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module Parser where
import Control.Applicative
import Control.Monad
import Data.Char
import Expr
import Imag
import Matrix
newtype Parser a = Parser (String -> Maybe (a, String))
parse :: Parser a -> String -> Maybe (a, String)
parse (Parser p) input = p input
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 <$> sep <*> x))
signed :: Num a => Parser a -> Parser a
signed p = do charP '-'
x <- p
return (-x)
<|> p
readParser :: Read a => Parser String -> Parser a
readParser p = read <$> p
charP :: Char -> Parser Char
charP c = satisfyChar (c ==)
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
imagP :: Parser Imag
imagP = Imag <$> (floatP <* charP 'i')
matrixP :: Parser (Matrix AExpr)
matrixP = Matrix <$> (charP '[' *> (sepBy (charP ';') matrixRowP) <* charP ']')
matrixRowP :: Parser (MatrixRow AExpr)
matrixRowP = charP '[' *> (sepBy (charP ',') aExprP) <* charP ']'
varP :: Parser Var
varP = some alphaP
funcExprP :: Parser FuncExpr
funcExprP = do name <- varP
charP '('
arg <- aExprP
charP ')'
return (FuncExpr name arg)
aExprP :: Parser AExpr
aExprP = do x <- termP
charP '+'
y <- aExprP
return (AExpr x y)
<|> (AExprSingle <$> termP)
termP :: Parser Term
termP = do f <- factorP
charP '*'
t <- termP
return (Term f t)
<|> (TermSingle <$> factorP)
factorP :: Parser Factor
factorP = do b <- baseP
charP '^'
e <- factorP
return (Factor b e)
<|> (FactorSingle <$> baseP)
baseP :: Parser Base
baseP = (charP '(' *> (Base <$> aExprP) <* charP ')')
<|> (BaseSingle <$> ExprI <$> imagP)
<|> (BaseSingle <$> ExprF <$> floatP)
<|> (BaseSingle <$> ExprM <$> matrixP)
<|> (BaseSingle <$> ExprFE <$> funcExprP)
<|> (BaseSingle <$> ExprV <$> varP)
funcDeclP :: Parser FuncDecl
funcDeclP = do name <- varP
charP '('
argName <- varP
charP ')'
return (FuncDecl name argName)
labelP :: Parser Label
labelP = varP <|> funcDeclP
evalP :: Parser Eval
evalP = do labelP
charP '='
(EvalDecl <$> exprP) <|> (EvalTry <$ charP '?')
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