Copyright	(c) 2019 Composewell Technologies
License	BSD3
Maintainer	streamly@composewell.com
Stability	experimental
Portability	GHC
Safe Haskell	None
Language	Haskell2010

Streamly.Data.Fold

Contents

Fold Type
Transformations
- Covariant Operations
Distributing
Partitioning
Unzipping

Description

Fold type represents an effectful action that consumes a value from an input stream and combines it with a single final value often called an accumulator, returning the resulting output accumulator. Values from a stream can be pushed to the fold and consumed one at a time. It can also be called a consumer of stream or a sink. It is a data representation of the standard foldl' function. A Fold can be turned into an effect (m b) using fold by supplying it the input stream.

Using this representation multiple folds can be combined efficiently using combinators; a stream can then be supplied to the combined fold and it would distribute the input to constituent folds according to the composition. For example, an applicative composition distributes the same input to the constituent folds and then combines the resulting fold outputs. Similarly, a partitioning combinator divides the input among constituent folds.

Performance Notes

Fold representation is more efficient than using streams when splitting streams. Fold m a b can be considered roughly equivalent to a fold action m b -> t m a -> m b (where t is a stream type and m is a Monad). Instead of using a Fold type one could just use a fold action of the shape m b -> t m a -> m b for folding streams. However, multiple such actions cannot be composed into a single fold function in an efficient manner. Using the Fold type we can efficiently split the stream across mutliple folds because it allows the compiler to perform stream fusion optimizations.

On the other hand, transformation operations (e.g. map) on stream types can be as efficient as transformations on Fold (e.g. lmap).

Programmer Notes

import qualified Streamly.Data.Fold as FL

More, not yet exposed, fold combinators can be found in Streamly.Internal.Data.Fold.

Synopsis

data Fold m a b
drain :: Monad m => Fold m a ()
drainBy :: Monad m => (a -> m b) -> Fold m a ()
last :: Monad m => Fold m a (Maybe a)
length :: Monad m => Fold m a Int
sum :: (Monad m, Num a) => Fold m a a
product :: (Monad m, Num a) => Fold m a a
maximumBy :: Monad m => (a -> a -> Ordering) -> Fold m a (Maybe a)
maximum :: (Monad m, Ord a) => Fold m a (Maybe a)
minimumBy :: Monad m => (a -> a -> Ordering) -> Fold m a (Maybe a)
minimum :: (Monad m, Ord a) => Fold m a (Maybe a)
mean :: (Monad m, Fractional a) => Fold m a a
variance :: (Monad m, Fractional a) => Fold m a a
stdDev :: (Monad m, Floating a) => Fold m a a
mconcat :: (Monad m, Monoid a) => Fold m a a
foldMap :: (Monad m, Monoid b) => (a -> b) -> Fold m a b
foldMapM :: (Monad m, Monoid b) => (a -> m b) -> Fold m a b
toList :: Monad m => Fold m a [a]
index :: Monad m => Int -> Fold m a (Maybe a)
head :: Monad m => Fold m a (Maybe a)
find :: Monad m => (a -> Bool) -> Fold m a (Maybe a)
lookup :: (Eq a, Monad m) => a -> Fold m (a, b) (Maybe b)
findIndex :: Monad m => (a -> Bool) -> Fold m a (Maybe Int)
elemIndex :: (Eq a, Monad m) => a -> Fold m a (Maybe Int)
null :: Monad m => Fold m a Bool
elem :: (Eq a, Monad m) => a -> Fold m a Bool
notElem :: (Eq a, Monad m) => a -> Fold m a Bool
all :: Monad m => (a -> Bool) -> Fold m a Bool
any :: Monad m => (a -> Bool) -> Fold m a Bool
and :: Monad m => Fold m Bool Bool
or :: Monad m => Fold m Bool Bool
sequence :: Monad m => Fold m a (m b) -> Fold m a b
mapM :: Monad m => (b -> m c) -> Fold m a b -> Fold m a c
tee :: Monad m => Fold m a b -> Fold m a c -> Fold m a (b, c)
distribute :: Monad m => [Fold m a b] -> Fold m a [b]
partition :: Monad m => Fold m b x -> Fold m c y -> Fold m (Either b c) (x, y)
unzip :: Monad m => Fold m a x -> Fold m b y -> Fold m (a, b) (x, y)

Fold Type

A Fold can be run over a stream using the fold combinator:

>>> S.fold FL.sum (S.enumerateFromTo 1 100)
5050

data Fold m a b Source #

Represents a left fold over an input stream of values of type a to a single value of type b in Monad m.

The fold uses an intermediate state s as accumulator. The step function updates the state and returns the new updated state. When the fold is done the final result of the fold is extracted from the intermediate state representation using the extract function.

Since: 0.7.0

Instances

Applicative m => Functor (Fold m a) Source #	Maps a function on the output of the fold (the type `b`).
Instance details Defined in Streamly.Internal.Data.Fold.Types Methods fmap :: (a0 -> b) -> Fold m a a0 -> Fold m a b # (<$) :: a0 -> Fold m a b -> Fold m a a0 #
Applicative m => Applicative (Fold m a) Source #	The fold resulting from `<*>` distributes its input to both the argument folds and combines their output using the supplied function.
Instance details Defined in Streamly.Internal.Data.Fold.Types Methods pure :: a0 -> Fold m a a0 # (<>) :: Fold m a (a0 -> b) -> Fold m a a0 -> Fold m a b # liftA2 :: (a0 -> b -> c) -> Fold m a a0 -> Fold m a b -> Fold m a c # (>) :: Fold m a a0 -> Fold m a b -> Fold m a b # (<*) :: Fold m a a0 -> Fold m a b -> Fold m a a0 #
(Monad m, Floating b) => Floating (Fold m a b) Source #	Combines the fold outputs using their `Floating` instances.
Instance details Defined in Streamly.Internal.Data.Fold.Types Methods pi :: Fold m a b # exp :: Fold m a b -> Fold m a b # log :: Fold m a b -> Fold m a b # sqrt :: Fold m a b -> Fold m a b # (**) :: Fold m a b -> Fold m a b -> Fold m a b # logBase :: Fold m a b -> Fold m a b -> Fold m a b # sin :: Fold m a b -> Fold m a b # cos :: Fold m a b -> Fold m a b # tan :: Fold m a b -> Fold m a b # asin :: Fold m a b -> Fold m a b # acos :: Fold m a b -> Fold m a b # atan :: Fold m a b -> Fold m a b # sinh :: Fold m a b -> Fold m a b # cosh :: Fold m a b -> Fold m a b # tanh :: Fold m a b -> Fold m a b # asinh :: Fold m a b -> Fold m a b # acosh :: Fold m a b -> Fold m a b # atanh :: Fold m a b -> Fold m a b # log1p :: Fold m a b -> Fold m a b # expm1 :: Fold m a b -> Fold m a b # log1pexp :: Fold m a b -> Fold m a b # log1mexp :: Fold m a b -> Fold m a b #
(Monad m, Fractional b) => Fractional (Fold m a b) Source #	Combines the fold outputs (type `b`) using their `Fractional` instances.
Instance details Defined in Streamly.Internal.Data.Fold.Types Methods (/) :: Fold m a b -> Fold m a b -> Fold m a b # recip :: Fold m a b -> Fold m a b # fromRational :: Rational -> Fold m a b #
(Monad m, Num b) => Num (Fold m a b) Source #	Combines the fold outputs (type `b`) using their `Num` instances.
Instance details Defined in Streamly.Internal.Data.Fold.Types Methods (+) :: Fold m a b -> Fold m a b -> Fold m a b # (-) :: Fold m a b -> Fold m a b -> Fold m a b # (*) :: Fold m a b -> Fold m a b -> Fold m a b # negate :: Fold m a b -> Fold m a b # abs :: Fold m a b -> Fold m a b # signum :: Fold m a b -> Fold m a b # fromInteger :: Integer -> Fold m a b #
(Semigroup b, Monad m) => Semigroup (Fold m a b) Source #	Combines the outputs of the folds (the type `b`) using their `Semigroup` instances.
Instance details Defined in Streamly.Internal.Data.Fold.Types Methods (<>) :: Fold m a b -> Fold m a b -> Fold m a b # sconcat :: NonEmpty (Fold m a b) -> Fold m a b # stimes :: Integral b0 => b0 -> Fold m a b -> Fold m a b #
(Semigroup b, Monoid b, Monad m) => Monoid (Fold m a b) Source #	Combines the outputs of the folds (the type `b`) using their `Monoid` instances.
Instance details Defined in Streamly.Internal.Data.Fold.Types Methods mempty :: Fold m a b # mappend :: Fold m a b -> Fold m a b -> Fold m a b # mconcat :: [Fold m a b] -> Fold m a b #

Full Folds

drain :: Monad m => Fold m a () Source #

A fold that drains all its input, running the effects and discarding the results.

Since: 0.7.0

drainBy :: Monad m => (a -> m b) -> Fold m a () Source #

drainBy f = lmapM f drain

Drain all input after passing it through a monadic function. This is the dual of mapM_ on stream producers.

Since: 0.7.0

last :: Monad m => Fold m a (Maybe a) Source #

Extract the last element of the input stream, if any.

Since: 0.7.0

length :: Monad m => Fold m a Int Source #

Determine the length of the input stream.

Since: 0.7.0

sum :: (Monad m, Num a) => Fold m a a Source #

Determine the sum of all elements of a stream of numbers. Returns additive identity (0) when the stream is empty. Note that this is not numerically stable for floating point numbers.

Since: 0.7.0

product :: (Monad m, Num a) => Fold m a a Source #

Determine the product of all elements of a stream of numbers. Returns multiplicative identity (1) when the stream is empty.

Since: 0.7.0

maximumBy :: Monad m => (a -> a -> Ordering) -> Fold m a (Maybe a) Source #

Determine the maximum element in a stream using the supplied comparison function.

Since: 0.7.0

maximum :: (Monad m, Ord a) => Fold m a (Maybe a) Source #

maximum = maximumBy compare

Determine the maximum element in a stream.

Since: 0.7.0

minimumBy :: Monad m => (a -> a -> Ordering) -> Fold m a (Maybe a) Source #

Computes the minimum element with respect to the given comparison function

Since: 0.7.0

minimum :: (Monad m, Ord a) => Fold m a (Maybe a) Source #

Determine the minimum element in a stream using the supplied comparison function.

Since: 0.7.0

mean :: (Monad m, Fractional a) => Fold m a a Source #

Compute a numerically stable arithmetic mean of all elements in the input stream.

Since: 0.7.0

variance :: (Monad m, Fractional a) => Fold m a a Source #

Compute a numerically stable (population) variance over all elements in the input stream.

Since: 0.7.0

stdDev :: (Monad m, Floating a) => Fold m a a Source #

Compute a numerically stable (population) standard deviation over all elements in the input stream.

Since: 0.7.0

Full Folds (Monoidal)

mconcat :: (Monad m, Monoid a) => Fold m a a Source #

Fold an input stream consisting of monoidal elements using mappend and mempty.

S.fold FL.mconcat (S.map Sum $ S.enumerateFromTo 1 10)

Since: 0.7.0

foldMap :: (Monad m, Monoid b) => (a -> b) -> Fold m a b Source #

foldMap f = map f mconcat

Make a fold from a pure function that folds the output of the function using mappend and mempty.

S.fold (FL.foldMap Sum) $ S.enumerateFromTo 1 10

Since: 0.7.0

foldMapM :: (Monad m, Monoid b) => (a -> m b) -> Fold m a b Source #

foldMapM f = mapM f mconcat

Make a fold from a monadic function that folds the output of the function using mappend and mempty.

S.fold (FL.foldMapM (return . Sum)) $ S.enumerateFromTo 1 10

Since: 0.7.0

Full Folds (To Containers)

Avoid using these folds in scalable or performance critical applications, they buffer all the input in GC memory which can be detrimental to performance if the input is large.

toList :: Monad m => Fold m a [a] Source #

Folds the input stream to a list.

Warning! working on large lists accumulated as buffers in memory could be very inefficient, consider using Streamly.Array instead.

Since: 0.7.0

Partial Folds

index :: Monad m => Int -> Fold m a (Maybe a) Source #

Lookup the element at the given index.

Since: 0.7.0

head :: Monad m => Fold m a (Maybe a) Source #

Extract the first element of the stream, if any.

Since: 0.7.0

find :: Monad m => (a -> Bool) -> Fold m a (Maybe a) Source #

Returns the first element that satisfies the given predicate.

Since: 0.7.0

lookup :: (Eq a, Monad m) => a -> Fold m (a, b) (Maybe b) Source #

In a stream of (key-value) pairs (a, b), return the value b of the first pair where the key equals the given value a.

Since: 0.7.0

findIndex :: Monad m => (a -> Bool) -> Fold m a (Maybe Int) Source #

Returns the first index that satisfies the given predicate.

Since: 0.7.0

elemIndex :: (Eq a, Monad m) => a -> Fold m a (Maybe Int) Source #

Returns the first index where a given value is found in the stream.

Since: 0.7.0

null :: Monad m => Fold m a Bool Source #

Return True if the input stream is empty.

Since: 0.7.0

elem :: (Eq a, Monad m) => a -> Fold m a Bool Source #

Return True if the given element is present in the stream.

Since: 0.7.0

notElem :: (Eq a, Monad m) => a -> Fold m a Bool Source #

Returns True if the given element is not present in the stream.

Since: 0.7.0

all :: Monad m => (a -> Bool) -> Fold m a Bool Source #

all p = lmap p and

| Returns True if all elements of a stream satisfy a predicate.

Since: 0.7.0

any :: Monad m => (a -> Bool) -> Fold m a Bool Source #

any p = lmap p or

| Returns True if any of the elements of a stream satisfies a predicate.

Since: 0.7.0

and :: Monad m => Fold m Bool Bool Source #

Returns True if all elements are True, False otherwise

Since: 0.7.0

or :: Monad m => Fold m Bool Bool Source #

Returns True if any element is True, False otherwise

Since: 0.7.0

Transformations

Unlike stream producer types (e.g. SerialT m a) which have only output side, folds have an input side as well as an output side. In the type Fold m a b, the input type is a and the output type is b. Transformations can be applied either on the input side or on the output side. The Functor instance of a fold maps on the output of the fold:

>>> S.fold (fmap show FL.sum) (S.enumerateFromTo 1 100)
"5050"

However, the input side or contravariant transformations are more interesting for folds. The following sections describe the input transformation operations on a fold. The names of the operations are consistent with their covariant counterparts in Streamly.Prelude, the only difference is that they are prefixed with l which stands for left assuming left side is the input side, notice that in Fold m a b the type variable a is on the left side.

Covariant Operations

sequence :: Monad m => Fold m a (m b) -> Fold m a b Source #

Flatten the monadic output of a fold to pure output.

Since: 0.7.0

mapM :: Monad m => (b -> m c) -> Fold m a b -> Fold m a c Source #

Map a monadic function on the output of a fold.

Since: 0.7.0

Distributing

The Applicative instance of a distributing Fold distributes one copy of the stream to each fold and combines the results using a function.

                |-------Fold m a b--------|
---stream m a---|                         |---m (b,c,...)
                |-------Fold m a c--------|
                |                         |
                           ...

To compute the average of numbers in a stream without going throught he stream twice:

>>> let avg = (/) <$> FL.sum <*> fmap fromIntegral FL.length
>>> S.fold avg (S.enumerateFromTo 1.0 100.0)
50.5

The Semigroup and Monoid instances of a distributing fold distribute the input to both the folds and combines the outputs using Monoid or Semigroup instances of the output types:

>>> import Data.Monoid (Sum)
>>> S.fold (FL.head <> FL.last) (fmap Sum $ S.enumerateFromTo 1.0 100.0)
Just (Sum {getSum = 101.0})

The Num, Floating, and Fractional instances work in the same way.

tee :: Monad m => Fold m a b -> Fold m a c -> Fold m a (b, c) Source #

Distribute one copy of the stream to each fold and zip the results.

                |-------Fold m a b--------|
---stream m a---|                         |---m (b,c)
                |-------Fold m a c--------|

>>> S.fold (FL.tee FL.sum FL.length) (S.enumerateFromTo 1.0 100.0)
(5050.0,100)

Since: 0.7.0

distribute :: Monad m => [Fold m a b] -> Fold m a [b] Source #

Distribute one copy of the stream to each fold and collect the results in a container.

                |-------Fold m a b--------|
---stream m a---|                         |---m [b]
                |-------Fold m a b--------|
                |                         |
                           ...

>>> S.fold (FL.distribute [FL.sum, FL.length]) (S.enumerateFromTo 1 5)
[15,5]

This is the consumer side dual of the producer side sequence operation.

Since: 0.7.0

Partitioning

Direct items in the input stream to different folds using a binary fold selector.

partition :: Monad m => Fold m b x -> Fold m c y -> Fold m (Either b c) (x, y) Source #

Compose two folds such that the combined fold accepts a stream of Either and routes the Left values to the first fold and Right values to the second fold.

partition = partitionBy id

Since: 0.7.0

Unzipping

unzip :: Monad m => Fold m a x -> Fold m b y -> Fold m (a, b) (x, y) Source #

Send the elements of tuples in a stream of tuples through two different folds.

                          |-------Fold m a x--------|
---------stream of (a,b)--|                         |----m (x,y)
                          |-------Fold m b y--------|

This is the consumer side dual of the producer side zip operation.

Since: 0.7.0