| 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 |
Control.Monad.Instances
Description
Documentation
class Functor f 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 https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or
https://github.com/quchen/articles/blob/master/second_functor_law.md
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 ZipList # | Since: base-2.1 |
| Functor Handler # | Since: base-4.6.0.0 |
| Functor Complex # | Since: base-4.9.0.0 |
| 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 First # | Since: base-4.9.0.0 |
| Functor Last # | Since: base-4.9.0.0 |
| Functor Max # | Since: base-4.9.0.0 |
| Functor Min # | Since: base-4.9.0.0 |
| 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 NonEmpty # | Since: base-4.9.0.0 |
| Functor STM # | Since: base-4.3.0.0 |
| Functor NoIO # | Since: base-4.8.0.0 |
| Functor Par1 # | Since: base-4.9.0.0 |
| Functor ArgDescr # | Since: base-4.7.0.0 |
| Functor ArgOrder # | Since: base-4.7.0.0 |
| Functor OptDescr # | Since: base-4.7.0.0 |
| Functor ReadP # | Since: base-2.1 |
| Functor ReadPrec # | Since: base-2.1 |
| Functor IO # | Since: base-2.1 |
| Functor Maybe # | Since: base-2.1 |
| Functor Solo # | Since: base-4.15 |
| Functor [] # | Since: base-2.1 |
| Monad m => Functor (WrappedMonad m) # | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
| Arrow a => Functor (ArrowMonad a) # | Since: base-4.6.0.0 |
Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
| Functor (ST s) # | Since: base-2.1 |
| Functor (Either a) # | Since: base-3.0 |
| Functor (Proxy :: Type -> Type) # | Since: base-4.7.0.0 |
| Functor (Arg a) # | Since: base-4.9.0.0 |
| Functor (Array i) # | Since: base-2.1 |
| Functor (U1 :: Type -> Type) # | Since: base-4.9.0.0 |
| Functor (V1 :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0 |
| Functor (ST s) # | Since: base-2.1 |
| Functor ((,) a) # | Since: base-2.1 |
| Arrow a => Functor (WrappedArrow a b) # | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
| Functor m => Functor (Kleisli m a) # | Since: base-4.14.0.0 |
| Functor (Const m :: Type -> Type) # | Since: base-2.1 |
| Functor f => Functor (Ap f) # | Since: base-4.12.0.0 |
| Functor f => Functor (Alt f) # | Since: base-4.8.0.0 |
| (Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) # | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source # (<$) :: a -> Generically1 f b -> Generically1 f a Source # | |
| Functor f => Functor (Rec1 f) # | Since: base-4.9.0.0 |
| Functor (URec (Ptr ()) :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0 |
| Functor (URec Char :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0 |
| Functor (URec Double :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0 |
| Functor (URec Float :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0 |
| Functor (URec Int :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0 |
| Functor (URec Word :: TYPE LiftedRep -> Type) # | Since: base-4.9.0.0 |
| Functor ((,,) a b) # | Since: base-4.14.0.0 |
| (Functor f, Functor g) => Functor (Product 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 (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 LiftedRep -> Type) # | Since: base-4.9.0.0 |
| Functor ((,,,) a b c) # | Since: base-4.14.0.0 |
| Functor ((->) r) # | Since: base-2.1 |
| (Functor f, Functor g) => Functor (Compose f g) # | 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 |
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:
- 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 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.
'as ' can be understood as the >>= bsdo expression
do a <- as bs a
(>>) :: 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.
'as ' can be understood as the >> bsdo expression
do as bs
Inject a value into the monadic type.
Instances
| Monad Complex # | Since: base-4.9.0.0 |
| 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 First # | Since: base-4.9.0.0 |
| Monad Last # | Since: base-4.9.0.0 |
| Monad Max # | Since: base-4.9.0.0 |
| Monad Min # | Since: base-4.9.0.0 |
| 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 NonEmpty # | Since: base-4.9.0.0 |
| Monad STM # | Since: base-4.3.0.0 |
| Monad NoIO # | Since: base-4.4.0.0 |
| Monad Par1 # | Since: base-4.9.0.0 |
| Monad ReadP # | Since: base-2.1 |
| Monad ReadPrec # | Since: base-2.1 |
| Monad IO # | Since: base-2.1 |
| Monad Maybe # | Since: base-2.1 |
| Monad Solo # | Since: base-4.15 |
| Monad [] # | Since: base-2.1 |
| Monad m => Monad (WrappedMonad m) # | 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-2.1 |
Defined in 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-2.1 |
| 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-2.1 |
| Monoid a => Monad ((,) a) # | Since: base-4.9.0.0 |
| Monad m => Monad (Kleisli m a) # | Since: base-4.14.0.0 |
| 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) # | 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-2.1 |
| Monad f => Monad (M1 i c f) # | Since: base-4.9.0.0 |