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
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.
fmap :: (a -> b) -> f a -> f b Source #
Using ApplicativeDo
: '
' can be understood as
the fmap
f asdo
expression
do a <- as pure (f a)
with an inferred Functor
constraint.
Instances
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
return
a>>=
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.
(>>=) :: 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 [] Source # | Since: 2.1 |
Monad Maybe Source # | Since: 2.1 |
Monad IO Source # | Since: 2.1 |
Monad Par1 Source # | Since: 4.9.0.0 |
Monad NonEmpty Source # | Since: 4.9.0.0 |
Monad NoIO Source # | Since: 4.4.0.0 |
Monad ReadP Source # | Since: 2.1 |
Monad ReadPrec Source # | Since: 2.1 |
Monad Down Source # | Since: 4.11.0.0 |
Monad Product Source # | Since: 4.8.0.0 |
Monad Sum Source # | Since: 4.8.0.0 |
Monad Dual Source # | Since: 4.8.0.0 |
Monad Last Source # | Since: 4.8.0.0 |
Monad First Source # | Since: 4.8.0.0 |
Monad STM Source # | Since: 4.3.0.0 |
Monad Identity Source # | Since: 4.8.0.0 |
Monad Option Source # | Since: 4.9.0.0 |
Monad Last Source # | Since: 4.9.0.0 |
Monad First Source # | Since: 4.9.0.0 |
Monad Max Source # | Since: 4.9.0.0 |
Monad Min Source # | Since: 4.9.0.0 |
Monad Complex Source # | Since: 4.9.0.0 |
Monad (Either e) Source # | Since: 4.4.0.0 |
Monad (U1 :: Type -> Type) Source # | Since: 4.9.0.0 |
Monoid a => Monad ((,) a) Source # | Since: 4.9.0.0 |
Monad (ST s) Source # | Since: 2.1 |
Monad (Proxy :: Type -> Type) Source # | Since: 4.7.0.0 |
ArrowApply a => Monad (ArrowMonad a) Source # | Since: 2.1 |
Defined in Control.Arrow (>>=) :: 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 m => Monad (WrappedMonad m) Source # | Since: 4.7.0.0 |
Defined in Control.Applicative (>>=) :: 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 # | |
Monad (ST s) Source # | Since: 2.1 |
Monad f => Monad (Rec1 f) Source # | Since: 4.9.0.0 |
(Monoid a, Monoid b) => Monad ((,,) a b) Source # | Since: 4.14.0.0 |
Monad f => Monad (Alt f) Source # | Since: 4.8.0.0 |
Monad f => Monad (Ap f) Source # | Since: 4.12.0.0 |
Monad m => Monad (Kleisli m a) Source # | Since: 4.14.0.0 |
Monad ((->) r :: Type -> Type) Source # | Since: 2.1 |
(Monad f, Monad g) => Monad (f :*: g) Source # | Since: 4.9.0.0 |
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) Source # | Since: 4.14.0.0 |
(Monad f, Monad g) => Monad (Product f g) Source # | Since: 4.9.0.0 |
Monad f => Monad (M1 i c f) Source # | Since: 4.9.0.0 |