第十次作业 消除左递归

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

解：

消除左递归：

E -> TE'

E' -> +TE' | ε

T -> FT'

T' -> *FT' | ε

F -> (E) | i

分析符号串：

FIRST集：

FIRST(TE') = { ( , i }

FIRST(+TE') = { + }

FIRST(FT')={ ( , i , * }

FIRST(*FT') = { * }

FIRST((E)) = { ( }

FIRST(i) = { i }

FOLLOW集：

FOLLOW(E) = { ) }

FOLLOW(E') = { # }

FOLLOW(T) = { E' }

FOLLOW(T) = { E' }

FOLLOW(F) = { ) }

SELECT集:

SELECT(E -> TE') = { ( , i }

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

SELECT(E' -> ε) = (FIRST(ε) - { ε }) U FOLLOW(E') = FOLLOW(E') = { ) , ε }

SELECT(T -> FT') = { ( , i }

SELECT(T' -> *FT') = { * }

SELECT(T' -> ε) = (FIRST(ε) - { ε }) U FOLLOW(T') = FOLLOW(T') = { ε,+,) }

SELECT(F -> (E) ) = { ( }

SELECT(F -> i) = { i }

 

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

 解：（2）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') = { a }

SELECT(A' -> ABe} = { a }

SELECT{A' -> ε) = { d , # }

SELECT{B -> dB') = { d }

SELECT(B' -> bB'} = { b }

SELECT(B' -> ε) = { e }

 

(3)S -> bS'

　 S' -> BaS' | ε

　 B -> ab

FIRST集：

FIRST(S) = { b }

FIRST(S') = { a , ε }

FIRST(B) = { a }

FOLLOW集：

FOLLOW(S) = { # }

FOLLOW(S') = { # }

FOLLOW(B) = { a }

SELECT集：

SELECT(S -> bS') = { b }

SELECT(S' -> BaS') = { a , ε}

SELECT(S' -> ε) = { # }

SELECT(B -> 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

解：

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) = { a , c , p }

SELECT(A -> a) = { a }

SELECT(A -> ε) = { p }

SELECT(A -> cA) = { c }

SELECT(A -> aA) = { a }

 

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

解：

FIRST集：

FIRST(Ap) = { a , c }

FIRST(Bq) = { b , d }

FIRST(a) = { a }

FIRST(c) = { c }

FIRST(b) = { b }

FIRST(dB) = { d }

FOLLOW集：

FOLLOW(S) = { # }

FOLLOW(A) = { p }

FOLLOW(B) = { q }

SELECT集：

SELECT(S -> Ap) = { a , c }

SELECT(S -> Bq) = { b , d }

SELECT(A -> a) = { a }

SELECT(A -> cA) = { c }

SELECT(B -> b) = { b }

SELECT(B -> dB) = { d }