作业十一

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

 

 

2.P101练习7（2）（3）文法改写，并分别求FIRST集、FOLLOW集，和SELECT集

 

(2)A→aABe|a

　B→Bb|d

消除左递归:

A→aA'

A'→ABe|ε

B→dB'

B'→bB'|ε

FIRST集:

FIRST(A)→{a}

FIRST(A')→{a,ε}

FIRST(B)→{d}

FIRST(B')→{b,ε}

FOLLOW集:

FOLLOW(A)→{d,#}

FOLLOW(A')→{d,#}

FOLLOW(B)→{e}

FOLLOW(B')→{e}

 SELECT集：

SELECT(A→aA')={d,#}

SELECT(A'→ABe)={a}

SELECT(A'→ε)={d,#}

SELECT(B→dB')={e}

SELECT(B'→bB')={b}

SELECT(B'→ε)={e}

 

（3）

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}

 

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

 

FIRST集：

 FIRST(Ap) = { a , c , p }

 FIRST(a) = { a }

 FIRST(ε) = { ε }

 FIRST(cA) = { c }

 FIRST(aA) = { a }

FOLLOW集：

 FOLLOW(A) = { p }

 FOLLOW(S) = { # }

SELECT集：

 SELECT(S→Ap) = FIRST(Ap) = { a , c , p }

 SELECT(a) = FIRST(a) = { a }

 SELECT(ε) = FOLLOW(A) = { p }

 SELECT(cA) =  FIRST(cA) = { c }

 SELECT(aA) = FIRST(aA) = { a }

 

S->Ap
S->Bq
A->a
A->cA
B->b
B->dB

FIRST集：

FIRST(Ap) = { a , c }

FIRST(Bp) = { 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->Bq) = 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 }