Question

我正在编写标准数学符号 - ＆gt; DC符合POSIX标准的格式转换器。它接受输入字符串，将其解析为中间数据类型，然后通过show将其转换为输出字符串。

这是使用的数据类型。我对数据类型没有任何问题 - ＆gt;输出字符串转换，它完美无缺：

data Expression = Expression :+ Expression
                | Expression :- Expression
                | Expression :* Expression
                | Expression :/ Expression
                | Expression :^ Expression
                | Cons String

infixr 0 :+
infixr 0 :-
infixr 1 :*
infixr 1 :/
infixr 2 :^

instance Show Expression where
  show (x :+ y) = unwords [show x, show y, "+"]
  show (x :- y) = unwords [show x, show y, "-"] 
  show (x :* y) = unwords [show x, show y, "*"]
  show (x :/ y) = unwords [show x, show y, "/"]
  show (x :^ y) = unwords [show x, show y, "^"]
  show (Cons y) = y

然而，Parsec解析器部分拒绝遵守定义的运算符优先级规则。显然，由于chainl1解析器定义中subexpression的使用方式：

expression :: Parser Expression
expression = do
  spaces
  x <- subexpression
  spaces >> eof >> return x

subexpression :: Parser Expression
subexpression = (
    (bracketed subexpression) <|>
    constant
  ) `chainl1` (
    try addition              <|>
    try substraction          <|>
    try multiplication        <|>
    try division              <|>
    try exponentiation
  )

addition       = operator '+' (:+)
substraction   = operator '-' (:-)
multiplication = operator '*' (:*)
division       = operator '/' (:/)
exponentiation = operator '^' (:^)

operator :: Char -> (a -> a -> a) -> Parser (a -> a -> a)
operator c op = do
  spaces >> char c >> spaces
  return op

bracketed :: Parser a -> Parser a
bracketed parser = do
  char '('
  x <- parser
  char ')'
  return x

constant :: Parser Expression
constant = do
  parity <- optionMaybe $ oneOf "-+"
  constant <- many1 (digit <|> char '.')
  return (if parity == Just '-'
    then (Cons $ '_':constant)
    else  Cons       constant)

有没有办法让解析器考虑运算符优先级规则而不必重写我的整个代码？

Answer 1

好吧，您不需要重写整个代码，但由于您的subexpression解析器根本不考虑优先级，因此您必须重写 - 实质上。

一种可能性是使用具有相同优先级的顶级运算符从子表达式的解析器构建它，

atom :: Parser Expression
atom = bracketed subexpression <|> constant

-- highest precedence operator is exponentiation, usually that's
-- right-associative, hence I use chainr1 here
powers :: Parser Expression
powers = atom `chainr1` try exponentiation

-- a multiplicative expression is a product or quotient of powers,
-- left-associative
multis :: Parser Expression
multis = powers `chainl1` (try multiplication <|> try division)

-- a subexpression is a sum (or difference) of multiplicative expressions
subexpression :: Parser Expression
subexpression = multis `chainl1` (try addition <|> try substraction)

另一个选择是让图书馆处理优先级和关联性并使用Text.Parsec.Expr，即buildExpressionParser：

table = [ [binary "^" (:^) AssocRight]
        , [binary "*" (:*) AssocLeft, binary "/" (:/) AssocLeft]
        , [binary "+" (:+) AssocLeft, binary "-" (:-) AssocLeft]
        ]

binary  name fun assoc = Infix (do{ string name; spaces; return fun }) assoc

subexpression = buildExpressionParser table atom

（要求bracketed parser和constant消耗使用过的令牌后的空格。

如何使Parsec chainl1函数遵循运算符优先级规则

1 个答案: