'
B'->bB' | ε
FIRST集:
FIRST(aA')={a}
FIRST(ABe)={a}
FIRST(ε)={ε}
FIRST(dB')={d}
FIRST(bB')={b}
FOLLOW集:
FOLLOW(A)={d,#}
FOLLOW(A')={d,#}
FOLLOW(B)={e}
FOLLOW(B')={e}
SELECT集:
SELECT(A->aA')=FIRST(aA')={a}
SELECT(A'->ABe)=FIRST(ABe)={a}
SELECT(A'->ε)=FIRST(ε)-{ε}UFOLLOW(A')=FOLLOW(A')={d,#}
SELECT(B->dB')=FIRST(dB')={d}
SELECT(B'->bB')=FIRST(bB')={b}
SELECT(B'->ε)=FIRST(ε)-{ε}UFOLLOW(B')=FOLLOW(B')={e}
(3)
S->Aa | b
A->SB
B->ab
first集:
FIRST(bS')={b}
FIRST(BaS')={a}
FIRST(ε)={ε}
FIRST(ab)={a}
follow集:
FOLLOW(S)={#}
FOLLOW(S')={#}
FOLLOW(B)={a}
select集:
SELECT(S->bS')=FIRST(bS')={b}
SELECT(S'->BaS')=FIRST(BaS')={a}
SELECT(S'->ε)=FIRST(ε)-{ε}UFOLLOW(S')=FOLLOW(S')={#}
SELECT(B->ab)=FIRST(ab)={a}
课堂练习:
求以下文法的FIRST集、FOLLOW集和SELECT集。
S->Ap
A->a |ε
A->cA
A->aA
(1)
S->Ap
A->a |ε
A->cA
A->aA
first集:
FIRST(Ap)={a,c,p}
FIRST(a)={a}
FIRST(ε)={ε}
FIRST(cA)={c}
FIRST(aA)={a}
follow集:
FOLLOW(S)={#}
FOLLOW(A)={p}
select集:
SELECT(S->Ap)=FIRST(Ap)={a,c,p}
SELECT(A->a)=FIRST(a)={a}
SELECT(A->ε)=FIRST(ε)-{ε}UFOLLOW(A)=FOLLOW(A)={p}
SELECT(A->cA)=FIRST(cA)={c}
SELECT(A->aA)=FIRST(aA)={a}
S->Ap
S->Bq
A->a
A->cA
B->b
B->dB
(2)
S->Ap
S->Bq
A->a
A->cA
B->b
B->dB
first集:
FIRST(Ap)={a,c}
FIRST(Bq)={b,d}
FIRST(a)={a}
FIRST(cA)={c}
FIRST(b)={b}
FIRST(dB)={d}
follow集:
FOLLOW(S)={#}
FOLLOW(A)={p}
FOLLOW(B)={q}
select集:
SELECT(S->Ap)=FIRST(Ap)={a,c}
SELECT(S->Bp)=FIRST(Bq)={b,d}
SELECT(A->a)=FIRST(a)={a}
SELECT(A->cA)=FIRST(cA)={c}
SELECT(B->b)=FIRST(b)={b}
SELECT(B->dB)=FIRST(dB)={d}