语义分析：C语言表达式的语法树生成——Python实现

  令狐冲慢慢走近，那汉子全身发抖，双膝一屈，跪倒在雪地之中。令狐冲怒道：“你辱我师妹，须饶你不得。”长剑指在他咽喉之上，心念一动，走近一步，低声问道：“写在雪人上的，是些什么字？”

  那汉子颤声道：“是……是……‘海枯……海枯……石烂，两……情……情不……不渝’。”自从世上有了“海枯石烂，两情不渝”这八个字以来，说得如此胆战心惊、丧魂落魄的，只怕这是破题儿第一遭了。

  令狐冲一呆，道：“嗯，是海枯石烂，两情不渝。”心头酸楚，长剑送出，刺入他咽喉。

——《笑傲江湖》

语义分析较困难的根本原因在于语法的可递归性，深层次的递归使得问题的分解看起来变得相当地复杂。但是如果能将递归问题转化为迭代问题，便能很大程度地简化此问题模型。递归转化为迭代的关键在于——找到最深层递归结构的全部特征，迭代化之，问题便迎刃而解。
  一般情况下，人们在面对复杂的递归问题时时，亦是依据其语法规则，找到其递归深层的结构，化解之，步步迭代，如此，问题便得到解决。人类的思维很是擅长将递归问题转化为迭代问题，而学习知识的过程，则可以看成是对各种各样语法规则的理解与掌握。
  一元操作符、二元操作符的递归问题，可以很简单的转化为迭代，多元操作符的情况稍复杂些。

所有的操作符及其优先级如下图：

如typeof、取地址、指针指向等，在这里并未实现。实现的包括有算数运算式、逻辑运算式、函数调用与括号。对于理解语义分析的过程，已足够。

对于不包含括号与函数的简单表达式，我们语义分析演算过程如下：

我们的数据结构：

 '''
 ____________________________ Syntax Tree
 Parenthesis:
 ["(",None]
 [")",None]
 Operators(grouped by precedence):
 Unary :
 1  + - ! ~           ["+",None] ["-",None] ["!",None] ["~",None]
 Binary :
 2  * / %            ["*",None] ["/",None] ["%",None]
 3  + -              ["+",None] ["-",None]
 4  << >>            ["<<",None] [">>",None]
 5  > >= < <=        [">",None] [">=",None] ["<",None] ["<=",None]
 6  == !=            ["==",None] ["!=",None]
 7  &                ["&",None]
 8  ^                ["^",None]
 9  |                ["|",None]
 10 &&               ["&&",None]
 11 ||               ["||",None]
 Ternary :
 12 expr ? expr : expr  ["?",None] [":",None] ["@expr","?:",listPtr0,listPtr1,listPtr2]
 13 expr , expr , expr...
 Var,Num,Expr,Function:
 ["@var","varName"]
 ["@num","num_string"]
 ["@expr","Operator",listPtr,...]
 ["@func","funcName",listPtr1,...]
 ["@expr_list",["@var"|"@num"|"@expr"|"@func",...],...]
 '''

这是我们最终的代码模块图：

其中形如 module_x_y 的函数，x表示此运算符的优先级，y表示横向序号，从零开始。代码注释已经写得很详细了，请看源代码：

 ######################################## global list
 OperatorList=['+','-','!','~',\
              '*','/','%',\
              '+','-',\
              '<<','>>',\
              '>','>=','<','<=',\
              '==','!=',\
              '&',\
              '^',\
              '|',\
              '&&',\
              '||',\
              '?',':'\
               ',']
 ''' 31 + 8 * 9 '''
 listToParse=[ ['@num',''] , ['+',None] , ['@num',''] , ['*',None] , ['@num',''] ]

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# + =: ^+A... | ...Op+A...
 def module_1_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ^+A...
     if i==0 and len(lis)>=2:
         if lis[right][0][0]=='@':
             rightPtr=lis[right]
             del lis[0:2]
             lis.insert(0,["@expr","+",rightPtr])
             return 0
     # process: ...Op+A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[left][0] in OperatorList:
             if lis[right][0][0]=='@':
                 rightPtr=lis[right]
                 del lis[i:i+2]
                 lis.insert(i,["@expr","+",rightPtr])
                 return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# - =: ^-A... | ...Op-A...
 def module_1_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ^-A...
     if i==0 and len(lis)>=2:
         if lis[right][0][0]=='@':
             rightPtr=lis[right]
             del lis[0:2]
             lis.insert(0,["@expr","-",rightPtr])
             return 0
     # process: ...Op-A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[left][0] in OperatorList:
             if lis[right][0][0]=='@':
                 rightPtr=lis[right]
                 del lis[i:i+2]
                 lis.insert(i,["@expr","-",rightPtr])
                 return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# ! =: ...!A...
 def module_1_2(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...!A...
     if len(lis)>=2 and right<len(lis):
         if lis[right][0][0]=='@':
             rightPtr=lis[right]
             del lis[i:i+2]
             lis.insert(i,["@expr","!",rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# ~ =: ...~A...
 def module_1_3(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...~A...
     if len(lis)>=2 and right<len(lis):
         if lis[right][0][0]=='@':
             rightPtr=lis[right]
             del lis[i:i+2]
             lis.insert(i,["@expr","~",rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# * =: ...A*A...
 def module_2_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A*A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","*",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# / =: ...A/A...
 def module_2_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A/A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","/",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# % =: ...A%A...
 def module_2_2(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A%A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","%",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# + =: ...A+A...
 def module_3_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A+A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","+",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# - =: ...A-A...
 def module_3_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A-A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","-",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# << =: ...A<<A...
 def module_4_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A<<A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","<<",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# >> =: ...A>>A...
 def module_4_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A>>A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr",">>",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# > =: ...A>A...
 def module_5_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A>A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr",">",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# >= =: ...A>=A...
 def module_5_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A>=A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr",">=",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# < =: ...A<A...
 def module_5_2(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A<A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","<",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# <= =: ...A<=A...
 def module_5_3(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A<=A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","<=",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# == =: ...A==A...
 def module_6_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A==A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","==",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# != =: ...A!=A...
 def module_6_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A!=A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","!=",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# & =: ...A&A...
 def module_7_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A&A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","&",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# ^ =: ...A^A...
 def module_8_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A^A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","^",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# | =: ...A|A...
 def module_9_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A|A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","|",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# && =: ...A&&A...
 def module_10_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A&&A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","&&",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# || =: ...A||A...
 def module_11_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A||A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","||",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# ?: =: ...A?A:A...
 #################             ^
 def module_12_0(lis,i):

     # left i right are both indexes :)
     first=i-3
     leftOp=i-2
     left=i-1
     right=i+1

     # process: ...A?A:A...
     #                ^
     if i>=3 and len(lis)>=5 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' and\
            lis[leftOp][0]=='?'   and lis[first][0][0]=='@':
             firstPtr=lis[first]
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[first:first+5]
             lis.insert(first,["@expr","?:",firstPtr,leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# , =: A,A,...A,A
 def module_13_0(lis,i):

     # process:  A,A,...A,A
     if len(lis)==1 and lis[0][0][0]!='@':
         return 1
     if len(lis)==1 and lis[0][0][0]=='@':
         return 0
     if (len(lis)%2)==1 :
         i=1
         if lis[0][0][0]!='@':
             return 1
         while i<len(lis):
             if lis[i+1][0][0]=='@' and lis[i][0]==',':
                 i=i+2
             else:
                 return 1
         ls=[['@expr_list']]
         i=0
         while i<len(lis):
             ls[0].append(lis[i])
             i=i+2
         del lis[:]
         lis[:]=ls[:]
         return 0
     return 1

上面的代码虽然很大，却是最简单的一部分了，其实可以采取一些方法显著地压缩代码量，但是时间有限。

下面给出一元运算符、二元运算符、三元运算符及逗号分隔符的语义分析过程，这是本文的核心代码之一：

 ######################################## global list
 # construct a module dictionary
 # module_dic_tuple[priority]['Operator'](lis,i)
 module_dic_tuple=({}, { '+':module_1_0,'-':module_1_1,'!':module_1_2,'~':module_1_3 },\
                   { '*':module_2_0,'/':module_2_1,'%':module_2_2 }, \
                   { '+':module_3_0,'-':module_3_1 },\
                   { '<<':module_4_0,'>>':module_4_1 },\
                   { '>':module_5_0,'>=':module_5_1,'<':module_5_2,'<=':module_5_3 },\
                   { '==':module_6_0,'!=':module_6_1 },\
                   { '&':module_7_0 },\
                   { '^':module_8_0 },\
                   { '|':module_9_0 },\
                   { '&&':module_10_0 },\
                   { '||':module_11_0 },\
                   { '?:':module_12_0 },\
                   { ',':module_13_0 } )

 operator_priority_tuple=( () , ('+', '-', '!', '~') , ('*','/','%'),\
                           ('+','-'),('<<','>>'),\
                           ('>','>=','<','<='),('==','!='),\
                           ('&'),('^'),('|'),('&&'),('||'),('?',':'),(',') )

 ############################# parse:unary,binary,ternary,comma expr
 ########### return value :
 ############# 0  parsed sucessfully
 ############# 1  syntax error
 def parse_simple_expr(lis):
     if len(lis)==0:
         return 1
     #if lis[len(lis)-1][0][0]!='@':
      #   return 1
     #if lis[0][0][0]!='@' and lis[0][0] not in ('+','-','!','~'):
      #   return 1
     for pri in range(1,12): # pri 1,2,3,4,5,6,7,8,9,10,11
         i=0
         while 1:
             if len(lis)==1 and lis[0][0][0]=='@':
                 return 0
             if i>=len(lis):
                 break
             if lis[i][0] in operator_priority_tuple[pri]:
                     if module_dic_tuple[pri][lis[i][0]](lis,i)==0:
                         i=0
                         continue
                     else:
                         i=i+1
                         continue
             else:
                 i=i+1
     for pri in range(12,13): # pri 12  # parse ...A?A:A...
         i=0
         while 1:
             if len(lis)==1 and lis[0][0][0]=='@':
                 return 0
             if i>=len(lis):
                 break
             if lis[i][0]==':':
                     if module_dic_tuple[pri]['?:'](lis,i)==0:
                         i=0
                         continue
                     else:
                         i=i+1
                         continue
             else:
                 i=i+1
     return module_dic_tuple[13][','](lis,0)
     return 1

上面代码中，使用了函数引用的词典链表来简化此部分的代码数量。

这一部分就不进行验证展示了，具体过程与前面的文章《一个简单的语义分析算法：单步算法——Python实现》中的描述类似。

实现了 parse_simple_expr 功能之后，剩下的函数与括号的语义分析变得简单些，演算过程如下：

代码实现：

 ########### return value :[intStatusCode,indexOf'(',indexOf')']
 ############# intStatusCode
 ############# 0  sucessfully
 ############# 1  no parenthesis matched
 ############# 2  list is null :(
 def module_parenthesis_place(lis):
     length=len(lis)
     err=0
     x=0
     y=0
     if length==0:
         return [2,None,None]
     try:
         x=lis.index([")",None])
     except:
         err=1
     lis.reverse()
     try:
         y=lis.index(["(",None],length-x-1)
     except:
         err=1
     lis.reverse()
     y=length-y-1
     if err==1:
         return [1,None,None]
     else:
         return [0,y,x]

 ############################# parse:unary binary ternary prenthesis function expr
 ########### return value :
 ############# 0  parsed sucessfully
 ############# 1  syntax error
 ############################# find first ')'
 def parse_comp_expr(lis):
     while 1:
         if len(lis)==0:
             return 1
         if len(lis)==1:
             if lis[0][0][0]=='@':
                 return 0
             else:
                 return 1
         place=module_parenthesis_place(lis)
         if place[0]==0:
             mirror=lis[(place[1]+1):place[2]]
             if parse_simple_expr(mirror)==0:
                 if place[1]>=1 and lis[place[1]-1][0]=='@var':
                     '''func'''
                     funcName=lis[place[1]-1][1]
                     del lis[place[1]-1:(place[2]+1)]
                     lis.insert(place[1]-1,["@func",funcName,mirror[0]])
                 else:
                     del lis[place[1]:(place[2]+1)]
                     lis.insert(place[1],mirror[0])
             else:
                 return 1
         else:
             return parse_simple_expr(lis)
     return 1

如此，代码到此结束。

下面给出实验结果：

>>> ls=[['(',None],['@var','f'],['(',None],['@num',''],[',',None],['@num',''],[',',None],['@num',''],[',',None],['!',None],['-',None],['@var','x'],['?',None],['@var','y'],[':',None],['~',None],['@var','z'],[')',None],['-',None],['@num',''],[')',None],['/',None],['@num','']]
>>> ls
[['(', None], ['@var', 'f'], ['(', None], ['@num', ''], [',', None], ['@num', ''], [',', None], ['@num', ''], [',', None], ['!', None], ['-', None], ['@var', 'x'], ['?', None], ['@var', 'y'], [':', None], ['~', None], ['@var', 'z'], [')', None], ['-', None], ['@num', ''], [')', None], ['/', None], ['@num', '']]
>>> len(ls)
23
>>> parse_comp_expr(ls);ls
0
[['@expr', '/', ['@expr', '-', ['@func', 'f', ['@expr_list', ['@num', ''], ['@num', ''], ['@num', ''], ['@expr', '?:', ['@expr', '!', ['@expr', '-', ['@var', 'x']]], ['@var', 'y'], ['@expr', '~', ['@var', 'z']]]]], ['@num', '']], ['@num', '']]]
>>> len(ls)
1
>>> 

附录：

本文的全部源代码如下：

 '''
 ____________________________Syntax & Syntax Tree
 Parenthesis:
 ["(",None]
 [")",None]
 Operators(grouped by precedence):
 Unary :
 1  + - ! ~           ["+",None] ["-",None] ["!",None] ["~",None]
 Binary :
 2  * / %            ["*",None] ["/",None] ["%",None]
 3  + -              ["+",None] ["-",None]
 4  << >>            ["<<",None] [">>",None]
 5  > >= < <=        [">",None] [">=",None] ["<",None] ["<=",None]
 6  == !=            ["==",None] ["!=",None]
 7  &                ["&",None]
 8  ^                ["^",None]
 9  |                ["|",None]
 10 &&               ["&&",None]
 11 ||               ["||",None]
 Ternary :
 12 expr ? expr : expr  ["?",None] [":",None] ["@expr","?:",listPtr0,listPtr1,listPtr2]
 13 expr , expr , expr...
 Var,Num,Expr,Function:
 ["@var","varName"]
 ["@num","num_string"]
 ["@expr","Operator",listPtr,...]
 ["@func","funcName",listPtr1,...]
 ["@expr_list",["@var"|"@num"|"@expr"|"@func",...],...]
 '''

 ######################################## global list
 OperatorList=['+','-','!','~',\
              '*','/','%',\
              '+','-',\
              '<<','>>',\
              '>','>=','<','<=',\
              '==','!=',\
              '&',\
              '^',\
              '|',\
              '&&',\
              '||',\
              '?',':'\
               ',']
 ''' 31 + 8 * 9 '''
 listToParse=[ ['@num',''] , ['+',None] , ['@num',''] , ['*',None] , ['@num',''] ]

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# + =: ^+A... | ...Op+A...
 def module_1_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ^+A...
     if i==0 and len(lis)>=2:
         if lis[right][0][0]=='@':
             rightPtr=lis[right]
             del lis[0:2]
             lis.insert(0,["@expr","+",rightPtr])
             return 0
     # process: ...Op+A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[left][0] in OperatorList:
             if lis[right][0][0]=='@':
                 rightPtr=lis[right]
                 del lis[i:i+2]
                 lis.insert(i,["@expr","+",rightPtr])
                 return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# - =: ^-A... | ...Op-A...
 def module_1_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ^-A...
     if i==0 and len(lis)>=2:
         if lis[right][0][0]=='@':
             rightPtr=lis[right]
             del lis[0:2]
             lis.insert(0,["@expr","-",rightPtr])
             return 0
     # process: ...Op-A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[left][0] in OperatorList:
             if lis[right][0][0]=='@':
                 rightPtr=lis[right]
                 del lis[i:i+2]
                 lis.insert(i,["@expr","-",rightPtr])
                 return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# ! =: ...!A...
 def module_1_2(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...!A...
     if len(lis)>=2 and right<len(lis):
         if lis[right][0][0]=='@':
             rightPtr=lis[right]
             del lis[i:i+2]
             lis.insert(i,["@expr","!",rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# ~ =: ...~A...
 def module_1_3(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...~A...
     if len(lis)>=2 and right<len(lis):
         if lis[right][0][0]=='@':
             rightPtr=lis[right]
             del lis[i:i+2]
             lis.insert(i,["@expr","~",rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# * =: ...A*A...
 def module_2_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A*A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","*",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# / =: ...A/A...
 def module_2_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A/A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","/",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# % =: ...A%A...
 def module_2_2(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A%A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","%",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# + =: ...A+A...
 def module_3_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A+A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","+",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# - =: ...A-A...
 def module_3_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A-A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","-",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# << =: ...A<<A...
 def module_4_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A<<A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","<<",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# >> =: ...A>>A...
 def module_4_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A>>A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr",">>",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# > =: ...A>A...
 def module_5_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A>A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr",">",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# >= =: ...A>=A...
 def module_5_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A>=A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr",">=",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# < =: ...A<A...
 def module_5_2(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A<A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","<",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# <= =: ...A<=A...
 def module_5_3(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A<=A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","<=",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# == =: ...A==A...
 def module_6_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A==A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","==",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# != =: ...A!=A...
 def module_6_1(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A!=A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","!=",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# & =: ...A&A...
 def module_7_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A&A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","&",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# ^ =: ...A^A...
 def module_8_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A^A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","^",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# | =: ...A|A...
 def module_9_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A|A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","|",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# && =: ...A&&A...
 def module_10_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A&&A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","&&",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# || =: ...A||A...
 def module_11_0(lis,i):

     # left i right are both indexes :)
     left=i-1
     right=i+1

     # process: ...A||A...
     if i>=1 and len(lis)>=3 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' :
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[left:left+3]
             lis.insert(left,["@expr","||",leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# ?: =: ...A?A:A...
 #################             ^
 def module_12_0(lis,i):

     # left i right are both indexes :)
     first=i-3
     leftOp=i-2
     left=i-1
     right=i+1

     # process: ...A?A:A...
     #                ^
     if i>=3 and len(lis)>=5 and right<len(lis):
         if lis[right][0][0]=='@' and lis[left][0][0]=='@' and\
            lis[leftOp][0]=='?'   and lis[first][0][0]=='@':
             firstPtr=lis[first]
             leftPtr=lis[left]
             rightPtr=lis[right]
             del lis[first:first+5]
             lis.insert(first,["@expr","?:",firstPtr,leftPtr,rightPtr])
             return 0

     return 1

 ########### return value :
 ############# 0  parsed some expresions
 ############# 1  done nothing but no errors happened
 ################# , =: A,A,...A,A
 def module_13_0(lis,i):

     # process:  A,A,...A,A
     if len(lis)==1 and lis[0][0][0]!='@':
         return 1
     if len(lis)==1 and lis[0][0][0]=='@':
         return 0
     if (len(lis)%2)==1 :
         i=1
         if lis[0][0][0]!='@':
             return 1
         while i<len(lis):
             if lis[i+1][0][0]=='@' and lis[i][0]==',':
                 i=i+2
             else:
                 return 1
         ls=[['@expr_list']]
         i=0
         while i<len(lis):
             ls[0].append(lis[i])
             i=i+2
         del lis[:]
         lis[:]=ls[:]
         return 0
     return 1

 ######################################## global list
 # construct a module dictionary
 # module_dic_tuple[priority]['Operator'](lis,i)
 module_dic_tuple=({}, { '+':module_1_0,'-':module_1_1,'!':module_1_2,'~':module_1_3 },\
                   { '*':module_2_0,'/':module_2_1,'%':module_2_2 }, \
                   { '+':module_3_0,'-':module_3_1 },\
                   { '<<':module_4_0,'>>':module_4_1 },\
                   { '>':module_5_0,'>=':module_5_1,'<':module_5_2,'<=':module_5_3 },\
                   { '==':module_6_0,'!=':module_6_1 },\
                   { '&':module_7_0 },\
                   { '^':module_8_0 },\
                   { '|':module_9_0 },\
                   { '&&':module_10_0 },\
                   { '||':module_11_0 },\
                   { '?:':module_12_0 },\
                   { ',':module_13_0 } )

 operator_priority_tuple=( () , ('+', '-', '!', '~') , ('*','/','%'),\
                           ('+','-'),('<<','>>'),\
                           ('>','>=','<','<='),('==','!='),\
                           ('&'),('^'),('|'),('&&'),('||'),('?',':'),(',') )

 ############################# parse:unary,binary,ternary,comma expr
 ########### return value :
 ############# 0  parsed sucessfully
 ############# 1  syntax error
 def parse_simple_expr(lis):
     if len(lis)==0:
         return 1
     #if lis[len(lis)-1][0][0]!='@':
      #   return 1
     #if lis[0][0][0]!='@' and lis[0][0] not in ('+','-','!','~'):
      #   return 1
     for pri in range(1,12): # pri 1,2,3,4,5,6,7,8,9,10,11
         i=0
         while 1:
             if len(lis)==1 and lis[0][0][0]=='@':
                 return 0
             if i>=len(lis):
                 break
             if lis[i][0] in operator_priority_tuple[pri]:
                     if module_dic_tuple[pri][lis[i][0]](lis,i)==0:
                         i=0
                         continue
                     else:
                         i=i+1
                         continue
             else:
                 i=i+1
     for pri in range(12,13): # pri 12  # parse ...A?A:A...
         i=0
         while 1:
             if len(lis)==1 and lis[0][0][0]=='@':
                 return 0
             if i>=len(lis):
                 break
             if lis[i][0]==':':
                     if module_dic_tuple[pri]['?:'](lis,i)==0:
                         i=0
                         continue
                     else:
                         i=i+1
                         continue
             else:
                 i=i+1
     return module_dic_tuple[13][','](lis,0)
     return 1

 ########### return value :[intStatusCode,indexOf'(',indexOf')']
 ############# intStatusCode
 ############# 0  sucessfully
 ############# 1  no parenthesis matched
 ############# 2  list is null :(
 def module_parenthesis_place(lis):
     length=len(lis)
     err=0
     x=0
     y=0
     if length==0:
         return [2,None,None]
     try:
         x=lis.index([")",None])
     except:
         err=1
     lis.reverse()
     try:
         y=lis.index(["(",None],length-x-1)
     except:
         err=1
     lis.reverse()
     y=length-y-1
     if err==1:
         return [1,None,None]
     else:
         return [0,y,x]

 ############################# parse:unary binary ternary prenthesis function expr
 ########### return value :
 ############# 0  parsed sucessfully
 ############# 1  syntax error
 ############################# find first ')'
 def parse_comp_expr(lis):
     while 1:
         if len(lis)==0:
             return 1
         if len(lis)==1:
             if lis[0][0][0]=='@':
                 return 0
             else:
                 return 1
         place=module_parenthesis_place(lis)
         if place[0]==0:
             mirror=lis[(place[1]+1):place[2]]
             if parse_simple_expr(mirror)==0:
                 if place[1]>=1 and lis[place[1]-1][0]=='@var':
                     '''func'''
                     funcName=lis[place[1]-1][1]
                     del lis[place[1]-1:(place[2]+1)]
                     lis.insert(place[1]-1,["@func",funcName,mirror[0]])
                 else:
                     del lis[place[1]:(place[2]+1)]
                     lis.insert(place[1],mirror[0])
             else:
                 return 1
         else:
             return parse_simple_expr(lis)
     return 1

由于当树结构稍复杂时，分析其结构很是耗费时间，接下来，我们将开发一个将代码中的树结构图形化显示的简陋工具。

如有问题或者建议，欢迎留言讨论 :)