作业 11 LL(1)文法的判断,递归下降分析程序
1. 文法 G(S):
(1)S -> AB
(2)A ->Da|ε
(3)B -> cC
(4)C -> aADC |ε
(5)D -> b|ε
验证文法 G(S)是不是 LL(1)文法?
解:
A->Da
A->ε
C->aADC
C->ε
D->b
D->ε
FIRST集:
First(Da) = {b,a}
First(ε) = {ε}
First(aADC) = {a}
First(b) = {b}
FOLLOW集:
Follow(A) = {c,b,a,#}
Follow(C) = {#}
Follow(D) = {a,#}
SELECT集:
Select(A->Da) = {b,a}
Select(A->ε) = {c,b,a,#}
Select(C->aADC) ={a}
Select(C->ε) = {#}
Select(D->b) = {b}
Select(D->ε) = {a,#}
由此可得:Select(A->Da) ∩ Select(A->ε) ≠ ∅
Select(C->aADC) ∩ Select(C->ε) =∅
Select(D->b) ∩ Select(D->ε) =∅
因此由LL(1)文法定义得知该文法不是LL(1)文法。
2.(上次作业)消除左递归之后的表达式文法是否是LL(1)文法?
解:
消除左递归:
(1) E->TE'
E'->+TE'|ε
(2) T->FT'
T'->*FT'|ε
(3) F->(E)|i
SELECT集:
Select(E->TE') = First(TE') = {(,i}
Select(E'->+TE') = First(+TE') = {+}
Select(E'->ε) = (First(ε) = {ε})∪Follow(E') = {),#}
Select(T->FT') = First(FT') = {(,i}
Select(T'->*FT') = First(+TE') = {*}
Select(T'->ε) = (First(ε) = {ε})∪Follow(T') = {+,),#}
Select( F->(E)) = First((E)) = {( }
Select( F->i) = First(i) = {i}
由此可得,Select(E'->+TE') ∩ Select(E'->ε) = ∅
Select(T'->*FT') ∩ Select(T'->ε) = ∅
Select( F->(E)) ∩ Select( F->i) = ∅
因此由LL(1)文法定义得知该文法是LL(1)文法。
3.接2,如果是LL(1)文法,写出它的递归下降语法分析程序代码。
E()
{T();
E'();
}
E'()
T()
T'()
F()
void ParseE(){
switch(lookahead){
case '(','i':
ParseT();
ParseE'();
break;
default:
print("syntax error \n");
exit(0);
}
}
void ParseE'(){
switch(lookahead){
case '+':
MatchToken('+');
ParseT();
ParseE'();
break;
case ')','#':
break;
default:
print("syntax error \n");
exit(0);
}
}
void ParseT(){
switch(lookahead){
case '(','i':
ParseF();
ParseT'();
break;
default:
print("syntax error \n");
exit(0);
}
}
void ParseT'(){
switch(lookahead){
case '*':
MatchToken('*');
ParseF();
ParseT'();
break;
case '+',')','#':
break;
default:
print("syntax error \n");
exit(0);
}
}
void ParseF(){
switch(lookahead){
case '(':
MatchToken('(');
ParseE();
MatchToken(')');
break;
case 'i':
MatchToken('i');
break;
default:
print("syntax error \n");
exit(0);
}
}
4.加上实验一的词法分析程序,形成可运行的语法分析程序,分析任意输入的符号串是不是合法的表达式。