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sMap :: forall a b (t1 :: a ~> b) (t2 :: [a]) . Sing t1 -> Sing t2 -> Sing (Apply (Apply (MapSym0 :: TyFun (a ~> b) ([a] ~> [b]) -> Type) t1) t2)

singletons-base Prelude.Singletons

No documentation available.
sMapM :: forall a (m :: Type -> Type) b (t1 :: a ~> m b) (t2 :: t a) . (STraversable t, SMonad m) => Sing t1 -> Sing t2 -> Sing (Apply (Apply (MapMSym0 :: TyFun (a ~> m b) (t a ~> m (t b)) -> Type) t1) t2)

singletons-base Prelude.Singletons

No documentation available.
sMapM_ :: forall a (m :: Type -> Type) b (t1 :: Type -> Type) (t2 :: a ~> m b) (t3 :: t1 a) . (SFoldable t1, SMonad m) => Sing t2 -> Sing t3 -> Sing (Apply (Apply (MapM_Sym0 :: TyFun (a ~> m b) (t1 a ~> m ()) -> Type) t2) t3)

singletons-base Prelude.Singletons

No documentation available.
sMappend :: forall (t1 :: a) (t2 :: a) . SMonoid a => Sing t1 -> Sing t2 -> Sing (Apply (Apply (MappendSym0 :: TyFun a (a ~> a) -> Type) t1) t2)

singletons-base Prelude.Singletons

No documentation available.
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]

numhask NumHask.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]
```
concatMap :: Foldable t => (a -> [b]) -> t a -> [b]

numhask NumHask.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

numhask NumHask.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

numhask NumHask.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"
```
foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m

numhask NumHask.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"
```

singletons-base	Prelude.Singletons

singletons-base	Prelude.Singletons

singletons-base	Prelude.Singletons

singletons-base	Prelude.Singletons

foldMap' :: (Foldable t, Monoid m) => (a -> m) -> t a -> m

numhask	NumHask.Prelude

A left-associative variant of foldMap that is strict in the accumulator. Use this method for strict reduction when partial results are merged via (<>).

Examples

Define a Monoid over finite bit strings under xor. Use it to strictly compute the xor of a list of Int values.

>>> :set -XGeneralizedNewtypeDeriving

>>> import Data.Bits (Bits, FiniteBits, xor, zeroBits)

>>> import Data.Foldable (foldMap')

>>> import Numeric (showHex)

>>> 

>>> newtype X a = X a deriving (Eq, Bounded, Enum, Bits, FiniteBits)

>>> instance Bits a => Semigroup (X a) where X a <> X b = X (a `xor` b)

>>> instance Bits a => Monoid    (X a) where mempty     = X zeroBits

>>> 

>>> let bits :: [Int]; bits = [0xcafe, 0xfeed, 0xdeaf, 0xbeef, 0x5411]

>>> (\ (X a) -> showString "0x" . showHex a $ "") $ foldMap' X bits
"0x42"

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