Copyright | (c) The University of Glasgow 2001 |
---|---|
License | BSD-style (see the file libraries/base/LICENSE) |
Maintainer | libraries@haskell.org |
Stability | provisional |
Portability | portable |
Safe Haskell | Safe |
Language | Haskell2010 |
Documentation
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.
Instances
Functor [] # | Since: base-2.1 |
Functor Maybe # | Since: base-2.1 |
Functor IO # | Since: base-2.1 |
Functor Par1 # | Since: base-4.9.0.0 |
Functor NonEmpty # | Since: base-4.9.0.0 |
Functor ReadP # | Since: base-2.1 |
Functor ReadPrec # | Since: base-2.1 |
Functor Down # | Since: base-4.11.0.0 |
Functor Product # | Since: base-4.8.0.0 |
Functor Sum # | Since: base-4.8.0.0 |
Functor Dual # | Since: base-4.8.0.0 |
Functor Last # | Since: base-4.8.0.0 |
Functor First # | Since: base-4.8.0.0 |
Functor STM # | Since: base-4.3.0.0 |
Functor Handler # | Since: base-4.6.0.0 |
Functor Identity # | Since: base-4.8.0.0 |
Functor ZipList # | Since: base-2.1 |
Functor ArgDescr # | Since: base-4.6.0.0 |
Functor OptDescr # | Since: base-4.6.0.0 |
Functor ArgOrder # | Since: base-4.6.0.0 |
Functor Option # | Since: base-4.9.0.0 |
Functor Last # | Since: base-4.9.0.0 |
Functor First # | Since: base-4.9.0.0 |
Functor Max # | Since: base-4.9.0.0 |
Functor Min # | Since: base-4.9.0.0 |
Functor Complex # | Since: base-4.9.0.0 |
Functor (Either a) # | Since: base-3.0 |
Functor (V1 :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (U1 :: Type -> Type) # | Since: base-4.9.0.0 |
Functor ((,) a) # | Since: base-2.1 |
Functor (ST s) # | Since: base-2.1 |
Functor (Proxy :: Type -> Type) # | Since: base-4.7.0.0 |
Arrow a => Functor (ArrowMonad a) # | Since: base-4.6.0.0 |
Defined in Control.Arrow fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 # | |
Monad m => Functor (WrappedMonad m) # | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a # | |
Functor (ST s) # | Since: base-2.1 |
Functor (Arg a) # | Since: base-4.9.0.0 |
Functor f => Functor (Rec1 f) # | Since: base-4.9.0.0 |
Functor (URec Char :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec Double :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec Float :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec Int :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec Word :: Type -> Type) # | Since: base-4.9.0.0 |
Functor (URec (Ptr ()) :: Type -> Type) # | Since: base-4.9.0.0 |
Functor f => Functor (Alt f) # | Since: base-4.8.0.0 |
Functor f => Functor (Ap f) # | Since: base-4.12.0.0 |
Functor (Const m :: Type -> Type) # | Since: base-2.1 |
Arrow a => Functor (WrappedArrow a b) # | Since: base-2.1 |
Defined in Control.Applicative fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
Functor ((->) r :: Type -> Type) # | Since: base-2.1 |
Functor (K1 i c :: Type -> Type) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :+: g) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :*: g) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Sum f g) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Product f g) # | Since: base-4.9.0.0 |
Functor f => Functor (M1 i c f) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :.: g) # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Compose f g) # | Since: base-4.9.0.0 |
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:
Furthermore, the Monad
and Applicative
operations should relate as follows:
The above laws imply:
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.
(>>=) :: 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.
Inject a value into the monadic type.
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: base-2.1 |
Monad Maybe # | Since: base-2.1 |
Monad IO # | Since: base-2.1 |
Monad Par1 # | Since: base-4.9.0.0 |
Monad NonEmpty # | Since: base-4.9.0.0 |
Monad ReadP # | Since: base-2.1 |
Monad ReadPrec # | Since: base-2.1 |
Monad Down # | Since: base-4.11.0.0 |
Monad Product # | Since: base-4.8.0.0 |
Monad Sum # | Since: base-4.8.0.0 |
Monad Dual # | Since: base-4.8.0.0 |
Monad Last # | Since: base-4.8.0.0 |
Monad First # | Since: base-4.8.0.0 |
Monad STM # | Since: base-4.3.0.0 |
Monad Identity # | Since: base-4.8.0.0 |
Monad Option # | Since: base-4.9.0.0 |
Monad Last # | Since: base-4.9.0.0 |
Monad First # | Since: base-4.9.0.0 |
Monad Max # | Since: base-4.9.0.0 |
Monad Min # | Since: base-4.9.0.0 |
Monad Complex # | Since: base-4.9.0.0 |
Monad (Either e) # | Since: base-4.4.0.0 |
Monad (U1 :: Type -> Type) # | Since: base-4.9.0.0 |
Monoid a => Monad ((,) a) # | Since: base-4.9.0.0 |
Monad (ST s) # | Since: base-2.1 |
Monad (Proxy :: Type -> Type) # | Since: base-4.7.0.0 |
ArrowApply a => Monad (ArrowMonad a) # | Since: base-2.1 |
Defined in Control.Arrow (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # return :: a0 -> ArrowMonad a a0 # fail :: String -> ArrowMonad a a0 # | |
Monad m => Monad (WrappedMonad m) # | Since: base-4.7.0.0 |
Defined in Control.Applicative (>>=) :: 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: base-2.1 |
Monad f => Monad (Rec1 f) # | Since: base-4.9.0.0 |
Monad f => Monad (Alt f) # | Since: base-4.8.0.0 |
Monad f => Monad (Ap f) # | Since: base-4.12.0.0 |
Monad ((->) r :: Type -> Type) # | Since: base-2.1 |
(Monad f, Monad g) => Monad (f :*: g) # | Since: base-4.9.0.0 |
(Monad f, Monad g) => Monad (Product f g) # | Since: base-4.9.0.0 |
Monad f => Monad (M1 i c f) # | Since: base-4.9.0.0 |