Portability | portable |
---|---|
Stability | provisional |
Maintainer | libraries@haskell.org |
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, Data.Maybe.Maybe
and System.IO.IO
satisfy these laws.
Functor [] | |
Functor IO | |
Functor [::] | |
Functor Maybe | |
Functor ReadP | |
Functor ReadPrec | |
Functor STM | |
Functor ZipList | |
Functor Id | |
Functor ((->) r) | |
Functor (Either a) | |
Functor ((,) a) | |
Functor (ST s) | |
Ix i => Functor (Array i) | |
Monad m => Functor (WrappedMonad m) | |
Functor (Const m) | |
Functor (StateR s) | |
Functor (StateL s) | |
Functor (ST s) | |
Arrow a => Functor (WrappedArrow a b) |
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.
Minimal complete definition: >>=
and return
.
Instances of Monad
should satisfy the following laws:
return a >>= k == k a m >>= return == m m >>= (\x -> k x >>= h) == (m >>= k) >>= h
Instances of both Monad
and Functor
should additionally satisfy the law:
fmap f xs == xs >>= return . f
The instances of Monad
for lists, Data.Maybe.Maybe
and System.IO.IO
defined in the Prelude satisfy these laws.
(>>=) :: forall a b. m a -> (a -> m b) -> m bSource
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 bSource
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.