Control.Monad

The Functor, Monad and MonadPlus classes, with some useful operations on monads.

Functor and monad classes

class Functor f where

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

fmap id  ==  id
fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b

Instances

Functor []

Since: 2.1

Methods

fmap :: (a -> b) -> [a] -> [b]

(<$) :: a -> [b] -> [a]

Functor Maybe

Since: 2.1

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b

(<$) :: a -> Maybe b -> Maybe a

Functor IO

Since: 2.1

Methods

fmap :: (a -> b) -> IO a -> IO b

(<$) :: a -> IO b -> IO a

Functor Par1

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b

(<$) :: a -> Par1 b -> Par1 a

Functor ReadP

Since: 2.1

Methods

fmap :: (a -> b) -> ReadP a -> ReadP b

(<$) :: a -> ReadP b -> ReadP a

Functor ReadPrec

Since: 2.1

Methods

fmap :: (a -> b) -> ReadPrec a -> ReadPrec b

(<$) :: a -> ReadPrec b -> ReadPrec a

Functor Last

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor First

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Functor Product

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

Functor Sum

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Sum a -> Sum b

(<$) :: a -> Sum b -> Sum a

Functor Dual

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Dual a -> Dual b

(<$) :: a -> Dual b -> Dual a

Functor STM

Since: 4.3.0.0

Methods

fmap :: (a -> b) -> STM a -> STM b

(<$) :: a -> STM b -> STM a

Functor Handler

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> Handler a -> Handler b

(<$) :: a -> Handler b -> Handler a

Functor Identity

Since: 4.8.0.0

Methods

fmap :: (a -> b) -> Identity a -> Identity b

(<$) :: a -> Identity b -> Identity a

Functor ZipList

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b

(<$) :: a -> ZipList b -> ZipList a

Functor ArgDescr

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> ArgDescr a -> ArgDescr b

(<$) :: a -> ArgDescr b -> ArgDescr a

Functor OptDescr

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> OptDescr a -> OptDescr b

(<$) :: a -> OptDescr b -> OptDescr a

Functor ArgOrder

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> ArgOrder a -> ArgOrder b

(<$) :: a -> ArgOrder b -> ArgOrder a

Functor NonEmpty

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b

(<$) :: a -> NonEmpty b -> NonEmpty a

Functor Option

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Option a -> Option b

(<$) :: a -> Option b -> Option a

Functor Last

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor First

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Functor Max

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Max a -> Max b

(<$) :: a -> Max b -> Max a

Functor Min

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Min a -> Min b

(<$) :: a -> Min b -> Min a

Functor Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b

(<$) :: a -> Complex b -> Complex a

Functor (Either a)

Since: 3.0

Methods

fmap :: (a -> b) -> Either a a -> Either a b

(<$) :: a -> Either a b -> Either a a

Functor (V1 *)

Methods

fmap :: (a -> b) -> V1 * a -> V1 * b

(<$) :: a -> V1 * b -> V1 * a

Functor (U1 *)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> U1 * a -> U1 * b

(<$) :: a -> U1 * b -> U1 * a

Functor ((,) a)

Since: 2.1

Methods

fmap :: (a -> b) -> (a, a) -> (a, b)

(<$) :: a -> (a, b) -> (a, a)

Functor (ST s)

Since: 2.1

Methods

fmap :: (a -> b) -> ST s a -> ST s b

(<$) :: a -> ST s b -> ST s a

Functor (Proxy *)

Since: 4.7.0.0

Methods

fmap :: (a -> b) -> Proxy * a -> Proxy * b

(<$) :: a -> Proxy * b -> Proxy * a

Arrow a => Functor (ArrowMonad a)

Since: 4.6.0.0

Methods

fmap :: (a -> b) -> ArrowMonad a a -> ArrowMonad a b

(<$) :: a -> ArrowMonad a b -> ArrowMonad a a

Monad m => Functor (WrappedMonad m)

Since: 2.1

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a

Functor (ST s)

Since: 2.1

Methods

fmap :: (a -> b) -> ST s a -> ST s b

(<$) :: a -> ST s b -> ST s a

Functor (Arg a)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Arg a a -> Arg a b

(<$) :: a -> Arg a b -> Arg a a

Functor f => Functor (Rec1 * f)

Methods

fmap :: (a -> b) -> Rec1 * f a -> Rec1 * f b

(<$) :: a -> Rec1 * f b -> Rec1 * f a

Functor (URec * Char)

Methods

fmap :: (a -> b) -> URec * Char a -> URec * Char b

(<$) :: a -> URec * Char b -> URec * Char a

Functor (URec * Double)

Methods

fmap :: (a -> b) -> URec * Double a -> URec * Double b

(<$) :: a -> URec * Double b -> URec * Double a

Functor (URec * Float)

Methods

fmap :: (a -> b) -> URec * Float a -> URec * Float b

(<$) :: a -> URec * Float b -> URec * Float a

Functor (URec * Int)

Methods

fmap :: (a -> b) -> URec * Int a -> URec * Int b

(<$) :: a -> URec * Int b -> URec * Int a

Functor (URec * Word)

Methods

fmap :: (a -> b) -> URec * Word a -> URec * Word b

(<$) :: a -> URec * Word b -> URec * Word a

Functor (URec * (Ptr ()))

Methods

fmap :: (a -> b) -> URec * (Ptr ()) a -> URec * (Ptr ()) b

(<$) :: a -> URec * (Ptr ()) b -> URec * (Ptr ()) a

Functor f => Functor (Alt * f)

Methods

fmap :: (a -> b) -> Alt * f a -> Alt * f b

(<$) :: a -> Alt * f b -> Alt * f a

Functor (Const * m)

Since: 2.1

Methods

fmap :: (a -> b) -> Const * m a -> Const * m b

(<$) :: a -> Const * m b -> Const * m a

Arrow a => Functor (WrappedArrow a b)

Since: 2.1

Methods

fmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b

(<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a

Functor ((->) LiftedRep LiftedRep r)

Since: 2.1

Methods

fmap :: (a -> b) -> (LiftedRep -> LiftedRep) r a -> (LiftedRep -> LiftedRep) r b

(<$) :: a -> (LiftedRep -> LiftedRep) r b -> (LiftedRep -> LiftedRep) r a

Functor (K1 * i c)

Methods

fmap :: (a -> b) -> K1 * i c a -> K1 * i c b

(<$) :: a -> K1 * i c b -> K1 * i c a

(Functor g, Functor f) => Functor ((:+:) * f g)

Methods

fmap :: (a -> b) -> (* :+: f) g a -> (* :+: f) g b

(<$) :: a -> (* :+: f) g b -> (* :+: f) g a

(Functor g, Functor f) => Functor ((:*:) * f g)

Methods

fmap :: (a -> b) -> (* :*: f) g a -> (* :*: f) g b

(<$) :: a -> (* :*: f) g b -> (* :*: f) g a

(Functor f, Functor g) => Functor (Sum * f g)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Sum * f g a -> Sum * f g b

(<$) :: a -> Sum * f g b -> Sum * f g a

(Functor f, Functor g) => Functor (Product * f g)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Product * f g a -> Product * f g b

(<$) :: a -> Product * f g b -> Product * f g a

Functor f => Functor (M1 * i c f)

Methods

fmap :: (a -> b) -> M1 * i c f a -> M1 * i c f b

(<$) :: a -> M1 * i c f b -> M1 * i c f a

(Functor g, Functor f) => Functor ((:.:) * * f g)

Methods

fmap :: (a -> b) -> (* :.: *) f g a -> (* :.: *) f g b

(<$) :: a -> (* :.: *) f g b -> (* :.: *) f g a

(Functor f, Functor g) => Functor (Compose * * f g)

Since: 4.9.0.0

Methods

fmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b

(<$) :: a -> Compose * * f g b -> Compose * * f g a

class Applicative m => Monad m where

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following laws:

• return a >>= k  =  k a

• m >>= return  =  m

• m >>= (\x -> k x >>= h)  =  (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• (<*>) = ap

The above laws imply:

• fmap f xs  =  xs >>= return . f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: forall a b. m a -> (a -> m b) -> m b infixl 1

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: forall a b. m a -> m b -> m b infixl 1

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a

Inject a value into the monadic type.

fail :: String -> m a

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression.

As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release.

Instances

Monad []

Since: 2.1

Methods

(>>=) :: [a] -> (a -> [b]) -> [b]

(>>) :: [a] -> [b] -> [b]

return :: a -> [a]

fail :: String -> [a]

Monad Maybe

Since: 2.1

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b

(>>) :: Maybe a -> Maybe b -> Maybe b

return :: a -> Maybe a

fail :: String -> Maybe a

Monad IO

Since: 2.1

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b

(>>) :: IO a -> IO b -> IO b

return :: a -> IO a

fail :: String -> IO a

Monad Par1

Since: 4.9.0.0

Methods

(>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b

(>>) :: Par1 a -> Par1 b -> Par1 b

return :: a -> Par1 a

fail :: String -> Par1 a

Monad ReadP

Since: 2.1

Methods

(>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b

(>>) :: ReadP a -> ReadP b -> ReadP b

return :: a -> ReadP a

fail :: String -> ReadP a

Monad ReadPrec

Since: 2.1

Methods

(>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b

(>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b

return :: a -> ReadPrec a

fail :: String -> ReadPrec a

Monad Last

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b

(>>) :: Last a -> Last b -> Last b

return :: a -> Last a

fail :: String -> Last a

Monad First

Methods

(>>=) :: First a -> (a -> First b) -> First b

(>>) :: First a -> First b -> First b

return :: a -> First a

fail :: String -> First a

Monad Product

Since: 4.8.0.0

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b

(>>) :: Product a -> Product b -> Product b

return :: a -> Product a

fail :: String -> Product a

Monad Sum

Since: 4.8.0.0

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b

(>>) :: Sum a -> Sum b -> Sum b

return :: a -> Sum a

fail :: String -> Sum a

Monad Dual

Since: 4.8.0.0

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b

(>>) :: Dual a -> Dual b -> Dual b

return :: a -> Dual a

fail :: String -> Dual a

Monad STM

Since: 4.3.0.0

Methods

(>>=) :: STM a -> (a -> STM b) -> STM b

(>>) :: STM a -> STM b -> STM b

return :: a -> STM a

fail :: String -> STM a

Monad Identity

Since: 4.8.0.0

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b

(>>) :: Identity a -> Identity b -> Identity b

return :: a -> Identity a

fail :: String -> Identity a

Monad NonEmpty

Since: 4.9.0.0

Methods

(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b

(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b

return :: a -> NonEmpty a

fail :: String -> NonEmpty a

Monad Option

Since: 4.9.0.0

Methods

(>>=) :: Option a -> (a -> Option b) -> Option b

(>>) :: Option a -> Option b -> Option b

return :: a -> Option a

fail :: String -> Option a

Monad Last

Since: 4.9.0.0

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b

(>>) :: Last a -> Last b -> Last b

return :: a -> Last a

fail :: String -> Last a

Monad First

Since: 4.9.0.0

Methods

(>>=) :: First a -> (a -> First b) -> First b

(>>) :: First a -> First b -> First b

return :: a -> First a

fail :: String -> First a

Monad Max

Since: 4.9.0.0

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b

(>>) :: Max a -> Max b -> Max b

return :: a -> Max a

fail :: String -> Max a

Monad Min

Since: 4.9.0.0

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b

(>>) :: Min a -> Min b -> Min b

return :: a -> Min a

fail :: String -> Min a

Monad Complex

Since: 4.9.0.0

Methods

(>>=) :: Complex a -> (a -> Complex b) -> Complex b

(>>) :: Complex a -> Complex b -> Complex b

return :: a -> Complex a

fail :: String -> Complex a

Monad (Either e)

Since: 4.4.0.0

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b

(>>) :: Either e a -> Either e b -> Either e b

return :: a -> Either e a

fail :: String -> Either e a

Monad (U1 *)

Since: 4.9.0.0

Methods

(>>=) :: U1 * a -> (a -> U1 * b) -> U1 * b

(>>) :: U1 * a -> U1 * b -> U1 * b

return :: a -> U1 * a

fail :: String -> U1 * a

Monoid a => Monad ((,) a)

Since: 4.9.0.0

Methods

(>>=) :: (a, a) -> (a -> (a, b)) -> (a, b)

(>>) :: (a, a) -> (a, b) -> (a, b)

return :: a -> (a, a)

fail :: String -> (a, a)

Monad (ST s)

Since: 2.1

Methods

(>>=) :: ST s a -> (a -> ST s b) -> ST s b

(>>) :: ST s a -> ST s b -> ST s b

return :: a -> ST s a

fail :: String -> ST s a

Monad (Proxy *)

Since: 4.7.0.0

Methods

(>>=) :: Proxy * a -> (a -> Proxy * b) -> Proxy * b

(>>) :: Proxy * a -> Proxy * b -> Proxy * b

return :: a -> Proxy * a

fail :: String -> Proxy * a

ArrowApply a => Monad (ArrowMonad a)

Since: 2.1

Methods

(>>=) :: ArrowMonad a a -> (a -> ArrowMonad a b) -> ArrowMonad a b

(>>) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a b

return :: a -> ArrowMonad a a

fail :: String -> ArrowMonad a a

Monad m => Monad (WrappedMonad m)

Methods

(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b

(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b

return :: a -> WrappedMonad m a

fail :: String -> WrappedMonad m a

Monad (ST s)

Since: 2.1

Methods

(>>=) :: ST s a -> (a -> ST s b) -> ST s b

(>>) :: ST s a -> ST s b -> ST s b

return :: a -> ST s a

fail :: String -> ST s a

Monad f => Monad (Rec1 * f)

Since: 4.9.0.0

Methods

(>>=) :: Rec1 * f a -> (a -> Rec1 * f b) -> Rec1 * f b

(>>) :: Rec1 * f a -> Rec1 * f b -> Rec1 * f b

return :: a -> Rec1 * f a

fail :: String -> Rec1 * f a

Monad f => Monad (Alt * f)

Methods

(>>=) :: Alt * f a -> (a -> Alt * f b) -> Alt * f b

(>>) :: Alt * f a -> Alt * f b -> Alt * f b

return :: a -> Alt * f a

fail :: String -> Alt * f a

Monad ((->) LiftedRep LiftedRep r)

Since: 2.1

Methods

(>>=) :: (LiftedRep -> LiftedRep) r a -> (a -> (LiftedRep -> LiftedRep) r b) -> (LiftedRep -> LiftedRep) r b

(>>) :: (LiftedRep -> LiftedRep) r a -> (LiftedRep -> LiftedRep) r b -> (LiftedRep -> LiftedRep) r b

return :: a -> (LiftedRep -> LiftedRep) r a

fail :: String -> (LiftedRep -> LiftedRep) r a

(Monad f, Monad g) => Monad ((:*:) * f g)

Since: 4.9.0.0

Methods

(>>=) :: (* :*: f) g a -> (a -> (* :*: f) g b) -> (* :*: f) g b

(>>) :: (* :*: f) g a -> (* :*: f) g b -> (* :*: f) g b

return :: a -> (* :*: f) g a

fail :: String -> (* :*: f) g a

(Monad f, Monad g) => Monad (Product * f g)

Since: 4.9.0.0

Methods

(>>=) :: Product * f g a -> (a -> Product * f g b) -> Product * f g b

(>>) :: Product * f g a -> Product * f g b -> Product * f g b

return :: a -> Product * f g a

fail :: String -> Product * f g a

Monad f => Monad (M1 * i c f)

Since: 4.9.0.0

Methods

(>>=) :: M1 * i c f a -> (a -> M1 * i c f b) -> M1 * i c f b

(>>) :: M1 * i c f a -> M1 * i c f b -> M1 * i c f b

return :: a -> M1 * i c f a

fail :: String -> M1 * i c f a

class (Alternative m, Monad m) => MonadPlus m where

Monads that also support choice and failure.

Methods

mzero :: m a

the identity of mplus. It should also satisfy the equations

mzero >>= f  =  mzero
v >> mzero   =  mzero

mplus :: m a -> m a -> m a

an associative operation

Instances

MonadPlus []

Since: 2.1

Methods

mzero :: [a]

mplus :: [a] -> [a] -> [a]

MonadPlus Maybe

Since: 2.1

Methods

mzero :: Maybe a

mplus :: Maybe a -> Maybe a -> Maybe a

MonadPlus IO

Since: 4.9.0.0

Methods

mzero :: IO a

mplus :: IO a -> IO a -> IO a

MonadPlus ReadP

Since: 2.1

Methods

mzero :: ReadP a

mplus :: ReadP a -> ReadP a -> ReadP a

MonadPlus ReadPrec

Since: 2.1

Methods

mzero :: ReadPrec a

mplus :: ReadPrec a -> ReadPrec a -> ReadPrec a

MonadPlus STM

Since: 4.3.0.0

Methods

mzero :: STM a

mplus :: STM a -> STM a -> STM a

MonadPlus Option

Since: 4.9.0.0

Methods

mzero :: Option a

mplus :: Option a -> Option a -> Option a

MonadPlus (U1 *)

Since: 4.9.0.0

Methods

mzero :: U1 * a

mplus :: U1 * a -> U1 * a -> U1 * a

MonadPlus (Proxy *)

Since: 4.9.0.0

Methods

mzero :: Proxy * a

mplus :: Proxy * a -> Proxy * a -> Proxy * a

(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a)

Since: 4.6.0.0

Methods

mzero :: ArrowMonad a a

mplus :: ArrowMonad a a -> ArrowMonad a a -> ArrowMonad a a

MonadPlus f => MonadPlus (Rec1 * f)

Since: 4.9.0.0

Methods

mzero :: Rec1 * f a

mplus :: Rec1 * f a -> Rec1 * f a -> Rec1 * f a

MonadPlus f => MonadPlus (Alt * f)

Methods

mzero :: Alt * f a

mplus :: Alt * f a -> Alt * f a -> Alt * f a

(MonadPlus f, MonadPlus g) => MonadPlus ((:*:) * f g)

Since: 4.9.0.0

Methods

mzero :: (* :*: f) g a

mplus :: (* :*: f) g a -> (* :*: f) g a -> (* :*: f) g a

(MonadPlus f, MonadPlus g) => MonadPlus (Product * f g)

Since: 4.9.0.0

Methods

mzero :: Product * f g a

mplus :: Product * f g a -> Product * f g a -> Product * f g a

MonadPlus f => MonadPlus (M1 * i c f)

Since: 4.9.0.0

Methods

mzero :: M1 * i c f a

mplus :: M1 * i c f a -> M1 * i c f a -> M1 * i c f a

Functions

Naming conventions

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

Basic Monad functions

mapM :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b)

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.

As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.

forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)

forM is mapM with its arguments flipped. For a version that ignores the results see forM_.

forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()

forM_ is mapM_ with its arguments flipped. For a version that doesn't ignore the results see forM.

As of base 4.8.0.0, forM_ is just for_, specialized to Monad.

sequence :: (Traversable t, Monad m) => t (m a) -> m (t a)

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence.

As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1

Same as >>=, but with the arguments interchanged.

(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1

Left-to-right Kleisli composition of monads.

(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c infixr 1

Right-to-left Kleisli composition of monads. (>=>), with the arguments flipped.

Note how this operator resembles function composition (.):

(.)   ::            (b ->   c) -> (a ->   b) -> a ->   c
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c

forever :: Applicative f => f a -> f b

forever act repeats the action infinitely.

void :: Functor f => f a -> f ()

void value discards or ignores the result of evaluation, such as the return value of an IO action.

Examples

Replace the contents of a Maybe Int with unit:

>>> void Nothing
Nothing
>>> void (Just 3)
Just ()

Replace the contents of an Either Int Int with unit, resulting in an Either Int '()':

>>> void (Left 8675309)
Left 8675309
>>> void (Right 8675309)
Right ()

Replace every element of a list with unit:

>>> void [1,2,3]
[(),(),()]

Replace the second element of a pair with unit:

>>> void (1,2)
(1,())

Discard the result of an IO action:

>>> mapM print [1,2]
1
2
[(),()]
>>> void $ mapM print [1,2]
1
2

Generalisations of list functions

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

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.

msum :: (Foldable t, MonadPlus m) => t (m a) -> m a

The sum of a collection of actions, generalizing concat. As of base 4.8.0.0, msum is just asum, specialized to MonadPlus.

mfilter :: MonadPlus m => (a -> Bool) -> m a -> m a

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

filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]

This generalizes the list-based filter function.

mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c])

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.

zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]

The zipWithM function generalizes zipWith to arbitrary applicative functors.

zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()

zipWithM_ is the extension of zipWithM which ignores the final result.

foldM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b

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.

Note: foldM is the same as foldlM

foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()

Like foldM, but discards the result.

replicateM :: Applicative m => Int -> m a -> m [a]

replicateM n act performs the action n times, gathering the results.

replicateM_ :: Applicative m => Int -> m a -> m ()

Like replicateM, but discards the result.

Conditional execution of monadic expressions

guard :: Alternative f => Bool -> f ()

guard b is pure () if b is True, and empty if b is False.

when :: Applicative f => Bool -> f () -> f ()

Conditional execution of Applicative expressions. For example,

when debug (putStrLn "Debugging")

will output the string Debugging if the Boolean value debug is True, and otherwise do nothing.

unless :: Applicative f => Bool -> f () -> f ()

The reverse of when.

Monadic lifting operators

liftM :: Monad m => (a1 -> r) -> m a1 -> m r

Promote a function to a monad.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r

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

liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r

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

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

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

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

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

Strict monadic functions

(<$!>) :: Monad m => (a -> b) -> m a -> m b infixl 4

Strict version of <$>.

Since: 4.8.0.0