Efficient representation of a left fold that preserves the fold's step function, initial accumulator, and extraction function

This allows the Applicative instance to assemble derived folds that traverse the container only once

A 'Fold a b' processes elements of type a and results in a value of type b.

Like Fold, but monadic.

A 'FoldM m a b' processes elements of type a and results in a monadic value of type m b.

Apply a strict left Fold to a Foldable container

Like fold, but monadic

Convert a strict left Fold into a scan

Convert a Fold into a prescan for any Traversable type

"Prescan" means that the last element of the scan is not included

Convert a Fold into a postscan for any Traversable type

"Postscan" means that the first element of the scan is not included

Fold all values within a container using mappend and mempty

Convert a "foldMap" to a Fold

Get the first element of a container or return Nothing if the container is empty

Get the last element of a container or return Nothing if the container is empty

Get the last element of a container or return a default value if the container is empty

Return the last N elements

Returns True if the container is empty, False otherwise

Return the length of the container

Returns True if all elements are True, False otherwise

Returns True if any element is True, False otherwise

(all predicate) returns True if all elements satisfy the predicate, False otherwise

(any predicate) returns True if any element satisfies the predicate, False otherwise

Computes the sum of all elements

Computes the product of all elements

Compute a numerically stable arithmetic mean of all elements

Compute a numerically stable (population) variance over all elements

Compute a numerically stable (population) standard deviation over all elements

Computes the maximum element

Computes the maximum element with respect to the given comparison function

Computes the minimum element

Computes the minimum element with respect to the given comparison function

(elem a) returns True if the container has an element equal to a, False otherwise

(notElem a) returns False if the container has an element equal to a, True otherwise

(find predicate) returns the first element that satisfies the predicate or Nothing if no element satisfies the predicate

(index n) returns the nth element of the container, or Nothing if the container has an insufficient number of elements

(lookup a) returns the element paired with the first matching item, or Nothing if none matches

(elemIndex a) returns the index of the first element that equals a, or Nothing if no element matches

(findIndex predicate) returns the index of the first element that satisfies the predicate, or Nothing if no element satisfies the predicate

Pick a random element, using reservoir sampling

Pick several random elements, using reservoir sampling

Converts an effectful function to a fold. Specialized version of sink.

Converts an effectful function to a fold

sink (f <> g) = sink f <> sink g -- if `(<>)` is commutative
sink mempty = mempty

Like length, except with a more general Num return value

Like index, except with a more general Integral argument

Fold all values into a list

Fold all values into a list, in reverse order

O(n log n). Fold values into a list with duplicates removed, while preserving their first occurrences

O(n^2). Fold values into a list with duplicates removed, while preserving their first occurrences

Fold values into a set

Fold values into a hash-set

Fold pairs into a map.

Fold pairs into a hash-map.

Fold all values into a vector

Fold all values into a vector

This is more efficient than vector but is impure

Upgrade a fold to accept the Fold type

Upgrade a more traditional fold to accept the Fold type

Upgrade a monadic fold to accept the FoldM type

Upgrade a more traditional monadic fold to accept the FoldM type

Generalize a Fold to a FoldM

generalize (pure r) = pure r

generalize (f <*> x) = generalize f <*> generalize x

Simplify a pure FoldM to a Fold

simplify (pure r) = pure r

simplify (f <*> x) = simplify f <*> simplify x

Shift a FoldM from one monad to another with a morphism such as lift or liftIO; the effect is the same as hoist.

Allows to continue feeding a FoldM even after passing it to a function that closes it.

For pure Folds, this is provided by the Comonad instance.

_Fold1 step returns a new Fold using just a step function that has the same type for the accumulator and the element. The result type is the accumulator type wrapped in Maybe. The initial accumulator is retrieved from the Foldable, the result is None for empty containers.

(premap f folder) returns a new Fold where f is applied at each step

fold (premap f folder) list = fold folder (map f list)

>>> fold (premap Sum mconcat) [1..10]
Sum {getSum = 55}

>>> fold mconcat (map Sum [1..10])
Sum {getSum = 55}

premap id = id

premap (f . g) = premap g . premap f

premap k (pure r) = pure r

premap k (f <*> x) = premap k f <*> premap k x

(premapM f folder) returns a new FoldM where f is applied to each input element

foldM (premapM f folder) list = foldM folder (map f list)

premapM id = id

premapM (f . g) = premap g . premap f

premapM k (pure r) = pure r

premapM k (f <*> x) = premapM k f <*> premapM k x

(prefilter f folder) returns a new Fold where the folder's input is used only when the input satisfies a predicate f

This can also be done with handles (handles (filtered f)) but prefilter does not need you to depend on a lens library.

(prefilterM f folder) returns a new Fold where the folder's input is used only when the input satisfies a monadic predicate f.

A handler for the upstream input of a Fold

Any lens, traversal, or prism will type-check as a Handler

(handles t folder) transforms the input of a Fold using a lens, traversal, or prism:

handles _1       :: Fold a r -> Fold (a, b) r
handles _Left    :: Fold a r -> Fold (Either a b) r
handles traverse :: Traversable t => Fold a r -> Fold (t a) r
handles folded   :: Foldable    t => Fold a r -> Fold (t a) r

>>> fold (handles traverse sum) [[1..5],[6..10]]
55

>>> fold (handles (traverse.traverse) sum) [[Nothing, Just 2, Just 7],[Just 13, Nothing, Just 20]]
42

>>> fold (handles (filtered even) sum) [1..10]
30

>>> fold (handles _2 mconcat) [(1,"Hello "),(2,"World"),(3,"!")]
"Hello World!"

handles id = id

handles (f . g) = handles f . handles g

handles t (pure r) = pure r

handles t (f <*> x) = handles t f <*> handles t x

(foldOver f folder xs) folds all values from a Lens, Traversal, Prism or Fold with the given folder

>>> foldOver (_Just . both) L.sum (Just (2, 3))
5

>>> foldOver (_Just . both) L.sum Nothing
0

L.foldOver f folder xs == L.fold folder (xs^..f)

L.foldOver (folded.f) folder == L.fold (handles f folder)

L.foldOver folded == L.fold

instance Monad m => Monoid (EndoM m a) where
    mempty = EndoM return
    mappend (EndoM f) (EndoM g) = EndoM (f <=< g)

A Handler for the upstream input of FoldM

Any lens, traversal, or prism will type-check as a HandlerM

(handlesM t folder) transforms the input of a FoldM using a lens, traversal, or prism:

handlesM _1       :: FoldM m a r -> FoldM (a, b) r
handlesM _Left    :: FoldM m a r -> FoldM (Either a b) r
handlesM traverse :: Traversable t => FoldM m a r -> FoldM m (t a) r
handlesM folded   :: Foldable    t => FoldM m a r -> FoldM m (t a) r

handlesM obeys these laws:

handlesM id = id

handlesM (f . g) = handlesM f . handlesM g

handlesM t (pure r) = pure r

handlesM t (f <*> x) = handlesM t f <*> handlesM t x

(foldOverM f folder xs) folds all values from a Lens, Traversal, Prism or Fold monadically with the given folder

L.foldOverM (folded.f) folder == L.foldM (handlesM f folder)

L.foldOverM folded == L.foldM

folded :: Foldable t => Fold (t a) a

handles folded :: Foldable t => Fold a r -> Fold (t a) r

>>> fold (handles (filtered even) sum) [1..10]
30

>>> foldM (handlesM (filtered even) (mapM_ print)) [1..10]
2
4
6
8
10