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Monad

The Monad library defines the MonadPlus class, and provides some useful operations on monads.

Bibliography:

Monads and Arrows: Theory and Applications
module Monad (
    MonadPlus(mzero, mplus),
    join, guard, when, unless, ap,
    msum,
    filterM, mapAndUnzipM, zipWithM, zipWithM_, foldM, 
    liftM, liftM2, liftM3, liftM4, liftM5,

    -- ...and what the Prelude exports
    Monad((>>=), (>>), return, fail),
    Functor(fmap),
    mapM, mapM_, sequence, sequence_, (=<<), 
    ) where


-- The MonadPlus class definition

class  (Monad m) => MonadPlus m  where
    mzero  :: m a
    mplus  :: m a -> m a -> m a


-- Instances of MonadPlus

instance  MonadPlus Maybe  where
    mzero                 = Nothing

    Nothing `mplus` ys    =  ys
    xs      `mplus` ys    =  xs

instance  MonadPlus []  where
    mzero =  []
    mplus = (++)


-- Functions    


msum  :: MonadPlus m => [m a] -> m a
msum xs  =  foldr mplus mzero xs

join             :: (Monad m) => m (m a) -> m a
join x           =  x >>= id

when             :: (Monad m) => Bool -> m () -> m ()
when p s         =  if p then s else return ()

unless           :: (Monad m) => Bool -> m () -> m ()
unless p s       =  when (not p) s

ap               :: (Monad m) => m (a -> b) -> m a -> m b
ap               =  liftM2 ($)

guard            :: MonadPlus m => Bool -> m ()
guard p          =  if p then return () else mzero

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 f a []     =  return a
foldM f a (x:xs) =  f a x >>= \ y -> foldM f y xs

filterM :: Monad m => (a -> m Bool) -> [a] -> m [a]
filterM p []     = return []
filterM p (x:xs) = do { b  <- p x;
ys <- filterM p xs; 
return (if b then (x:ys) else ys)
   }

liftM            :: (Monad m) => (a -> b) -> (m a -> m b)
liftM f          =  \a -> do { a' <- a; return (f a') }

liftM2           :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c)
liftM2 f         =  \a b -> do { a' <- a; b' <- b; return (f a' b') }

liftM3           :: (Monad m) => (a -> b -> c -> d) ->
                                 (m a -> m b -> m c -> m d)
liftM3 f         =  \a b c -> do { a' <- a; b' <- b; c' <- c;
   return (f a' b' c') }

liftM4           :: (Monad m) => (a -> b -> c -> d -> e) ->
                                 (m a -> m b -> m c -> m d -> m e)
liftM4 f         =  \a b c d -> do { a' <- a; b' <- b; c' <- c; d' <- d;
     return (f a' b' c' d') }

liftM5           :: (Monad m) => (a -> b -> c -> d -> e -> f) ->
                                 (m a -> m b -> m c -> m d -> m e -> m f)
liftM5 f         =  \a b c d e -> do { a' <- a; b' <- b; c' <- c; d' <- d;
       e' <- e; return (f a' b' c' d' e') }