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.

Methods

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

Instances

Functor []

Methods

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

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

Functor IO

Methods

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

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

Functor Maybe

Methods

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

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

Functor ReadP

Methods

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

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

Functor ReadPrec

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 STM

Methods

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

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

Functor Handler

Methods

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

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

Functor ZipList

Methods

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

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

Functor Identity

Methods

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

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

Functor ArgDescr

Methods

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

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

Functor OptDescr

Methods

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

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

Functor ArgOrder

Methods

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

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

Functor ((->) r)

Methods

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

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

Functor (Either a)

Methods

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

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

Functor ((,) a)

Methods

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

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

Functor (ST s)

Methods

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

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

Functor (Proxy *)

Methods

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

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

Arrow a => Functor (ArrowMonad a)

Methods

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

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

Monad m => Functor (WrappedMonad m)

Methods

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

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

Functor (Const m)

Methods

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

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

Functor (ST s)

Methods

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

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

Functor f => Functor (Alt * f)

Methods

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

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

Arrow a => Functor (WrappedArrow a b)

Methods

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

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

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.

Instances

Monad []

Methods

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

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

return :: a -> [a]

fail :: String -> [a]

Monad IO

Methods

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

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

return :: a -> IO a

fail :: String -> IO a

Monad Maybe

Methods

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

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

return :: a -> Maybe a

fail :: String -> Maybe a

Monad ReadP

Methods

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

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

return :: a -> ReadP a

fail :: String -> ReadP a

Monad ReadPrec

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 STM

Methods

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

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

return :: a -> STM a

fail :: String -> STM a

Monad Identity

Methods

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

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

return :: a -> Identity a

fail :: String -> Identity a

Monad ((->) r)

Methods

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

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

return :: a -> r -> a

fail :: String -> r -> a

Monad (Either e)

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 (ST s)

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 *)

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)

Methods

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

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

return :: b -> ArrowMonad a b

fail :: String -> ArrowMonad a b

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)

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 (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

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

Monads that also support choice and failure.

Minimal complete definition

Nothing

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 []

Methods

mzero :: [a]

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

MonadPlus Maybe

Methods

mzero :: Maybe a

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

MonadPlus ReadP

Methods

mzero :: ReadP a

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

MonadPlus ReadPrec

Methods

mzero :: ReadPrec a

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

MonadPlus STM

Methods

mzero :: STM a

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

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

Methods

mzero :: ArrowMonad a b

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

MonadPlus f => MonadPlus (Alt * f)

Methods

mzero :: Alt * f a

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

forever :: Monad m => m a -> m 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 :: Monad m => (a -> m Bool) -> [a] -> m [a]

This generalizes the list-based filter function.

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

The zipWithM function generalizes zipWith to arbitrary monads.

zipWithM_ :: Monad 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 :: Monad m => Int -> m a -> m [a]

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

replicateM_ :: Monad 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