1 % -----------------------------------------------------------------------------
2 % $Id: Monad.lhs,v 1.11 2000/06/30 13:39:35 simonmar Exp $
4 % (c) The University of Glasgow, 1994-2000
7 \section[Monad]{Module @Monad@}
11 ( MonadPlus ( -- class context: Monad
12 mzero -- :: (MonadPlus m) => m a
13 , mplus -- :: (MonadPlus m) => m a -> m a -> m a
15 , join -- :: (Monad m) => m (m a) -> m a
16 , guard -- :: (MonadPlus m) => Bool -> m ()
17 , when -- :: (Monad m) => Bool -> m () -> m ()
18 , unless -- :: (Monad m) => Bool -> m () -> m ()
19 , ap -- :: (Monad m) => (m (a -> b)) -> (m a) -> m b
20 , msum -- :: (MonadPlus m) => [m a] -> m a
21 , filterM -- :: (Monad m) => (a -> m Bool) -> [m a] -> m [a]
22 , mapAndUnzipM -- :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])
23 , zipWithM -- :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]
24 , zipWithM_ -- :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()
25 , foldM -- :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a
27 , liftM -- :: (Monad m) => (a -> b) -> (m a -> m b)
28 , liftM2 -- :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c)
33 , Monad((>>=), (>>), return, fail)
36 , mapM -- :: (Monad m) => (a -> m b) -> [a] -> m [b]
37 , mapM_ -- :: (Monad m) => (a -> m b) -> [a] -> m ()
38 , sequence -- :: (Monad m) => [m a] -> m [a]
39 , sequence_ -- :: (Monad m) => [m a] -> m ()
40 , (=<<) -- :: (Monad m) => (a -> m b) -> m a -> m b
46 %*********************************************************
48 \subsection{Monadic classes: @MonadPlus@}
50 %*********************************************************
54 class Monad m => MonadPlus m where
56 mplus :: m a -> m a -> m a
58 instance MonadPlus [] where
62 instance MonadPlus Maybe where
65 Nothing `mplus` ys = ys
70 %*********************************************************
72 \subsection{Functions mandated by the Prelude}
74 %*********************************************************
77 guard :: MonadPlus m => Bool -> m ()
82 -- This subsumes the list-based filter function.
84 filterM :: (Monad m) => ( a -> m Bool ) -> [a] -> m [a]
85 filterM _predM [] = return []
86 filterM predM (x:xs) = do
88 ys <- filterM predM xs
89 return (if flg then x:ys else ys)
91 -- This subsumes the list-based concat function.
93 msum :: MonadPlus m => [m a] -> m a
95 msum = foldr mplus mzero
99 %*********************************************************
101 \subsection{Other monad functions}
103 %*********************************************************
106 join :: (Monad m) => m (m a) -> m a
109 mapAndUnzipM :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])
110 mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip
112 zipWithM :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]
113 zipWithM f xs ys = sequence (zipWith f xs ys)
115 zipWithM_ :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()
116 zipWithM_ f xs ys = sequence_ (zipWith f xs ys)
118 foldM :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a
119 foldM _ a [] = return a
120 foldM f a (x:xs) = f a x >>= \fax -> foldM f fax xs
122 unless :: (Monad m) => Bool -> m () -> m ()
123 unless p s = if p then return () else s
125 when :: (Monad m) => Bool -> m () -> m ()
126 when p s = if p then s else return ()
128 ap :: (Monad m) => m (a->b) -> m a -> m b
131 liftM :: (Monad m) => (a1 -> r) -> m a1 -> m r
132 liftM2 :: (Monad m) => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
133 liftM3 :: (Monad m) => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
134 liftM4 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
135 liftM5 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
137 liftM f m1 = do { x1 <- m1; return (f x1) }
138 liftM2 f m1 m2 = do { x1 <- m1; x2 <- m2; return (f x1 x2) }
139 liftM3 f m1 m2 m3 = do { x1 <- m1; x2 <- m2; x3 <- m3; return (f x1 x2 x3) }
140 liftM4 f m1 m2 m3 m4 = do { x1 <- m1; x2 <- m2; x3 <- m3; x4 <- m4; return (f x1 x2 x3 x4) }
141 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) }