2 % (c) The AQUA Project, Glasgow University, 1994-1999
4 \section[Monad]{Module @Monad@}
7 {-# OPTIONS -fno-implicit-prelude #-}
10 ( MonadPlus ( -- class context: Monad
11 mzero -- :: (MonadPlus m) => m a
12 , mplus -- :: (MonadPlus m) => m a -> m a -> m a
14 , join -- :: (Monad m) => m (m a) -> m a
15 , guard -- :: (Monad m) => Bool -> m ()
16 , when -- :: (Monad m) => Bool -> m () -> m ()
17 , unless -- :: (Monad m) => Bool -> m () -> m ()
18 , ap -- :: (Monad m) => (m (a -> b)) -> (m a) -> m b
19 , msum -- :: (MonadPlus m) => [m a] -> m a
20 , filterM -- :: (Monad m) => (a -> m Bool) -> [m a] -> m [a]
21 , mapAndUnzipM -- :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])
22 , zipWithM -- :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]
23 , zipWithM_ -- :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()
24 , foldM -- :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a
26 , liftM -- :: (Monad m) => (a -> b) -> (m a -> m b)
27 , liftM2 -- :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c)
32 , Monad((>>=), (>>), return, fail)
35 , mapM -- :: (Monad m) => (a -> m b) -> [a] -> m [b]
36 , mapM_ -- :: (Monad m) => (a -> m b) -> [a] -> m ()
37 , sequence -- :: (Monad m) => [m a] -> m [a]
38 , sequence_ -- :: (Monad m) => [m a] -> m ()
39 , (=<<) -- :: (Monad m) => (a -> m b) -> m a -> m b
45 import PrelMaybe ( Maybe(..) )
48 %*********************************************************
50 \subsection{Monadic classes: @MonadPlus@}
52 %*********************************************************
56 class Monad m => MonadPlus m where
58 mplus :: m a -> m a -> m a
60 instance MonadPlus [] where
64 instance MonadPlus Maybe where
67 Nothing `mplus` ys = ys
72 %*********************************************************
74 \subsection{Functions mandated by the Prelude}
76 %*********************************************************
79 sequence :: Monad m => [m a] -> m [a]
80 sequence [] = return []
81 sequence (m:ms) = do { x <- m; xs <- sequence ms; return (x:xs) }
83 sequence_ :: Monad m => [m a] -> m ()
84 sequence_ = foldr (>>) (return ())
86 mapM :: Monad m => (a -> m b) -> [a] -> m [b]
87 mapM f as = sequence (map f as)
89 mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
90 mapM_ f as = sequence_ (map f as)
92 guard :: MonadPlus m => Bool -> m ()
97 -- This subsumes the list-based filter function.
99 filterM :: (Monad m) => ( a -> m Bool ) -> [a] -> m [a]
100 filterM _predM [] = return []
101 filterM predM (x:xs) = do
103 ys <- filterM predM xs
104 return (if flg then x:ys else ys)
106 -- This subsumes the list-based concat function.
108 msum :: MonadPlus m => [m a] -> m a
109 msum = foldr mplus mzero
111 {-# SPECIALISE (=<<) :: (a -> [b]) -> [a] -> [b] #-}
112 (=<<) :: Monad m => (a -> m b) -> m a -> m b
117 %*********************************************************
119 \subsection{Other monad functions}
121 %*********************************************************
124 join :: (Monad m) => m (m a) -> m a
127 mapAndUnzipM :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])
128 mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip
130 zipWithM :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]
131 zipWithM f xs ys = sequence (zipWith f xs ys)
133 zipWithM_ :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()
134 zipWithM_ f xs ys = sequence_ (zipWith f xs ys)
136 foldM :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a
137 foldM _ a [] = return a
138 foldM f a (x:xs) = f a x >>= \fax -> foldM f fax xs
140 unless :: (Monad m) => Bool -> m () -> m ()
141 unless p s = if p then return () else s
143 when :: (Monad m) => Bool -> m () -> m ()
144 when p s = if p then s else return ()
146 ap :: (Monad m) => m (a->b) -> m a -> m b
149 liftM :: (Monad m) => (a1 -> r) -> m a1 -> m r
150 liftM2 :: (Monad m) => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
151 liftM3 :: (Monad m) => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
152 liftM4 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
153 liftM5 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
155 liftM f m1 = do { x1 <- m1; return (f x1) }
156 liftM2 f m1 m2 = do { x1 <- m1; x2 <- m2; return (f x1 x2) }
157 liftM3 f m1 m2 m3 = do { x1 <- m1; x2 <- m2; x3 <- m3; return (f x1 x2 x3) }
158 liftM4 f m1 m2 m3 m4 = do { x1 <- m1; x2 <- m2; x3 <- m3; x4 <- m4; return (f x1 x2 x3 x4) }
159 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) }