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%
% (c) The AQUA Project, Glasgow University, 1994-1999
%
\section[Monad]{Module @Monad@}
\begin{code}
{-# OPTIONS -fno-implicit-prelude #-}
module Monad
( MonadPlus ( -- class context: Monad
mzero -- :: (MonadPlus m) => m a
, mplus -- :: (MonadPlus m) => m a -> m a -> m a
)
, join -- :: (Monad m) => m (m a) -> m a
, guard -- :: (Monad m) => Bool -> m ()
, when -- :: (Monad m) => Bool -> m () -> m ()
, unless -- :: (Monad m) => Bool -> m () -> m ()
, ap -- :: (Monad m) => (m (a -> b)) -> (m a) -> m b
, msum -- :: (MonadPlus m) => [m a] -> m a
, filterM -- :: (Monad m) => (a -> m Bool) -> [m a] -> m [a]
, mapAndUnzipM -- :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])
, zipWithM -- :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]
, zipWithM_ -- :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()
, foldM -- :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a
, liftM -- :: (Monad m) => (a -> b) -> (m a -> m b)
, liftM2 -- :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c)
, liftM3 -- :: ...
, liftM4 -- :: ...
, liftM5 -- :: ...
, Monad((>>=), (>>), return, fail)
, Functor(fmap)
, mapM -- :: (Monad m) => (a -> m b) -> [a] -> m [b]
, mapM_ -- :: (Monad m) => (a -> m b) -> [a] -> m ()
, sequence -- :: (Monad m) => [m a] -> m [a]
, sequence_ -- :: (Monad m) => [m a] -> m ()
, (=<<) -- :: (Monad m) => (a -> m b) -> m a -> m b
) where
import PrelList
import PrelTup
import PrelBase
import PrelMaybe ( Maybe(..) )
infixr 1 =<<
\end{code}
%*********************************************************
%* *
\subsection{Monadic classes: @MonadPlus@}
%* *
%*********************************************************
\begin{code}
class Monad m => MonadPlus m where
mzero :: m a
mplus :: m a -> m a -> m a
instance MonadPlus [] where
mzero = []
mplus = (++)
instance MonadPlus Maybe where
mzero = Nothing
Nothing `mplus` ys = ys
xs `mplus` _ys = xs
\end{code}
%*********************************************************
%* *
\subsection{Functions mandated by the Prelude}
%* *
%*********************************************************
\begin{code}
sequence :: Monad m => [m a] -> m [a]
sequence [] = return []
sequence (m:ms) = do { x <- m; xs <- sequence ms; return (x:xs) }
sequence_ :: Monad m => [m a] -> m ()
{-# INLINE sequence_ #-}
sequence_ = foldr (>>) (return ())
mapM :: Monad m => (a -> m b) -> [a] -> m [b]
{-# INLINE mapM #-}
mapM f as = sequence (map f as)
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
{-# INLINE mapM_ #-}
mapM_ f as = sequence_ (map f as)
guard :: MonadPlus m => Bool -> m ()
guard pred
| pred = return ()
| otherwise = mzero
-- This subsumes the list-based filter function.
filterM :: (Monad m) => ( a -> m Bool ) -> [a] -> m [a]
filterM _predM [] = return []
filterM predM (x:xs) = do
flg <- predM x
ys <- filterM predM xs
return (if flg then x:ys else ys)
-- This subsumes the list-based concat function.
msum :: MonadPlus m => [m a] -> m a
{-# INLINE msum #-}
msum = foldr mplus mzero
{-# SPECIALISE (=<<) :: (a -> [b]) -> [a] -> [b] #-}
(=<<) :: Monad m => (a -> m b) -> m a -> m b
f =<< x = x >>= f
\end{code}
%*********************************************************
%* *
\subsection{Other monad functions}
%* *
%*********************************************************
\begin{code}
join :: (Monad m) => m (m a) -> m a
join x = x >>= id
mapAndUnzipM :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])
mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip
zipWithM :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]
zipWithM f xs ys = sequence (zipWith f xs ys)
zipWithM_ :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()
zipWithM_ f xs ys = sequence_ (zipWith f xs ys)
foldM :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a
foldM _ a [] = return a
foldM f a (x:xs) = f a x >>= \fax -> foldM f fax xs
unless :: (Monad m) => Bool -> m () -> m ()
unless p s = if p then return () else s
when :: (Monad m) => Bool -> m () -> m ()
when p s = if p then s else return ()
ap :: (Monad m) => m (a->b) -> m a -> m b
ap = liftM2 ($)
liftM :: (Monad m) => (a1 -> r) -> m a1 -> m r
liftM2 :: (Monad m) => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM3 :: (Monad m) => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
liftM4 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
liftM5 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
liftM f m1 = do { x1 <- m1; return (f x1) }
liftM2 f m1 m2 = do { x1 <- m1; x2 <- m2; return (f x1 x2) }
liftM3 f m1 m2 m3 = do { x1 <- m1; x2 <- m2; x3 <- m3; return (f x1 x2 x3) }
liftM4 f m1 m2 m3 m4 = do { x1 <- m1; x2 <- m2; x3 <- m3; x4 <- m4; return (f x1 x2 x3 x4) }
liftM5 f m1 m2 m3 m4 m5 = do { x1 <- m1; x2 <- m2; x3 <- m3; x4 <- m4; x5 <- m5; return (f x1 x2 x3 x4 x5) }
\end{code}
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