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module Parser where
import Control.Applicative
import Control.Monad
import Data.Char
import Atom
import Expr
newtype Parser a = Parser { parse :: String -> Maybe (a, String) }
parseStrict :: Parser a -> String -> Maybe a
parseStrict p input = case parse p input of Just (a, "") -> Just a
_ -> Nothing
instance Functor Parser where
-- fmap :: (a -> b) -> Parser a -> Parser b
fmap f (Parser p) = Parser new_p
where new_p s = do
(x, s') <- p s
return (f x, s')
instance Applicative Parser where
-- pure :: a -> Parser a
pure x = Parser (\s -> Just (x, s))
-- (<*>) :: Parser (a -> b) -> Parser a -> Parser b
(Parser p1) <*> (Parser p2) = Parser new_p
where new_p s = do
(f, s') <- p1 s
(x, s'') <- p2 s'
return (f x, s'')
instance Alternative Parser where
-- empty :: Parser a
empty = Parser (\_ -> Nothing)
-- (<|>) :: Parser a -> Parser a -> Parser a
(Parser p1) <|> (Parser p2) = Parser new_p
where new_p s = p1 s <|> p2 s
instance Monad Parser where
-- return :: a -> Parser a
return x = pure x
-- (>>=) :: Parser a -> (a -> Parser b) -> Parser b
(Parser p1) >>= f = Parser new_p
where new_p s = do
(x, s') <- p1 s
parse (f x) s'
satisfyChar :: (Char -> Bool) -> Parser Char
satisfyChar f = Parser p
where p [] = Nothing
p (c:cs) = if f c then Just (c, cs)
else Nothing
-- sepBy :: Parser b -> Parser a -> Parser [a]
-- sepBy sep x = (:) <$> x <*> (many (sep *> x))
-- sepByMap :: (b -> a -> a) -> Parser b -> Parser a -> Parser [a]
-- sepByMap f sep x = (:) <$> x <*> (many (f <$> sep <*> x))
chainl :: Parser a -> Parser (a -> a -> a) -> a -> Parser a
chainl p op a = chainl1 p op <|> pure a
chainl1 :: Parser a -> Parser (a -> a -> a) -> Parser a
chainl1 p op = do first <- p
rest first
where rest prev = do f <- op
e <- p
rest (f prev e)
<|> return prev
signed :: Num a => Parser a -> Parser a
signed p = do charP '-'
x <- p
return (-x)
<|> p
readParser :: Read a => Parser String -> Parser a
readParser p = read <$> p
infixOp :: String -> (a -> a -> a) -> Parser (a -> a -> a)
infixOp opStr f = stringP opStr *> pure f
parenthesize :: Parser a -> Parser a
parenthesize p = charP '(' *> p <* charP ')'
charP :: Char -> Parser Char
charP c = satisfyChar (c ==)
stringP :: String -> Parser String
stringP s = sequenceA $ charP <$> s
alphaP :: Parser Char
alphaP = satisfyChar isAlpha
digitsP :: Parser String
digitsP = some (satisfyChar isDigit) -- at least one digit to avoid read exception
spacesP :: Parser String
spacesP = many (satisfyChar isSpace)
unsignedIntP :: Parser Int
unsignedIntP = readParser digitsP
intP :: Parser Int
intP = signed unsignedIntP
unsignedFloatP :: Parser Float
unsignedFloatP = readParser p
where p = do pos <- digitsP
charP '.'
dec <- digitsP
return (pos ++ "." ++ dec)
<|> digitsP
floatP :: Parser Float
floatP = signed unsignedFloatP
imaginaryP :: Parser Atom
imaginaryP = AImaginary <$> (floatP <* charP 'i')
rationalP :: Parser Atom
rationalP = ARational <$> floatP
termOpP :: Parser (Expr -> Expr -> Expr)
termOpP = infixOp "+" Add <|> infixOp "-" Sub
factorOpP :: Parser (Expr -> Expr -> Expr)
factorOpP = infixOp "*" Mul <|> infixOp "/" Div <|> infixOp "%" Mod
expOpP :: Parser (Expr -> Expr -> Expr)
expOpP = infixOp "^" Exp
exprP :: Parser Expr
exprP = termP `chainl1` termOpP
termP :: Parser Expr
termP = factorP `chainl1` factorOpP
factorP :: Parser Expr
factorP = endpointP `chainl1` expOpP
where endpointP = parenthesisP <|> (EAtom <$> atomP)
parenthesisP :: Parser Expr
parenthesisP = parenthesize exprP
atomP :: Parser Atom
atomP = imaginaryP <|> rationalP
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