base-4.5.0.0: Basic libraries

Portability portable provisional libraries@haskell.org Safe

Description

`Functor` and `Monad` instances for `(->) r` and `Functor` instances for `(,) a` and `Either a`.

Synopsis

# Documentation

class Functor f whereSource

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.

Methods

fmap :: (a -> b) -> f a -> f bSource

Instances

 Functor [] Functor IO 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) Functor (ST s) Monad m => Functor (WrappedMonad m) Functor (Const m) Functor (StateR s) Functor (StateL s) Arrow a => Functor (WrappedArrow a b)

class Monad m whereSource

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 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.

return :: a -> m aSource

Inject a value into the monadic type.

fail :: String -> m aSource

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.

Instances