# map package:base

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, ...]
```
this means that map id == id

#### Examples

```>>> map (+1) [1, 2, 3]
[2,3,4]
```
```>>> map id [1, 2, 3]
[1,2,3]
```
```>>> map (\n -> 3 * n + 1) [1, 2, 3]
[4,7,10]
```
Map a function over a NonEmpty stream.
Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.

#### Examples

mapM is literally a traverse with a type signature restricted to Monad. Its implementation may be more efficient due to additional power of Monad.
Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM. mapM_ is just like traverse_, but specialised to monadic actions.
An associative operation NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.
The mapAccumL function behaves like a combination of fmap and foldl; it applies a function to each element of a structure, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new structure.

#### Examples

Basic usage:
```>>> mapAccumL (\a b -> (a + b, a)) 0 [1..10]
(55,[0,1,3,6,10,15,21,28,36,45])
```
```>>> mapAccumL (\a b -> (a <> show b, a)) "0" [1..5]
("012345",["0","01","012","0123","01234"])
```
The mapAccumR function behaves like a combination of fmap and foldr; it applies a function to each element of a structure, passing an accumulating parameter from right to left, and returning a final value of this accumulator together with the new structure.

#### Examples

Basic usage:
```>>> mapAccumR (\a b -> (a + b, a)) 0 [1..10]
(55,[54,52,49,45,40,34,27,19,10,0])
```
```>>> mapAccumR (\a b -> (a <> show b, a)) "0" [1..5]
("054321",["05432","0543","054","05","0"])
```
The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result list. If it is Just b, then b is included in the result list.

#### Examples

Using mapMaybe f x is a shortcut for catMaybes \$ map f x in most cases:
```>>> import GHC.Internal.Text.Read ( readMaybe )

>>> mapMaybe readMaybeInt ["1", "Foo", "3"]
[1,3]

>>> catMaybes \$ map readMaybeInt ["1", "Foo", "3"]
[1,3]
```
If we map the Just constructor, the entire list should be returned:
```>>> mapMaybe Just [1,2,3]
[1,2,3]
```
The mapAndUnzipM function maps its first argument over a list, returning the result as a pair of lists. This function is mainly used with complicated data structures or a state monad.
This function maps one exception into another as proposed in the paper "A semantics for imprecise exceptions".
The mapAccumM function behaves like a combination of mapM and mapAccumL that traverses the structure while evaluating the actions and passing an accumulating parameter from left to right. It returns a final value of this accumulator together with the new structure. The accumulator is often used for caching the intermediate results of a computation.

#### Examples

Basic usage:
```>>> let expensiveDouble a = putStrLn ("Doubling " <> show a) >> pure (2 * a)

>>> :{
mapAccumM (\cache a -> case lookup a cache of
Nothing -> expensiveDouble a >>= \double -> pure ((a, double):cache, double)
Just double -> pure (cache, double)
) [] [1, 2, 3, 1, 2, 3]
:}
Doubling 1
Doubling 2
Doubling 3
([(3,6),(2,4),(1,2)],[2,4,6,2,4,6])
```
mapM f is equivalent to sequence . map f.
Map a function over all the elements of a container and concatenate the resulting lists.

#### Examples

Basic usage:
```>>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
[1,2,3,10,11,12,100,101,102,1000,1001,1002]
```
```>>> concatMap (take 3) (Just [1..])
[1,2,3]
```
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)
```
Map each element of the structure into a monoid, and combine the results with (<>). This fold is right-associative and lazy in the accumulator. For strict left-associative folds consider foldMap' instead.

#### Examples

Basic usage:
```>>> foldMap Sum [1, 3, 5]
Sum {getSum = 9}
```
```>>> foldMap Product [1, 3, 5]
Product {getProduct = 15}
```
```>>> foldMap (replicate 3) [1, 2, 3]
[1,1,1,2,2,2,3,3,3]
```
When a Monoid's (<>) is lazy in its second argument, foldMap can return a result even from an unbounded structure. For example, lazy accumulation enables Data.ByteString.Builder to efficiently serialise large data structures and produce the output incrementally:
```>>> import qualified Data.ByteString.Lazy as L

>>> import qualified Data.ByteString.Builder as B

>>> let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20

>>> let lbs = B.toLazyByteString \$ foldMap bld [0..]

>>> L.take 64 lbs
"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
```
Given a means of mapping the elements of a structure to lists, computes the concatenation of all such lists in order.

#### Examples

Basic usage:
```>>> biconcatMap (take 3) (fmap digitToInt) ([1..], "89")
[1,2,3,8,9]
```
```>>> biconcatMap (take 3) (fmap digitToInt) (Left [1..])
[1,2,3]
```
```>>> biconcatMap (take 3) (fmap digitToInt) (Right "89")
[8,9]
```
Combines the elements of a structure, given ways of mapping them to a common monoid.
```bifoldMap f g ≡ bifoldr (mappend . f) (mappend . g) mempty
```

#### Examples

Basic usage:
```>>> bifoldMap (take 3) (fmap digitToInt) ([1..], "89")
[1,2,3,8,9]
```
```>>> bifoldMap (take 3) (fmap digitToInt) (Left [1..])
[1,2,3]
```
```>>> bifoldMap (take 3) (fmap digitToInt) (Right "89")
[8,9]
```
Map over both arguments at the same time.
```bimap f g ≡ first f . second g
```

#### Examples

```>>> bimap toUpper (+1) ('j', 3)
('J',4)
```
```>>> bimap toUpper (+1) (Left 'j')
Left 'J'
```
```>>> bimap toUpper (+1) (Right 3)
Right 4
```
A default definition of bifoldMap in terms of the Bitraversable operations.
```bifoldMapDefault f g ≡
getConst . bitraverse (Const . f) (Const . g)
```
The bimapAccumL function behaves like a combination of bimap and bifoldl; it traverses a structure from left to right, threading a state of type a and using the given actions to compute new elements for the structure.

#### Examples

Basic usage:
```>>> bimapAccumL (\acc bool -> (acc + 1, show bool)) (\acc string -> (acc * 2, reverse string)) 3 (True, "foo")
(8,("True","oof"))
```
The bimapAccumR function behaves like a combination of bimap and bifoldr; it traverses a structure from right to left, threading a state of type a and using the given actions to compute new elements for the structure.

#### Examples

Basic usage:
```>>> bimapAccumR (\acc bool -> (acc + 1, show bool)) (\acc string -> (acc * 2, reverse string)) 3 (True, "foo")
(7,("True","oof"))
```
A default definition of bimap in terms of the Bitraversable operations.
```bimapDefault f g ≡
runIdentity . bitraverse (Identity . f) (Identity . g)
```