编译原理（四）自顶向下语法分析方法、LL(1)文法的判别、非LL(1)文法转换为LL(1)文法

柔光的暖阳◎ 2023-02-18 14:29 8阅读 0赞

#### 本文要点 ####

1.  理解 “能使用自顶向下分析技术的文法必须是LL(1)文法”
2.  LL(1)文法的充要条件
3.  LL(1)文法的判别
4.  某些 非LL(1)文法 到 LL(1)文法 的等价变换  
    1.提取左公共因子  
    2.消除左递归（直接左递归、间接左递归）
5.  不确定的自顶向下分析思想
6.  确定的自顶向下分析方法  
    1.递归子程序法  
    2.预测分析法\[判别LL(1)文法；构造预测分析表；分析输入串\]  
    ![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70]

# 4.1 确定的自顶向下分析思想 #

**主要思想：**  
从文法的开始符号出发，如何根据当前的单词符号，  
唯一地确定选用哪个产生式来替换相应的VN向下推导。  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70 1]  
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# 4.2 LL(1)文法的判别 #

判别步骤：

1.  求出能推出ε的非终结符
2.  计算FIRST集
3.  计算FOLLOW集
4.  计算SELECT集
5.  判别是否是LL(1)文法  
    ![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70 9]  
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# 4.3 某些非LL(1)文法到LL(1)文法的等价变换 #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70 18]

### 4.3.1 提取左公共因子 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70 19]  
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### 4.3.2 提取隐含的左公共因子 ###

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### 4.3.3 不能在有限步骤内提取完左公共因子的文法 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70 22]

### 4.3.4 消除左递归 ###

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### 4.3.5 消除直接左递归 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70 24]

### 4.3.6 消除间接左递归 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70 25]

### 4.3.7 消除文法中一切左递归 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70 26]  
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# 4.4 确定的自顶向下分析方法 #

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构造预测分析表的方法：  
对每个VT或“\#”用符号a表示。  
若a∈SELECT（A–>α），则把A–>α放入M\[A,a\]中。  
（所有空白的M\[A,a\]表示出错。）  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3N0YXJfb2Zfc2NpZW5jZQ_size_16_color_FFFFFF_t_70 33]  
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# 4.5 不确定的自顶向下分析思想 #

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