base-3.0.0.0: Basic librariesContentsIndex
Control.Monad.Instances
Portabilityportable
Stabilityprovisional
Maintainerlibraries@haskell.org
Description
Functor and Monad instances for (->) r and Functor instances for (,) a and Either a.
Synopsis
class Functor f where
fmap :: (a -> b) -> f a -> f b
class Monad m where
(>>=) :: forall a b . m a -> (a -> m b) -> m b
(>>) :: forall a b . m a -> m b -> m b
return :: a -> m a
fail :: String -> m a
Documentation
class Functor f where

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 defined in the Prelude satisfy these laws.

Methods
fmap :: (a -> b) -> f a -> f b
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class 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.

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, Maybe and IO defined in the Prelude satisfy these laws.

Methods
(>>=) :: forall a b . m a -> (a -> m b) -> m b
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
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
return :: a -> m a
Inject a value into the monadic type.
fail :: String -> m a
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.
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