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isSubmapOf :: (Ord k, Eq a) => Map k a -> Map k a -> Bool

rio RIO.Map

This function is defined as (isSubmapOf = isSubmapOfBy (==)).

isSubmapOfBy :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool

rio	RIO.Map

The expression (isSubmapOfBy f t1 t2) returns True if all keys in t1 are in tree t2, and when f returns True when applied to their respective values. For example, the following expressions are all True:

isSubmapOfBy (==) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<=) (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1),('b',2)])

But the following are all False:

isSubmapOfBy (==) (fromList [('a',2)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (<)  (fromList [('a',1)]) (fromList [('a',1),('b',2)])
isSubmapOfBy (==) (fromList [('a',1),('b',2)]) (fromList [('a',1)])

Note that isSubmapOfBy (_ _ -> True) m1 m2 tests whether all the keys in m1 are also keys in m2.

biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c]

rio RIO.Prelude

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]
```

bifoldMap :: (Bifoldable p, Monoid m) => (a -> m) -> (b -> m) -> p a b -> m

rio	RIO.Prelude

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]

bimap :: Bifunctor p => (a -> b) -> (c -> d) -> p a c -> p b d

rio	RIO.Prelude

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

bimapAccumL :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)

rio RIO.Prelude

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"))
```
bimapAccumR :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)

rio RIO.Prelude

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"))
```
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]

rio RIO.Prelude

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 :: Functor f => (a -> b) -> f a -> f b

rio RIO.Prelude

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)
```
foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m

rio RIO.Prelude

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"
```

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