第十次作业-消除左递归

1.将以下文法消除左递归，并分析符号串 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

E->TE'

E'->+TE'|ε

T->FT'

T'->*FT'|ε

F->(E)|i

FIRST集

FIRST(TE')={（，i }

FIRST(+TE')={ + }

FIRST(ε)={ ε }

FIRST(FT')={（，i }

FIRST(*FT')={ * } 

FIRST((E))={（ }

FIRST((E)|i)={ i }

FOLLOW集

FOLLOW(E)={#，）}

FOLLOW(E')={ ）}

FOLLOW(T)={ + }

FOLLOW(T')={ + }

FOLLOW(F)={ * }

SELECT集

SELECT(E->TE')={（，i }

SELECT(E'->+TE')={ + }

SELECT(E'->ε)={ ）}

SELECT(T->FT')={（，i }

SELECT(T'->*FT')={ * } 

SELECT(T'->ε)={ + }

SELECT(F->(E))={（  }

SELECT(F->i)={ i }

分析符号串 i*i+i

 

 

2.教材101页7(2) (3)

 (2) A->aABe|a

      B->Bb|d

提取左公因子：A->aA'      A'->ABe|ε

消除左递归：B->dB'          B'->bB'|ε

① FIRST集：

First(aA') = {a}

First(ABe) = {A}

First(ε) = {ε}

First(dB') = {d}

First(bB') = {b}

First(ε) = {ε}

② FOLLOW集：

Follow(A) = {Be}

Follow(A') = {#}

Follow(B) = {e}

Follow(B') = {#}

③ SELECT集：

Select(A->aA') = First(aA') = {a}

Select(A'->ABe) = First(ABe) = {A}

Select(A'->ε) = First(ε) = {ε}∪Follow(A') = {#}

Select(B->dB') = First(dB') = {d}

Select(B'->bB') = First(bB') = {b}

Select(B'->ε) = First(ε) = {ε}∪Follow(B') = {#}

(3) S->Aa|b

     A->SB

     B->ab

将A->SB代入S->Aa|b可得：S->SBa|b

消除左递归：S->bS'      S'->BaS'|ε     B->ab

① FIRST集：

First(SBa) = {S}

First(b) = {b}

First(bS') = {b}

First(BaS') = {B}

First(ε) = {ε}

First(ab) = {a}

② FOLLOW集：

Follow(S) = {B}

Follow(S') = {#}

Follow(B) = {a}

③ SELECT集：

 Select(S->SBa) = First(SBa) = {S}

 Select(S->b) = First(b) = {b}

 Select(S->bS') = First(bS') = {b}

 Select(S'->BaS') = First(BaS') = {B}

 Select(S->ε) = First(ε) = {ε}∪Follow(S') = {#}

 Select(B->ab) = First(ab) = {a}

3.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 FIRST集：

First(S) = First(Ap) = {a,c,p}

First(a) = {a}

First(ε) = {ε}

First(cA) = {c}

First(aA) = {a}

② FOLLOW集：

Follow(S) = {#}

Follow(A) = {p}

 ③ SELECT集：

Select(S->Ap)= First(Ap) = {a,c,p}

Select(A->a)= First(a) = {a}

Select(A->ε)= First(ε) = {ε}∪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

① FIRST集：

First(S1) = First(Ap) ={a,c}

First(S2) = First(Bq) ={b,d}

First(a) = {a}

First(cA) = {c}

First(b) = {b}

First(dB) = {d}

② FOLLOW集：

Follow(S) = {#}

Follow(A) = {p}

Follow(B) = {q}

③ SELECT集：

Select(S->Ap) = Fisrt(Ap) = {A}

Select(S->Bq) = Fisrt(Bq) = {B}

Select(A->a) = Fisrt(a) = {a}

Select(A->cA) = Fisrt(cA) = {c}

Select(B->b) = Fisrt(b) = {b}

Select(B->dB) = Fisrt(dB) = {d}