# :: (a -> b) -> [a] -> [b] -package:deepseq

map f xs is the list obtained by applying f to each element of xs, i.e.,
```map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]
```
```>>> map (+1) [1, 2, 3]
[2,3,4]
```
An infix synonym for fmap. The name of this operator is an allusion to \$. Note the similarities between their types:
```(\$)  ::              (a -> b) ->   a ->   b
(<\$>) :: Functor f => (a -> b) -> f a -> f b
```
Whereas \$ is function application, <\$> is function application lifted over a Functor.

#### Examples

Convert from a Maybe Int to a Maybe String using show:
```>>> show <\$> Nothing
Nothing

>>> show <\$> Just 3
Just "3"
```
Convert from an Either Int Int to an Either Int String using show:
```>>> show <\$> Left 17
Left 17

>>> show <\$> Right 17
Right "17"
```
Double each element of a list:
```>>> (*2) <\$> [1,2,3]
[2,4,6]
```
Apply even to the second element of a pair:
```>>> even <\$> (2,2)
(2,True)
```
fmap is used to apply a function of type (a -> b) to a value of type f a, where f is a functor, to produce a value of type f b. Note that for any type constructor with more than one parameter (e.g., Either), only the last type parameter can be modified with fmap (e.g., b in `Either a b`). Some type constructors with two parameters or more have a Bifunctor instance that allows both the last and the penultimate parameters to be mapped over.

#### Examples

Convert from a Maybe Int to a Maybe String using show:
```>>> fmap show Nothing
Nothing

>>> fmap show (Just 3)
Just "3"
```
Convert from an Either Int Int to an Either Int String using show:
```>>> fmap show (Left 17)
Left 17

>>> fmap show (Right 17)
Right "17"
```
Double each element of a list:
```>>> fmap (*2) [1,2,3]
[2,4,6]
```
Apply even to the second element of a pair:
```>>> fmap even (2,2)
(2,True)
```
It may seem surprising that the function is only applied to the last element of the tuple compared to the list example above which applies it to every element in the list. To understand, remember that tuples are type constructors with multiple type parameters: a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over with fmap). It explains why fmap can be used with tuples containing values of different types as in the following example:
```>>> fmap even ("hello", 1.0, 4)
("hello",1.0,True)
```
Lift a function to actions. Equivalent to Functor's fmap but implemented using only Applicative's methods: `liftA f a = pure f * a` As such this function may be used to implement a Functor instance from an Applicative one.
This function may be used as a value for fmap in a Functor instance, provided that traverse is defined. (Using fmapDefault with a Traversable instance defined only by sequenceA will result in infinite recursion.)
```fmapDefault f ≡ runIdentity . traverse (Identity . f)
```
This function may be used as a value for fmap in a Functor instance, provided that traverse is defined. (Using fmapDefault with a Traversable instance defined only by sequenceA will result in infinite recursion.)
```fmapDefault f ≡ runIdentity . traverse (Identity . f)
```
A suitable default definition for fmap for a Comonad. Promotes a function to a comonad. You can only safely use liftW to define fmap if your Comonad defines extend, not just duplicate, since defining extend in terms of duplicate uses fmap!
```fmap f = liftW f = extend (f . extract)
```
O(n) Map a function over a vector.
Flipped version of <\$>.
```(<&>) = flip fmap
```

#### Examples

Apply (+1) to a list, a Just and a Right:
```>>> Just 2 <&> (+1)
Just 3
```
```>>> [1,2,3] <&> (+1)
[2,3,4]
```
```>>> Right 3 <&> (+1)
Right 4
```