编译原理实验二 tiny文法的LL(1)分析

通过LL(1)分析方法对tiny的文法进行处理，然后输入tiny程序，进行语法分析，其中也包含了词法扫描，词法扫描使用DFA状态图的循环扫描方法。

1、文法的规范化：消除文法中的左递归和提取文法的左公因子，并且对tiny的文法进行拆解，比如一条文法有几个选择，则拆成几条，最后的文法规则整理结果如下：

0 program --> stmt-sequence
1 stmt-sequence --> statement stmt'
2 stmt' --> ;statement stmt'
3 stmt' --> $
4 statement --> if-stmt
5 statement --> repeat-stmt
6 statement --> assign-stmt
7 statement --> read-stmt
8 statement --> write-stmt
9 statement --> While-stmt
10 statement --> Dowhile-stmt
11 statement --> for-stmt
12 if-stmt --> if exp then stmt-sequence else-part' end
13 else-part' --> else stmt-sequence
14 else-part' --> $
15 repeat-stmt --> repeat stmt-sequence until exp
16 assign-stmt --> identifier := exp
17 read-stmt --> read identifier
18 write-stmt --> write exp
19 exp --> simple-exp cmp-exp'
20 cmp-exp' --> comparison-op simple-exp
21 cmp-exp' --> $
22 comparison-op --> <
23 comparison-op --> =
24 simple-exp --> term term'
25 term' --> addop term
26 term' --> $
27 addop --> +
28 addop --> -
29 term --> factor factor'
30 factor' --> mulop factor
31 factor' --> $
32 mulop --> *
33 mulop --> /
34 mulop --> %
35 factor --> (exp)
36 factor --> number
37 factor --> identifier
38 While-stmt --> while exp do  stmt-sequence  endwhile
39 Dowhile-stmt --> do stmt-sequence  while  exp
40 for-stmt --> for identifier := simple-exp for-choose'
41 for-choose' --> to simple-exp  do stmt-sequence enddo
42 for-choose' --> downto simple-exp do stmt-sequence enddo

注：每条文法前面的标号是自行添加上去以便查看和分析，不属于程序处理范围。其中第0条文法中program为开始符号，’$’表示空推导，” -->”表示推导符号。

2、求出终结符号集和非终结符号集

扫描文法，求出终结符号集TerminalSet，非终结符号集NonTerminalSet。其中推导符号左边的token，全都属于非终结符号集，第一遍扫描可以求出非终结符号集。然后对文法推导符号右边的token进行扫描，消除掉属于非终结符号的token，剩下的token就都属于终结符号集。处理结果如下：

终结符号集：;
if then end else repeat until identifier := read write < = + - * / % ( )
number while do endwhile for to enddo downto

非终结符号集：program
stmt-sequence stmt' statement if-stmt else-part' repeat-stmt assign-stmt
read-stmt write-stmt exp cmp-exp' comparison-op simple-exp term' addop term
factor' mulop factor While-stmt Dowhile-stmt for-stmt for-choose'

3、求出first集合

first集合的求解算法伪代码自行google，具体实现见下面附件的代码。结果如下（其中字符’$’表示空推导）：

program: if repeat identifier read write while do for
stmt-sequence: if repeat identifier read write while do for
stmt': ; $
statement: if repeat identifier read write while do for
if-stmt: if
else-part': else $
repeat-stmt: repeat
assign-stmt: identifier
read-stmt: read
write-stmt: write
exp: ( number identifier
cmp-exp': $ < =
comparison-op: < =
simple-exp: ( number identifier
term': $ + -
addop: + -
term: ( number identifier
factor': $ * / %
mulop: * / %
factor: ( number identifier
While-stmt: while
Dowhile-stmt: do
for-stmt: for
for-choose': to downto

4、求出follow集合

follow集合求解算法伪代码也自行google，结果如下（其中字符’#’表示输入的结束）：

program: #
stmt-sequence: # else end until endwhile while enddo
stmt': # else end until endwhile while enddo
statement: ; # else end until endwhile while enddo
if-stmt: ; # else end until endwhile while enddo
else-part': end
repeat-stmt: ; # else end until endwhile while enddo
assign-stmt: ; # else end until endwhile while enddo
read-stmt: ; # else end until endwhile while enddo
write-stmt: ; # else end until endwhile while enddo
exp: then ; # ) do else end until endwhile while enddo
cmp-exp': then ; # ) do else end until endwhile while enddo
comparison-op: ( number identifier
simple-exp: < = then ; # to downto do ) else end until endwhile while enddo
term': < = then ; # to downto do ) else end until endwhile while enddo
addop: ( number identifier
term: + - < = then ; # to downto do ) else end until endwhile while enddo
factor': + - < = then ; # to downto do ) else end until endwhile while enddo
mulop: ( number identifier
factor: * / % + - < = then ; # to downto do ) else end until endwhile while enddo
While-stmt: ; # else end until endwhile while enddo
Dowhile-stmt: ; # else end until endwhile while enddo
for-stmt: ; # else end until endwhile while enddo
for-choose': ; # else end until endwhile while enddo

5、构造LL(1)分析表M[A,a]算法

文法规则的序号，见步骤1中的排序



6、分析算法，构造LL(1)分析树

为了在分析过程中构造分析树，除了分析栈，还要多开一个保存分析树节点的栈。

1）但分析栈中的栈顶元素和用户输入的token，值相等或类型匹配时，就把两个栈的栈顶元素出栈。

2）但进行文法规则的替换时，把两个栈的栈顶元素出栈，根据替换的文法规则，新建分析树节点（文法推导符号右部有多少个非终结符号/终结符号，就要建立多少个节点），然后这些新建节点作为刚才分析树栈中出栈token的子节点，连接好，之后再压入分析树节点的栈中。

3）栈顶元素是空推导时，则两个栈分析出栈，不做其他操作。

具体实现见代码。。。

7、文件cs的关系

共有3个类：父类Tiny，包含了tiny语言的特殊符号、保留字以及几个判断函数；子类TinyScan继承自Tiny，实现tiny的词法分析功能；子类SyntaxParse继承自Tiny，实现tiny的文法分析功能。

1）类Tiny的相关信息



2）类TinyScan的相关信息



3）类SyntaxParse的相关信息





代码文件：http://cid-780607117452312e.office.live.com/self.aspx/.Public/syntax%20parse.rar