Python递归下降Parser怎么实现

expr ::= expr + term
     | expr - term 
     | term
term ::= term * factor
     | term / factor
     | factor
factor ::= (expr)
     | NUM

expr ::= term { (+|-) term }*
term ::= factor { (*|/) factor }*
factor ::= (expr) 
       | NUM

class ExpressionEvaluator():
    ...
    def expr(self):
        ...
    def term(self):
        ...
    def factor(self):
        ...

import re
import collections

# 定义匹配token的模式
NUM = r'(?P<NUM>\d+)'  # \d表示匹配数字，+表示任意长度
PLUS = r'(?P<PLUS>\+)'  # 注意转义
MINUS = r'(?P<MINUS>-)'
TIMES = r'(?P<TIMES>\*)'  # 注意转义
DIVIDE = r'(?P<DIVIDE>/)'
LPAREN = r'(?P<LPAREN>\()'  # 注意转义
RPAREN = r'(?P<RPAREN>\))'  # 注意转义
WS = r'(?P<WS>\s+)'  # 别忘记空格，\s表示空格，+表示任意长度

master_pat = re.compile(
    '|'.join([NUM, PLUS, MINUS, TIMES, DIVIDE, LPAREN, RPAREN, WS]))

# Tokenizer
Token = collections.namedtuple('Token', ['type', 'value'])


def generate_tokens(text):
    scanner = master_pat.scanner(text)
    for m in iter(scanner.match, None):
        tok = Token(m.lastgroup, m.group())
        if tok.type != 'WS':  # 过滤掉空格符
            yield tok

class ExpressionEvaluator():
    """ 递归下降的Parser实现，每个语法规则都对应一个方法，
    使用 ._accept()方法来测试并接受当前处理的token，不匹配不报错，
    使用 ._except()方法来测试当前处理的token，并在不匹配的时候抛出语法错误
    """

    def parse(self, text):
        """ 对外调用的接口 """
        self.tokens = generate_tokens(text)
        self.tok, self.next_tok = None, None  # 已匹配的最后一个token，下一个即将匹配的token
        self._next()  # 转到下一个token
        return self.expr()  # 开始递归

    def _next(self):
        """ 转到下一个token """
        self.tok, self.next_tok = self.next_tok, next(self.tokens, None)

    def _accept(self, tok_type):
        """ 如果下一个token与tok_type匹配，则转到下一个token """
        if self.next_tok and self.next_tok.type == tok_type:
            self._next()
            return True
        else:
            return False

    def _except(self, tok_type):
        """ 检查是否匹配，如果不匹配则抛出异常 """
        if not self._accept(tok_type):
            raise SyntaxError("Excepted"+tok_type)

    # 接下来是语法规则，每个语法规则对应一个方法
    
    def expr(self):
        """ 对应规则： expression ::= term { ('+'|'-') term }* """
        exprval = self.term() # 取第一项
        while self._accept("PLUS") or self._accept("DIVIDE"): # 如果下一项是"+"或"-"
            op = self.tok.type 
            # 再取下一项，即运算符右值
            right = self.term() 
            if op == "PLUS":
                exprval += right
            elif op == "MINUS":
                exprval -= right
        return exprval
            
    def term(self):
        """ 对应规则： term ::= factor { ('*'|'/') factor }* """
        
        termval = self.factor() # 取第一项
        while self._accept("TIMES") or self._accept("DIVIDE"): # 如果下一项是"+"或"-"
            op = self.tok.type 
            # 再取下一项，即运算符右值
            right = self.factor() 
            if op == "TIMES":
                termval *= right
            elif op == "DIVIDE":
                termval /= right
        return termval          
            
        
    def factor(self):
        """ 对应规则： factor ::= NUM | ( expr ) """
        if self._accept("NUM"): # 递归出口
            return int(self.tok.value)
        elif self._accept("LPAREN"):
            exprval = self.expr() # 继续递归下去求表达式值
            self._except("RPAREN") # 别忘记检查是否有右括号，没有则抛出异常
            return exprval
        else:
            raise SyntaxError("Expected NUMBER or LPAREN")

e = ExpressionEvaluator()
print(e.parse("2"))
print(e.parse("2+3"))
print(e.parse("2+3*4"))
print(e.parse("2+(3+4)*5"))

print(e.parse("2 + (3 + * 4)"))

class ExpressionTreeBuilder(ExpressionEvaluator):
    def expr(self):
            """ 对应规则： expression ::= term { ('+'|'-') term }* """
            exprval = self.term() # 取第一项
            while self._accept("PLUS") or self._accept("DIVIDE"): # 如果下一项是"+"或"-"
                op = self.tok.type 
                # 再取下一项，即运算符右值
                right = self.term() 
                if op == "PLUS":
                    exprval = ('+', exprval, right)
                elif op == "MINUS":
                    exprval -= ('-', exprval, right)
            return exprval
    
    def term(self):
        """ 对应规则： term ::= factor { ('*'|'/') factor }* """
        
        termval = self.factor() # 取第一项
        while self._accept("TIMES") or self._accept("DIVIDE"): # 如果下一项是"+"或"-"
            op = self.tok.type 
            # 再取下一项，即运算符右值
            right = self.factor() 
            if op == "TIMES":
                termval = ('*', termval, right)
            elif op == "DIVIDE":
                termval = ('/', termval, right)
        return termval          
    
    def factor(self):
        """ 对应规则： factor ::= NUM | ( expr ) """
        if self._accept("NUM"): # 递归出口
            return int(self.tok.value) # 字符串转整形
        elif self._accept("LPAREN"):
            exprval = self.expr() # 继续递归下去求表达式值
            self._except("RPAREN") # 别忘记检查是否有右括号，没有则抛出异常
            return exprval
        else:
            raise SyntaxError("Expected NUMBER or LPAREN")

print(e.parse("2+3"))
print(e.parse("2+3*4"))
print(e.parse("2+(3+4)*5"))
print(e.parse('2+3+4'))

items ::= items ',' item 
      | item

def items(self):
    itemsval = self.items() # 取第一项，然而此处会无穷递归！
    if itemsval and self._accept(','):
        itemsval.append(self.item())
    else:
        itemsval = [self.item()]

expr ::= factor { ('+'|'-'|'*'|'/') factor }*
factor ::= '(' expr ')'
       | NUM