作业十一——LL(1)文法的判断

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?

答:

证明:FIRST(Da) = {b, a}

   FIRST(ε) = {ε}

   FIRST(aADC) = {a}

   FIRST(b) = {b}

   FOLLOW(A) = {c, b, a, #}

   FOLLOW(C) = {#,}

   FOLLOW(D) = {a, #}

   SELECT(A -> Da) = FIRST(Da) = {b, a}

   SELECT(A -> ε) = FIRST(ε) - {ε}UFOLLOW(A) = FOLLOW(A) = {c, b, a, #}

   因为SELECT(A -> Da) ∩ SELECT(A -> ε) ≠ Ø

   所以G(S)不是 LL(1)文法。

2.法消除左递归之后的表达式文法是否是LL(1)文法?

答:文法为:(1)E -> TE'

      (2)E' -> +TE' | ε

      (3)T -> FT'

      (4)T' -> *FT' | ε

      (5)F -> (E) | i

  FIRST(+TE') = {+}

  FIRST(ε) = {ε}

  FIRST(*FT') = {*}

  FIRST((E)) = { ( }

  FIRST(i) = {i}

  FOLLOW(E') = { ), # }

  FOLLOW(T') = {+, ), #}

  FOLLOW(F) = {*, +, ), #}

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

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

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

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

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

  SELECT(F->i)=FIRST(i)={i}

  因为SELECT(E' -> +TE') ∩ SELECT(E' -> ε) = Ø

    SELECT(T' -> *FT') ∩ SELECT(T' -> ε) = Ø

    SELECT(F -> (E)) ∩ SELECT(F -> i) = Ø

  所以此表达式文法是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()

答:SELECT集:

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

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

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

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

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

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

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

  SELECT(F->i)=FIRST(i)={i}

  递归下降语法分析程序:

  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。

 

posted @ 2019-11-21 18:51  Mr-Lin  阅读(...)  评论(...编辑  收藏