Compiler construction 删除可为空的产品

我正在为pascal的子集创建一个词法分析器，这是编译器红龙教科书后面推荐的一个编程项目。我正在将语法更改为LL，以便创建解析表。我忽略了犹豫不决的模糊性，并且相信这是唯一存在的模糊性。我刚刚删除了所有的epsilon产品。在我继续进行左因子分解之前，我想得到一些关于我是否正确删除了ε乘积的反馈。我已经盯着这个看了很长一段时间了，所以我真的不确定我是否错过了一些会在以后引起问题的东西，并且没有人来检查它。我知道这是一个很长的帖子，我真的不知道去哪里让知道的人检查。我真的很感谢你的时间

原始语法：

<statement> →
    if <expression> then <statement>
<factor> → id
<program> →
     <program> id (<identifier_list>);
     <declarations>
     <subprogram_declarations>
     <compound_statement>
     .
<identifier_list> →
     id
     | <identifier_list>, id
<declarations> →
     <declarations> var id : <type>;
     |E
<type> → 
     <standard_type>
     |array[num..num] of <standard_type>
<standard type> →
     integer
     | real
<subprogram_declarations> →
     <subprogram_declarations> <subprogram_declaration>;
     |E
<subprogram_declaration> →
     <subprogram_head declarations> 
     <subprogram_declarations> 
     <compound_statement>
<subprogram_head> → 
     function id <arguments> : <standard_type>;
<arguments> → 
    (<parameter_list>)
    | E
<parameter_list> →
     id : <type> 
     | <parameter_list>; id : <type>
<compound statement> →
     begin
     <optional_statements>
     end
<optional_statements> →
     <statement_list>
     | E
<statement_list> →
     <statement>
     |<statement_list>; <statement>
<statement> →
     <variable> assignop <expression>
     | <procedure_statement>
     | <compound_statement>
     | if <expression then statement> else <statement>
     | while <expression> do <statement>
     | if <expression> then <statement>
<variable> → 
     id
     | id [<expression> ]
<expression_list> →
     <expression>
     |<expression_list> , <expression>
<expression> →
     <simple_expression>
     | <simple_expression> relop <simple_expression>
<simple_expression> →
     <term>
     | sign <term>
     | <simple_expression> addop <term>
<term> →
     <factor>
     | <term> mulop <factor>
<factor> →
     id
     | id (<expression_list>)
     | num
     | (<expression>)
     | not <factor>
     | id [<expression>]
<sign> →
     + | -

→
若然
→ 身份证件
→
id（）；
.
→
身份证件
|，id
→
变量id:；
|E
→ 
|的数组[num..num]
→
整数
|真实的
→
;
|E
→
→ 
函数id:；
→ 
()
|E
→
身份证件：
| ; 身份证件：
→
开始
终止
→
|E
→
|; 
→
转让
| 
| 
|否则
|而你呢
|若然
→ 
身份证件
|id[]
→
| , 
→
|重播
→
|标志
|阿多普
→
|穆洛普
→
身份证件
|id（）
|num
| ()
|不是
|id[]
→
+ | -

语法后ε产生消除

<statement> →
    if <expression> then <statement>
<factor> → id
<program> →
     <program><id (<identifier_list>);
     <declarations>
     <subprogram_declarations>
     .
     |<program> id (<identifier_list>);
      <subprogram_declarations>
      .
     |<program>id (<identifier_list>);
      <declarations>
      .
     |<program> id (<identifier_list>);
      .
     |<program><id (<identifier_list>);
      <declarations>
      <subprogram_declarations>
      begin
      <statement_list>
      end
      .
     |<program> id (<identifier_list>);
      <subprogram_declarations>
      begin
      <statement_list>
      end
      .
     |<program>id (<identifier_list>);
      <declarations>
      begin
      <statement_list>
      end
      .
     |<program> id (<identifier_list>);
      begin
      <statement_list>
      end
      .
<identifier_list> →
     id
     | <identifier_list>, id
<declarations> →
     <declarations> var id : <type>;
<type> → 
     <standard_type>
     |array[num..num] of standard_type
<standard type> →
     <integer>
     | <real>
     <subprogram_declarations> →
     <subprogram_declarations>  <subprogram_declaration>;
<subprogram_declaration> →
     <subprogram_head> <declarations> 
     <subprogram_declarations >
     begin
     <statement_list>
     end
     |<subprogram_head>
      <subprogram_declarations >
      begin
      <statement_list>
      end
     |<subprogram_head> <declarations> 
      begin
      <statement_list>
      end
     |<subprogram_head>
      begin
      <statement_list>
      end
     |<subprogram_head> <declarations> 
      <subprogram_declarations >
     |<subprogram_head>
      <subprogram_declarations >
     |<subprogram_head> <declarations> 
     |<subprogram_head>
<subprogram_head> → 
      function id (<parameter_list>) : <standard_type>;
      |function id : <standard_type>;
<parameter_list> →
     id : <type> 
     |<parameter_list>; id : <type>
<statement_list> →
     <statement>
     |<statement_list>;< statement>
<statement> →
     <variable> assignop <expression>
     | <procedure_statement>
     | <compound_statement>
     | if <expression> then <statement> else <statement>
     | while <expression> do <statement>
     | if <expression> then <statement>
<variable> → 
     id
     |id [<expression>]
<expression_list> →
     <expression>
     |<expression_list> , <expression>
<expression> →
     <simple_expression>
     | <simple_expression> relop <simple_expression>
<simple_expression> →
     <term>
     | <sign> <term>
     | <simple_expression> addop <term>
<term> →
     <factor>
     | <term> mulop <factor>
<factor> →
     id
     | id (<expression_list>)
     | num
     | (<expression>)
     | not <factor>
     | id [<expression>]
<sign> →
     + | -

→
若然
→ 身份证件
→
 <subprogram_head> → 
      function id <arguments> : <standard_type>;
 <arguments> → 
      (<parameter_list>)
      | E

<subprogram_head> → 
     function id (<parameter_list>) : <standard_type>;
     |function id : <standard_type>;