This is the completed code for anyone interested:
-- {-# LANGUAGE NoImplicitPrelude #-}
module MonadicParsingInHaskell () where
import Control.Monad (liftM, ap)
import Data.Char
import GHC.Types
import GHC.Base hiding ((++), many, MonadPlus)
import Data.List (concat)
import Prelude ((-), (+),(*), div)
newtype Parser a = Parser (String -> [(a,String)])
instance Functor Parser where
fmap = liftM
instance Applicative Parser where
pure a = Parser (\cs -> [(a,cs)]) -- same as return
(<*>) = ap
class Monad m => MonadZero m where
zero :: m a
class MonadZero m => MonadPlus m where
(++) :: m a -> m a -> m a
instance MonadZero [] where
zero :: [a]
zero = []
instance MonadPlus [] where
(++) :: [a] -> [a] -> [a]
[] ++ ys = ys
(x : xs) ++ ys = x : (xs ++ ys)
instance Monad Parser where
return :: a -> Parser a
return a = Parser (\cs -> [(a,cs)])
(>>=) :: Parser a -> (a -> Parser b) -> Parser b
p >>= f = Parser (\cs -> concat [parse (f a) cs' | (a,cs') <- parse p cs])
item :: Parser Char
item = Parser (\cs -> case cs of
"" -> []
(c:cs) -> [(c,cs)])
p :: Parser (Char,Char)
p = do {c <- item; item; d <- item; return (c,d)}
instance MonadPlus Parser where
p ++ q = Parser (\cs -> parse p cs ++ parse q cs)
instance MonadZero Parser where
zero = Parser (\cs -> [])
parse :: Parser a -> String -> [(a, String)]
parse (Parser p) = p
many :: Parser a -> Parser [a]
many p = many1 p +++ return []
many' :: Parser a -> Parser [a]
many' p = many p +++ return []
(+++) :: Parser a -> Parser a -> Parser a
p +++ q = Parser (\cs -> case parse (p ++ q) cs of
[] -> []
(x:xs) -> [x])
sat :: (Char -> Bool) -> Parser Char
sat p = do {c <- item; if p c then return c else zero}
char :: Char -> Parser Char
char c = sat (c ==)
string :: String -> Parser String
string "" = return ""
string (c:cs) = do {char c; string cs; return (c:cs)}
many1 :: Parser a -> Parser [a]
many1 p = do {a <- p; as <- many p; return (a:as)}
sepby :: Parser a -> Parser b -> Parser [a]
p `sepby` sep = (p `sepby1` sep) +++ return []
sepby1 :: Parser a -> Parser b -> Parser [a]
p `sepby1` sep = do a <-p
as <- many (do {sep; p})
return (a:as)
chainl :: Parser a -> Parser (a -> a -> a) -> a -> Parser a
chainl p op a = (p `chainl1` op) +++ return a
chainl1 :: Parser a -> Parser (a -> a -> a) -> Parser a
p `chainl1` op = do {a <- p; rest a}
where
rest a = (do f <- op
b <- p
rest (f a b))
+++ return a
space :: Parser String
space = many (sat isSpace)
token :: Parser a -> Parser a
token p = do
a <- p; space; return a
symb :: String -> Parser String
symb cs = token (string cs)
apply :: Parser a -> String -> [(a,String)]
apply p = parse (do {space; p})
expr :: Parser Int
expr = term `chainl1` addop
addop :: Parser (Int -> Int -> Int)
addop = do {symb "+"; return (+)} +++ do {symb "-"; return (-)}
mulop :: Parser (Int -> Int -> Int)
mulop = do {symb "*"; return (*)} +++ do {symb "/"; return div}
term :: Parser Int
term = factor `chainl1` mulop
factor :: Parser Int
factor = digit +++ do {symb "("; n <- expr; symb ")"; return n}
digit :: Parser Int
digit = do {x <- token (sat isDigit); return (ord x - ord '0')}
