base-4.9.0.0: Basic libraries

Description

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

Synopsis

class Functor f where Source #

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 Source #

Instances

 Functor [] Source # Methodsfmap :: (a -> b) -> [a] -> [b] Source #(<$) :: a -> [b] -> [a] Source # Source # Methodsfmap :: (a -> b) -> Maybe a -> Maybe b Source #(<$) :: a -> Maybe b -> Maybe a Source # Source # Methodsfmap :: (a -> b) -> IO a -> IO b Source #(<$) :: a -> IO b -> IO a Source # Source # Methodsfmap :: (a -> b) -> V1 a -> V1 b Source #(<$) :: a -> V1 b -> V1 a Source # Source # Methodsfmap :: (a -> b) -> U1 a -> U1 b Source #(<$) :: a -> U1 b -> U1 a Source # Source # Methodsfmap :: (a -> b) -> Par1 a -> Par1 b Source #(<$) :: a -> Par1 b -> Par1 a Source # Source # Methodsfmap :: (a -> b) -> ReadP a -> ReadP b Source #(<$) :: a -> ReadP b -> ReadP a Source # Source # Methodsfmap :: (a -> b) -> ReadPrec a -> ReadPrec b Source #(<$) :: a -> ReadPrec b -> ReadPrec a Source # Source # Methodsfmap :: (a -> b) -> Last a -> Last b Source #(<$) :: a -> Last b -> Last a Source # Source # Methodsfmap :: (a -> b) -> First a -> First b Source #(<$) :: a -> First b -> First a Source # Source # Methodsfmap :: (a -> b) -> Product a -> Product b Source #(<$) :: a -> Product b -> Product a Source # Source # Methodsfmap :: (a -> b) -> Sum a -> Sum b Source #(<$) :: a -> Sum b -> Sum a Source # Source # Methodsfmap :: (a -> b) -> Dual a -> Dual b Source #(<$) :: a -> Dual b -> Dual a Source # Source # Methodsfmap :: (a -> b) -> STM a -> STM b Source #(<$) :: a -> STM b -> STM a Source # Source # Methodsfmap :: (a -> b) -> Handler a -> Handler b Source #(<$) :: a -> Handler b -> Handler a Source # Source # Methodsfmap :: (a -> b) -> ZipList a -> ZipList b Source #(<$) :: a -> ZipList b -> ZipList a Source # Source # Methodsfmap :: (a -> b) -> ArgDescr a -> ArgDescr b Source #(<$) :: a -> ArgDescr b -> ArgDescr a Source # Source # Methodsfmap :: (a -> b) -> OptDescr a -> OptDescr b Source #(<$) :: a -> OptDescr b -> OptDescr a Source # Source # Methodsfmap :: (a -> b) -> ArgOrder a -> ArgOrder b Source #(<$) :: a -> ArgOrder b -> ArgOrder a Source # Source # Methodsfmap :: (a -> b) -> Complex a -> Complex b Source #(<$) :: a -> Complex b -> Complex a Source # Source # Methodsfmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source #(<$) :: a -> NonEmpty b -> NonEmpty a Source # Source # Methodsfmap :: (a -> b) -> Option a -> Option b Source #(<$) :: a -> Option b -> Option a Source # Source # Methodsfmap :: (a -> b) -> Last a -> Last b Source #(<$) :: a -> Last b -> Last a Source # Source # Methodsfmap :: (a -> b) -> First a -> First b Source #(<$) :: a -> First b -> First a Source # Source # Methodsfmap :: (a -> b) -> Max a -> Max b Source #(<$) :: a -> Max b -> Max a Source # Source # Methodsfmap :: (a -> b) -> Min a -> Min b Source #(<$) :: a -> Min b -> Min a Source # Source # Methodsfmap :: (a -> b) -> Identity a -> Identity b Source #(<$) :: a -> Identity b -> Identity a Source # Functor ((->) r) Source # Methodsfmap :: (a -> b) -> (r -> a) -> r -> b Source #(<$) :: a -> (r -> b) -> r -> a Source # Source # Methodsfmap :: (a -> b) -> Either a a -> Either a b Source #(<$) :: a -> Either a b -> Either a a Source # Functor f => Functor (Rec1 f) Source # Methodsfmap :: (a -> b) -> Rec1 f a -> Rec1 f b Source #(<$) :: a -> Rec1 f b -> Rec1 f a Source # Source # Methodsfmap :: (a -> b) -> URec Char a -> URec Char b Source #(<$) :: a -> URec Char b -> URec Char a Source # Source # Methodsfmap :: (a -> b) -> URec Double a -> URec Double b Source #(<$) :: a -> URec Double b -> URec Double a Source # Source # Methodsfmap :: (a -> b) -> URec Float a -> URec Float b Source #(<$) :: a -> URec Float b -> URec Float a Source # Source # Methodsfmap :: (a -> b) -> URec Int a -> URec Int b Source #(<$) :: a -> URec Int b -> URec Int a Source # Source # Methodsfmap :: (a -> b) -> URec Word a -> URec Word b Source #(<$) :: a -> URec Word b -> URec Word a Source # Functor (URec (Ptr ())) Source # Methodsfmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b Source #(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a Source # Functor ((,) a) Source # Methodsfmap :: (a -> b) -> (a, a) -> (a, b) Source #(<$) :: a -> (a, b) -> (a, a) Source # Functor (ST s) Source # Methodsfmap :: (a -> b) -> ST s a -> ST s b Source #(<$) :: a -> ST s b -> ST s a Source # Source # Methodsfmap :: (a -> b) -> Proxy * a -> Proxy * b Source #(<$) :: a -> Proxy * b -> Proxy * a Source # Arrow a => Functor (ArrowMonad a) Source # Methodsfmap :: (a -> b) -> ArrowMonad a a -> ArrowMonad a b Source #(<$) :: a -> ArrowMonad a b -> ArrowMonad a a Source # Monad m => Functor (WrappedMonad m) Source # Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source #(<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # Functor (ST s) Source # Methodsfmap :: (a -> b) -> ST s a -> ST s b Source #(<$) :: a -> ST s b -> ST s a Source # Functor (Arg a) Source # Methodsfmap :: (a -> b) -> Arg a a -> Arg a b Source #(<$) :: a -> Arg a b -> Arg a a Source # Functor (K1 i c) Source # Methodsfmap :: (a -> b) -> K1 i c a -> K1 i c b Source #(<$) :: a -> K1 i c b -> K1 i c a Source # (Functor f, Functor g) => Functor ((:+:) f g) Source # Methodsfmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b Source #(<$) :: a -> (f :+: g) b -> (f :+: g) a Source # (Functor f, Functor g) => Functor ((:*:) f g) Source # Methodsfmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b Source #(<$) :: a -> (f :*: g) b -> (f :*: g) a Source # (Functor f, Functor g) => Functor ((:.:) f g) Source # Methodsfmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b Source #(<$) :: a -> (f :.: g) b -> (f :.: g) a Source # Functor f => Functor (Alt * f) Source # Methodsfmap :: (a -> b) -> Alt * f a -> Alt * f b Source #(<$) :: a -> Alt * f b -> Alt * f a Source # Source # Methodsfmap :: (a -> b) -> Const * m a -> Const * m b Source #(<$) :: a -> Const * m b -> Const * m a Source # Arrow a => Functor (WrappedArrow a b) Source # Methodsfmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source #(<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a Source # Functor f => Functor (M1 i c f) Source # Methodsfmap :: (a -> b) -> M1 i c f a -> M1 i c f b Source #(<$) :: a -> M1 i c f b -> M1 i c f a Source # (Functor f, Functor g) => Functor (Product * f g) Source # Methodsfmap :: (a -> b) -> Product * f g a -> Product * f g b Source #(<$) :: a -> Product * f g b -> Product * f g a Source # (Functor f, Functor g) => Functor (Sum * f g) Source # Methodsfmap :: (a -> b) -> Sum * f g a -> Sum * f g b Source #(<$) :: a -> Sum * f g b -> Sum * f g a Source # (Functor f, Functor g) => Functor (Compose * * f g) Source # Methodsfmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b Source #(<$) :: a -> Compose * * f g b -> Compose * * f g a Source #

class Applicative m => Monad m where Source #

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 Source #

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 Source #

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 Source #

Inject a value into the monadic type.

fail :: String -> m a Source #

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

Monads that also support choice and failure.

Methods

mzero :: m a Source #

the identity of mplus. It should also satisfy the equations

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

mplus :: m a -> m a -> m a Source #

an associative operation

Instances

# 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) Source #

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 () Source #

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) Source #

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 () Source #

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) Source #

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 () Source #

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 Source #

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

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

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

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 Source #

forever act repeats the action infinitely.

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

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 Source # 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 Source # 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 Source # 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] Source # This generalizes the list-based filter function. mapAndUnzipM :: Applicative m => (a -> m (b, c)) -> [a] -> m ([b], [c]) Source # 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] Source # The zipWithM function generalizes zipWith to arbitrary applicative functors. zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m () Source # 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 Source # 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 () Source # Like foldM, but discards the result. replicateM :: Applicative m => Int -> m a -> m [a] Source # replicateM n act performs the action n times, gathering the results. replicateM_ :: Applicative m => Int -> m a -> m () Source # Like replicateM, but discards the result. ## Conditional execution of monadic expressions guard :: Alternative f => Bool -> f () Source # guard b is pure () if b is True, and empty if b is False. when :: Applicative f => Bool -> f () -> f () Source # 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 () Source # The reverse of when. ## Monadic lifting operators liftM :: Monad m => (a1 -> r) -> m a1 -> m r Source # Promote a function to a monad. liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r Source # 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 Source # 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 Source # 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 Source # 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 Source # 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 Source #

Strict version of <\$>`.

Since: 4.8.0.0