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

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`

satisfy these laws.

Functor [] Source | |

Functor IO Source | |

Functor Maybe Source | |

Functor ReadP Source | |

Functor ReadPrec Source | |

Functor Last Source | |

Functor First Source | |

Functor STM Source | |

Functor Handler Source | |

Functor ZipList Source | |

Functor Identity Source | |

Functor ArgDescr Source | |

Functor OptDescr Source | |

Functor ArgOrder Source | |

Functor ((->) r) Source | |

Functor (Either a) Source | |

Functor ((,) a) Source | |

Functor (ST s) Source | |

Functor (Proxy *) Source | |

Arrow a => Functor (ArrowMonad a) Source | |

Monad m => Functor (WrappedMonad m) Source | |

Functor (Const m) Source | |

Functor (ST s) Source | |

Functor f => Functor (Alt * f) Source | |

Arrow a => Functor (WrappedArrow a b) Source |

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 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.

(>>=) :: 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.

(>>) :: 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.

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.

Monad [] Source | |

Monad IO Source | |

Monad Maybe Source | |

Monad ReadP Source | |

Monad ReadPrec Source | |

Monad Last Source | |

Monad First Source | |

Monad STM Source | |

Monad Identity Source | |

Monad ((->) r) Source | |

Monad (Either e) Source | |

Monad (ST s) Source | |

Monad (Proxy *) Source | |

ArrowApply a => Monad (ArrowMonad a) Source | |

Monad m => Monad (WrappedMonad m) Source | |

Monad (ST s) Source | |

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