{-# LANGUAGE Trustworthy #-} {-# LANGUAGE NoImplicitPrelude #-} ----------------------------------------------------------------------------- -- | -- Module : Control.Monad -- Copyright : (c) The University of Glasgow 2001 -- License : BSD-style (see the file libraries/base/LICENSE) -- -- Maintainer : libraries@haskell.org -- Stability : provisional -- Portability : portable -- -- The 'Functor', 'Monad' and 'MonadPlus' classes, -- with some useful operations on monads. module Control.Monad ( -- * Functor and monad classes Functor(fmap) , Monad((>>=), (>>), return, fail) , MonadPlus ( mzero , mplus ) -- * Functions -- ** Naming conventions -- $naming -- ** Basic @Monad@ functions , mapM , mapM_ , forM , forM_ , sequence , sequence_ , (=<<) , (>=>) , (<=<) , forever , void -- ** Generalisations of list functions , join , msum , mfilter , filterM , mapAndUnzipM , zipWithM , zipWithM_ , foldM , foldM_ , replicateM , replicateM_ -- ** Conditional execution of monadic expressions , guard , when , unless -- ** Monadic lifting operators , liftM , liftM2 , liftM3 , liftM4 , liftM5 , ap ) where import Data.Maybe import GHC.List import GHC.Base infixr 1 =<< -- ----------------------------------------------------------------------------- -- Prelude monad functions -- | Same as '>>=', but with the arguments interchanged. {-# SPECIALISE (=<<) :: (a -> [b]) -> [a] -> [b] #-} (=<<) :: Monad m => (a -> m b) -> m a -> m b f =<< x = x >>= f -- | Evaluate each action in the sequence from left to right, -- and collect the results. sequence :: Monad m => [m a] -> m [a] {-# INLINE sequence #-} sequence ms = foldr k (return []) ms where k m m' = do { x <- m; xs <- m'; return (x:xs) } -- | Evaluate each action in the sequence from left to right, -- and ignore the results. sequence_ :: Monad m => [m a] -> m () {-# INLINE sequence_ #-} sequence_ ms = foldr (>>) (return ()) ms -- | @'mapM' f@ is equivalent to @'sequence' . 'map' f@. mapM :: Monad m => (a -> m b) -> [a] -> m [b] {-# INLINE mapM #-} mapM f as = sequence (map f as) -- | @'mapM_' f@ is equivalent to @'sequence_' . 'map' f@. mapM_ :: Monad m => (a -> m b) -> [a] -> m () {-# INLINE mapM_ #-} mapM_ f as = sequence_ (map f as) -- ----------------------------------------------------------------------------- -- The MonadPlus class definition -- | Monads that also support choice and failure. class Monad m => MonadPlus m where -- | the identity of 'mplus'. It should also satisfy the equations -- -- > mzero >>= f = mzero -- > v >> mzero = mzero -- mzero :: m a -- | an associative operation 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 -- ----------------------------------------------------------------------------- -- Functions mandated by the Prelude -- | @'guard' b@ is @'return' ()@ if @b@ is 'True', -- and 'mzero' if @b@ is 'False'. guard :: (MonadPlus m) => Bool -> m () guard True = return () guard False = mzero -- | This generalizes the list-based 'filter' function. filterM :: (Monad m) => (a -> m Bool) -> [a] -> m [a] filterM _ [] = return [] filterM p (x:xs) = do flg <- p x ys <- filterM p xs return (if flg then x:ys else ys) -- | 'forM' is 'mapM' with its arguments flipped forM :: Monad m => [a] -> (a -> m b) -> m [b] {-# INLINE forM #-} forM = flip mapM -- | 'forM_' is 'mapM_' with its arguments flipped forM_ :: Monad m => [a] -> (a -> m b) -> m () {-# INLINE forM_ #-} forM_ = flip mapM_ -- | This generalizes the list-based 'concat' function. msum :: MonadPlus m => [m a] -> m a {-# INLINE msum #-} msum = foldr mplus mzero infixr 1 <=<, >=> -- | Left-to-right Kleisli composition of monads. (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> (a -> m c) f >=> g = \x -> f x >>= g -- | Right-to-left Kleisli composition of monads. @('>=>')@, with the arguments flipped (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> (a -> m c) (<=<) = flip (>=>) -- | @'forever' act@ repeats the action infinitely. forever :: (Monad m) => m a -> m b {-# INLINE forever #-} forever a = let a' = a >> a' in a' -- Use explicit sharing here, as it is prevents a space leak regardless of -- optimizations. -- | @'void' value@ discards or ignores the result of evaluation, such as the return value of an 'IO' action. void :: Functor f => f a -> f () void = fmap (const ()) -- ----------------------------------------------------------------------------- -- Other monad functions -- | The 'join' function is the conventional monad join operator. It is used to -- remove one level of monadic structure, projecting its bound argument into the -- outer level. join :: (Monad m) => m (m a) -> m a join x = x >>= id -- | The 'mapAndUnzipM' function maps its first argument over a list, returning -- the result as a pair of lists. This function is mainly used with complicated -- data structures or a state-transforming monad. mapAndUnzipM :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c]) mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip -- | The 'zipWithM' function generalizes 'zipWith' to arbitrary monads. zipWithM :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c] zipWithM f xs ys = sequence (zipWith f xs ys) -- | 'zipWithM_' is the extension of 'zipWithM' which ignores the final result. zipWithM_ :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m () zipWithM_ f xs ys = sequence_ (zipWith f xs ys) {- | The 'foldM' function is analogous to 'foldl', except that its result is encapsulated in a monad. Note that 'foldM' works from left-to-right over the list arguments. This could be an issue where @('>>')@ and the `folded function' are not commutative. > foldM f a1 [x1, x2, ..., xm] == > do > a2 <- f a1 x1 > a3 <- f a2 x2 > ... > f am xm If right-to-left evaluation is required, the input list should be reversed. -} 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 -- | Like 'foldM', but discards the result. foldM_ :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m () foldM_ f a xs = foldM f a xs >> return () -- | @'replicateM' n act@ performs the action @n@ times, -- gathering the results. replicateM :: (Monad m) => Int -> m a -> m [a] replicateM n x = sequence (replicate n x) -- | Like 'replicateM', but discards the result. replicateM_ :: (Monad m) => Int -> m a -> m () replicateM_ n x = sequence_ (replicate n x) {- | Conditional execution of monadic expressions. For example, > when debug (putStr "Debugging\n") will output the string @Debugging\\n@ if the Boolean value @debug@ is 'True', and otherwise do nothing. -} when :: (Monad m) => Bool -> m () -> m () when p s = if p then s else return () -- | The reverse of 'when'. unless :: (Monad m) => Bool -> m () -> m () unless p s = if p then return () else s -- | Promote a function to a monad. liftM :: (Monad m) => (a1 -> r) -> m a1 -> m r liftM f m1 = do { x1 <- m1; return (f x1) } -- | Promote a function to a monad, scanning the monadic arguments from -- left to right. For example, -- -- > liftM2 (+) [0,1] [0,2] = [0,2,1,3] -- > liftM2 (+) (Just 1) Nothing = Nothing -- liftM2 :: (Monad m) => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r liftM2 f m1 m2 = do { x1 <- m1; x2 <- m2; return (f x1 x2) } -- | Promote a function to a monad, scanning the monadic arguments from -- left to right (cf. 'liftM2'). liftM3 :: (Monad m) => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r liftM3 f m1 m2 m3 = do { x1 <- m1; x2 <- m2; x3 <- m3; return (f x1 x2 x3) } -- | Promote a function to a monad, scanning the monadic arguments from -- left to right (cf. 'liftM2'). liftM4 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r liftM4 f m1 m2 m3 m4 = do { x1 <- m1; x2 <- m2; x3 <- m3; x4 <- m4; return (f x1 x2 x3 x4) } -- | Promote a function to a monad, scanning the monadic arguments from -- left to right (cf. 'liftM2'). liftM5 :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r 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) } {- | In many situations, the 'liftM' operations can be replaced by uses of 'ap', which promotes function application. > return f `ap` x1 `ap` ... `ap` xn is equivalent to > liftMn f x1 x2 ... xn -} ap :: (Monad m) => m (a -> b) -> m a -> m b ap = liftM2 id -- ----------------------------------------------------------------------------- -- Other MonadPlus functions -- | Direct 'MonadPlus' equivalent of 'filter' -- @'filter'@ = @(mfilter:: (a -> Bool) -> [a] -> [a]@ -- applicable to any 'MonadPlus', for example -- @mfilter odd (Just 1) == Just 1@ -- @mfilter odd (Just 2) == Nothing@ mfilter :: (MonadPlus m) => (a -> Bool) -> m a -> m a mfilter p ma = do a <- ma if p a then return a else mzero {- $naming The functions in this library use the following naming conventions: * A postfix \'@M@\' always stands for a function in the Kleisli category: The monad type constructor @m@ is added to function results (modulo currying) and nowhere else. So, for example, > filter :: (a -> Bool) -> [a] -> [a] > filterM :: (Monad m) => (a -> m Bool) -> [a] -> m [a] * A postfix \'@_@\' changes the result type from @(m a)@ to @(m ())@. Thus, for example: > sequence :: Monad m => [m a] -> m [a] > sequence_ :: Monad m => [m a] -> m () * A prefix \'@m@\' generalizes an existing function to a monadic form. Thus, for example: > sum :: Num a => [a] -> a > msum :: MonadPlus m => [m a] -> m a -}