把下面的文法改成LL(1)的（编译原理-自上而下分析）

把下面的文法改写为LL(1)的：

Declist -> Declist;Decl | Decl
Decl -> IdList:Type
IdList -> IdList,id | id （该产生式书上似乎有错误，此处已纠正）
Type -> ScalarType | array (ScalarTypeList) of Type
ScalarType -> id | Bound. .Bound
Bound ->Sign IntLiteral | id
Sign -> + | - | ε
ScalarTypeList -> ScalarTypeList,ScalarType | ScalarType

①消除左递归
DecList -> Decl Declist’
Declist’ -> ;Decl Declist’ | ε
Decl -> IdList:Type
IdList -> id IdIist’
IdList’ -> ,id IdList’ | ε
Type -> ScalarType | array (ScalarTypeList) of Type
ScalarType -> id | Bound. .Bound
Bound ->Sign IntLiteral | id
Sign -> + | - | ε
ScalarTypeList -> ScalarType ScarlarTypeList’
ScalarTypeList’ -> ,ScalarType ScalarTypeList’ | ε

②判断是否满足LL(1)型文法的另外两个条件
FIRST(;Decl Declist’)∩FIRST(ε)={;}∩{ε}=∅
FIRST(,id IdList’)∩FIRST(ε)={,}∩{ε}=∅
FIRST(ScalarType)∩FIRST(array (ScalarTypeList) of Type)={id,+,-,IntLiteral}∩{array}=∅
FIRST(id)∩FIRST(Bound. .Bound)={id}∩{id,+,-,IntLiteral}≠∅ ×
FIRST(Sign IntLiteral)∩FIRST(id)={+,-,IntLiteral}∩{id}=∅
FIRST(+)∩FIRST(-)∩FIRST(ε)={+}∩{-}∩{ε}=∅
FIRST(,ScalarType ScalarTypeList’)∩FIRST(ε)={,}∩{ε}=∅

上面第五行不满足要求，故需要对相应产生式提取作左因子
原产生式：
ScalarType -> id | Bound. .Bound
提取左因子后：
ScalarType -> id ScalarType’ | Sigh IntLiteral…Bound
ScalarType’ -> ε | . .Bound

此外，还需要第三个条件
FIRST(Declist’)∩FOLLOW(Declist’)={;,ε}∩{#}=∅
FIRST(IdList’)∩FOLLOW(IdList’)={, ,ε}∩{:}=∅
FIRST(ScalarType’)∩FOLLOW(ScalarType’)={ε,.}∩{;,#}=∅
FIRST(Sign)∩FOLLOW(Sign)={+,-,ε}∩{IntLiteral}=∅
FIRST(ScalarTypeList’)∩FOLLOW(ScalarTypeList’)={, ,ε}∩{)}=∅

综合三个条件，修改后的文法为LL(1)型文法

（来源：《程序设计语言编译原理》，国防工业出版社，第3版）