Safe Haskell | Safe |
---|---|

Language | Haskell2010 |

- class Applicative m => Monad m where
- (>>=) :: Monad m => forall a b. m a -> (a -> m b) -> m b
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
- join :: Monad m => m (m a) -> m a
- foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- foldlM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m ()
- foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b
- foldrM_ :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m ()
- (<$!>) :: Monad m => (a -> b) -> m a -> m b
- (>>) :: Monad m => forall a b. m a -> m b -> m b
- fail :: Monad m => forall a. String -> m a
- return :: Monad m => forall a. a -> m a

# Monad class

class Applicative m => 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.

Instances of `Monad`

should satisfy the following laws:

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.

(>>=) :: m a -> (a -> m b) -> m b infixl 1 #

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: m a -> m b -> m b infixl 1 #

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.

As part of the MonadFail proposal (MFP), this function is moved
to its own class `MonadFail`

(see Control.Monad.Fail for more
details). The definition here will be removed in a future
release.

Monad [] | |

Monad Maybe | |

Monad IO | |

Monad U1 | |

Monad Par1 | |

Monad Q | |

Monad Identity | |

Monad Min | |

Monad Max | |

Monad First | |

Monad Last | |

Monad Option | |

Monad NonEmpty | |

Monad Complex | |

Monad Dual | |

Monad Sum | |

Monad Product | |

Monad First | |

Monad Last | |

Monad Seq | |

Monad Product # | |

Monad Sum # | |

Monad ((->) r) | |

Monad (Either e) | |

Monad f => Monad (Rec1 f) | |

Monoid a => Monad ((,) a) | |

Monad m => Monad (WrappedMonad m) | |

ArrowApply a => Monad (ArrowMonad a) | |

Monad (Proxy *) | |

Monad (State s) | |

(Monad f, Monad g) => Monad ((:*:) f g) | |

Monad f => Monad (Alt * f) | |

(Monad m, Error e) => Monad (ErrorT e m) | |

Monad m => Monad (StateT s m) | |

Monad (Tagged k s) | |

Monad f => Monad (M1 i c f) | |

(Monad f, Monad g) => Monad (Product * f g) | |

# Functions

## Naming conventions

The functions in this library use the following naming conventions:

- A postfix '
`M`

' always stands for a function in the Kleisli category: The monad type constructor`m`

is added to function results (modulo currying) and nowhere else. So, for example,

filter :: (a -> Bool) -> [a] -> [a] filterM :: (Monad m) => (a -> m Bool) -> [a] -> m [a]

- A postfix '
`_`

' changes the result type from`(m a)`

to`(m ())`

. Thus, for example:

sequence :: Monad m => [m a] -> m [a] sequence_ :: Monad m => [m a] -> m ()

- A prefix '
`m`

' generalizes an existing function to a monadic form. Thus, for example:

sum :: Num a => [a] -> a msum :: MonadPlus m => [m a] -> m a

## Basic `Monad`

functions

(>>=) :: Monad m => 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.

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #

Same as `>>=`

, but with the arguments interchanged.

(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #

Left-to-right Kleisli composition of monads.

join :: Monad m => m (m a) -> m a #

The `join`

function is the conventional monad join operator. It
is used to remove one level of monadic structure, projecting its
bound argument into the outer level.

## Generalisations of list functions

foldlM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m () Source #

Like `foldlM`

, but discards the result.

foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b #

Monadic fold over the elements of a structure, associating to the right, i.e. from right to left.

foldrM_ :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m () Source #

Like `foldrM`

, but discards the result.

## Strict monadic functions

## Avoid

(>>) :: Monad m => 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.

fail :: Monad m => forall a. 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.

As part of the MonadFail proposal (MFP), this function is moved
to its own class `MonadFail`

(see Control.Monad.Fail for more
details). The definition here will be removed in a future
release.