| 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 | Trustworthy |
| Language | Haskell2010 |
Control.Monad.Instances
Description
Documentation
class Functor (f :: Type -> Type) where Source #
A type f is a Functor if it provides a function fmap which, given any types a and b
lets you apply any function from (a -> b) to turn an f a into an f b, preserving the
structure of f. Furthermore f needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap and
the first law, so you need only check that the former condition holds.
See these articles by School of Haskell or
David Luposchainsky
for an explanation.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b Source #
fmap is used to apply a function of type (a -> b) to a value of type f a,
where f is a functor, to produce a value of type f b.
Note that for any type constructor with more than one parameter (e.g., Either),
only the last type parameter can be modified with fmap (e.g., b in `Either a b`).
Some type constructors with two parameters or more have a Bifunctor
Examples
Convert from a Maybe IntMaybe String
using show:
>>>fmap show NothingNothing>>>fmap show (Just 3)Just "3"
Convert from an Either Int IntEither Int String using show:
>>>fmap show (Left 17)Left 17>>>fmap show (Right 17)Right "17"
Double each element of a list:
>>>fmap (*2) [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>fmap even (2,2)(2,True)
It may seem surprising that the function is only applied to the last element of the tuple
compared to the list example above which applies it to every element in the list.
To understand, remember that tuples are type constructors with multiple type parameters:
a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance
is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over
with fmap).
It explains why fmap can be used with tuples containing values of different types as in the
following example:
>>>fmap even ("hello", 1.0, 4)("hello",1.0,True)
Instances
| Functor Complex Source # | Since: base-4.9.0.0 |
| Functor First Source # | Since: base-4.9.0.0 |
| Functor Last Source # | Since: base-4.9.0.0 |
| Functor Max Source # | Since: base-4.9.0.0 |
| Functor Min Source # | Since: base-4.9.0.0 |
| Functor ArgDescr Source # | Since: base-4.7.0.0 |
| Functor ArgOrder Source # | Since: base-4.7.0.0 |
| Functor OptDescr Source # | Since: base-4.7.0.0 |
| Functor NonEmpty | @since base-4.9.0.0 |
| 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 First | @since base-4.8.0.0 |
| Functor Last | @since base-4.8.0.0 |
| Functor Down | @since base-4.11.0.0 |
| Functor Dual | @since base-4.8.0.0 |
| Functor Product | @since base-4.8.0.0 |
| Functor Sum | @since base-4.8.0.0 |
| Functor ZipList | @since base-2.01 |
| Functor NoIO | @since base-4.8.0.0 |
| Functor Par1 | @since base-4.9.0.0 |
| Functor P | @since base-4.8.0.0 |
| Functor ReadP | @since base-2.01 |
| Functor ReadPrec | @since base-2.01 |
| Functor IO | @since base-2.01 |
| Functor Maybe | @since base-2.01 |
| Functor Solo | @since base-4.15 |
| Functor [] | @since base-2.01 |
| Monad m => Functor (WrappedMonad m) Source # | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
| Functor (Arg a) Source # | Since: base-4.9.0.0 |
| Functor (Array i) | @since base-2.01 |
| Arrow a => Functor (ArrowMonad a) | @since base-4.6.0.0 |
Defined in GHC.Internal.Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
| Functor (ST s) | @since base-2.01 |
| Functor (Either a) | @since base-3.0 |
| Functor (StateL s) | @since base-4.0 |
| Functor (StateR s) | @since base-4.0 |
| Functor (Proxy :: Type -> Type) | @since base-4.7.0.0 |
| Functor (U1 :: Type -> Type) | @since base-4.9.0.0 |
| Functor (V1 :: Type -> Type) | @since base-4.9.0.0 |
| Functor (ST s) | @since base-2.01 |
| Functor ((,) a) | @since base-2.01 |
| Arrow a => Functor (WrappedArrow a b) Source # | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
| Functor m => Functor (Kleisli m a) | @since base-4.14.0.0 |
| Functor (Const m :: Type -> Type) | @since base-2.01 |
| Monad m => Functor (StateT s m) | @since base-4.18.0.0 |
| Functor f => Functor (Ap f) | @since base-4.12.0.0 |
| Functor f => Functor (Alt f) | @since base-4.8.0.0 |
| (Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) | @since base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source # (<$) :: a -> Generically1 f b -> Generically1 f a Source # | |
| Functor f => Functor (Rec1 f) | @since base-4.9.0.0 |
| Functor (URec (Ptr ()) :: Type -> Type) | @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 ((,,) a b) | @since base-4.14.0.0 |
| (Functor f, Functor g) => Functor (Product f g) Source # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Sum f g) Source # | 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 (K1 i c :: Type -> Type) | @since base-4.9.0.0 |
| Functor ((,,,) a b c) | @since base-4.14.0.0 |
| Functor ((->) r) | @since base-2.01 |
| (Functor f, Functor g) => Functor (Compose f g) Source # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :.: g) | @since base-4.9.0.0 |
| Functor f => Functor (M1 i c f) | @since base-4.9.0.0 |
| Functor ((,,,,) a b c d) | @since base-4.18.0.0 |
| Functor ((,,,,,) a b c d e) | @since base-4.18.0.0 |
| Functor ((,,,,,,) a b c d e f) | @since base-4.18.0.0 |
class Applicative m => Monad (m :: Type -> Type) 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:
- Left identity
returna>>=k = k a- Right identity
m>>=return= m- Associativity
m>>=(\x -> k x>>=h) = (m>>=k)>>=h
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 List, Maybe and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: 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.
'as ' can be understood as the >>= bsdo expression
do a <- as bs a
An alternative name for this function is 'bind', but some people may refer to it as 'flatMap', which results from it being equivialent to
\x f ->join(fmapf x) :: Monad m => m a -> (a -> m b) -> m b
which can be seen as mapping a value with
Monad m => m a -> m (m b) and then 'flattening' m (m b) to m b using join.
(>>) :: 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.
'as ' can be understood as the >> bsdo expression
do as bs
or in terms of (>>=)
as >>= const bs
Inject a value into the monadic type.
This function should not be different from its default implementation
as pure. The justification for the existence of this function is
merely historic.
Instances
| Monad Complex Source # | Since: base-4.9.0.0 |
| Monad First Source # | Since: base-4.9.0.0 |
| Monad Last Source # | Since: base-4.9.0.0 |
| Monad Max Source # | Since: base-4.9.0.0 |
| Monad Min Source # | Since: base-4.9.0.0 |
| Monad NonEmpty | @since base-4.9.0.0 |
| Monad STM | @since base-4.3.0.0 |
| Monad Identity | @since base-4.8.0.0 |
| Monad First | @since base-4.8.0.0 |
| Monad Last | @since base-4.8.0.0 |
| Monad Down | @since base-4.11.0.0 |
| Monad Dual | @since base-4.8.0.0 |
| Monad Product | @since base-4.8.0.0 |
| Monad Sum | @since base-4.8.0.0 |
| Monad NoIO | @since base-4.4.0.0 |
| Monad Par1 | @since base-4.9.0.0 |
| Monad P | @since base-2.01 |
| Monad ReadP | @since base-2.01 |
| Monad ReadPrec | @since base-2.01 |
| Monad IO | @since base-2.01 |
| Monad Maybe | @since base-2.01 |
| Monad Solo | @since base-4.15 |
| Monad [] | @since base-2.01 |
| Monad m => Monad (WrappedMonad m) Source # | Since: base-4.7.0.0 |
Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # return :: a -> WrappedMonad m a Source # | |
| ArrowApply a => Monad (ArrowMonad a) | @since base-2.01 |
Defined in GHC.Internal.Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # return :: a0 -> ArrowMonad a a0 Source # | |
| Monad (ST s) | @since base-2.01 |
| Monad (Either e) | @since base-4.4.0.0 |
| Monad (Proxy :: Type -> Type) | @since base-4.7.0.0 |
| Monad (U1 :: Type -> Type) | @since base-4.9.0.0 |
| Monad (ST s) | @since base-2.01 |
| Monoid a => Monad ((,) a) | @since base-4.9.0.0 |
| Monad m => Monad (Kleisli m a) | @since base-4.14.0.0 |
| Monad m => Monad (StateT s m) | @since base-4.18.0.0 |
| Monad f => Monad (Ap f) | @since base-4.12.0.0 |
| Monad f => Monad (Alt f) | @since base-4.8.0.0 |
| Monad f => Monad (Rec1 f) | @since base-4.9.0.0 |
| (Monoid a, Monoid b) => Monad ((,,) a b) | @since base-4.14.0.0 |
| (Monad f, Monad g) => Monad (Product f g) Source # | Since: base-4.9.0.0 |
| (Monad f, Monad g) => Monad (f :*: g) | @since base-4.9.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | @since base-4.14.0.0 |
| Monad ((->) r) | @since base-2.01 |
| Monad f => Monad (M1 i c f) | @since base-4.9.0.0 |