    {-| This module provides efficient and streaming left folds that you can combine
        using 'Applicative' style.

        Import this module qualified to avoid clashing with the Prelude:

    >>> import qualified Control.Foldl as L

        Use 'fold' to apply a 'Fold' to a list:

    >>> L.fold L.sum [1..100]
    5050

        'Fold's are 'Applicative's, so you can combine them using 'Applicative'
        combinators:

    >>> import Control.Applicative
    >>> let average = (/) <$> L.sum <*> L.genericLength

        Taking the sum, the sum of squares, ..., upto the sum of x^5

    >>> import Data.Traversable
    >>> let powerSums = sequenceA [L.premap (^n) L.sum | n <- [1..5]]
    >>> L.fold powerSums [1..10]
    [55,385,3025,25333,220825]

        These combined folds will still traverse the list only once, streaming
        efficiently over the list in constant space without space leaks:

    >>> L.fold average [1..10000000]
    5000000.5
    >>> L.fold ((,) <$> L.minimum <*> L.maximum) [1..10000000]
    (Just 1,Just 10000000)

        You might want to try enabling the @-flate-dmd-anal@ flag when compiling
        executables that use this library to further improve performance.
    -}

    {-# LANGUAGE BangPatterns              #-}
    {-# LANGUAGE ExistentialQuantification #-}
    {-# LANGUAGE FlexibleContexts          #-}
    {-# LANGUAGE RankNTypes                #-}
    {-# LANGUAGE Trustworthy               #-}

    module Control.Foldl (
        -- * Fold Types
          Fold(..)
        , FoldM(..)

        -- * Folding
        , fold
        , foldM
        , scan
        , prescan
        , postscan

        -- * Folds
        , Control.Foldl.mconcat
        , Control.Foldl.foldMap
        , head
        , last
        , lastDef
        , lastN
        , null
        , length
        , and
        , or
        , all
        , any
        , sum
        , product
        , mean
        , variance
        , std
        , maximum
        , maximumBy
        , minimum
        , minimumBy
        , elem
        , notElem
        , find
        , index
        , lookup
        , elemIndex
        , findIndex
        , random
        , randomN
        , Control.Foldl.mapM_
        , sink

        -- * Generic Folds
        , genericLength
        , genericIndex

        -- * Container folds
        , list
        , revList
        , nub
        , eqNub
        , set
        , hashSet
        , map
        , hashMap
        , vector
        , vectorM

        -- * Utilities
        -- $utilities
        , purely
        , purely_
        , impurely
        , impurely_
        , generalize
        , simplify
        , hoists
        , duplicateM
        , _Fold1
        , premap
        , premapM
        , prefilter
        , prefilterM
        , Handler
        , handles
        , foldOver
        , EndoM(..)
        , HandlerM
        , handlesM
        , foldOverM
        , folded
        , filtered
        , groupBy
        , either
        , eitherM

        -- * Re-exports
        -- $reexports
        , module Control.Monad.Primitive
        , module Data.Foldable
        , module Data.Vector.Generic
        ) where

    import Control.Foldl.Optics (_Left, _Right)
    import Control.Applicative
    import Control.Foldl.Internal (Maybe'(..), lazy, Either'(..), Pair(..), hush)
    import Control.Monad ((<=<))
    import Control.Monad.Primitive (PrimMonad, RealWorld)
    import Control.Comonad
    import Data.Foldable (Foldable)
    import Data.Functor.Identity (Identity, runIdentity)
    import Data.Functor.Contravariant (Contravariant(..))
    import Data.Map.Strict (Map, alter)
    import Data.Maybe (fromMaybe)
    import Data.Monoid hiding ((<>))
    import Data.Semigroup (Semigroup(..))
    import Data.Semigroupoid (Semigroupoid)
    import Data.Profunctor
    import Data.Sequence ((|>))
    import Data.Vector.Generic (Vector, Mutable)
    import Data.Vector.Generic.Mutable (MVector)
    import Data.Hashable (Hashable)
    import Data.Traversable
    import System.Random.MWC (GenIO, createSystemRandom, uniformR)
    import Prelude hiding
        ( head
        , last
        , null
        , length
        , and
        , or
        , all
        , any
        , sum
        , product
        , maximum
        , minimum
        , elem
        , notElem
        , lookup
        , map
        , either
        )

    import qualified Data.Foldable               as F
    import qualified Data.List                   as List
    import qualified Data.Sequence               as Seq
    import qualified Data.Set                    as Set
    import qualified Data.Map.Strict             as Map
    import qualified Data.HashMap.Strict         as HashMap
    import qualified Data.HashSet                as HashSet
    import qualified Data.Vector.Generic         as V
    import qualified Data.Vector.Generic.Mutable as M
    import qualified VectorBuilder.Builder
    import qualified VectorBuilder.Vector
    import qualified Data.Semigroupoid

    {-| 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__.
    -}
    data Fold a b
      -- | @Fold @ @ step @ @ initial @ @ extract@
      = forall x. Fold (x -> a -> x) x (x -> b)

    instance Functor (Fold a) where
        fmap f (Fold step begin done) = Fold step begin (f . done)
        {-# INLINE fmap #-}

    instance Profunctor Fold where
        lmap = premap
        rmap = fmap

    instance Choice Fold where
      right' (Fold step begin done) = Fold (liftA2 step) (Right begin) (fmap done)
      {-# INLINE right' #-}

    instance Comonad (Fold a) where
        extract (Fold _ begin done) = done begin
        {-#  INLINE extract #-}

        duplicate (Fold step begin done) = Fold step begin (\x -> Fold step x done)
        {-#  INLINE duplicate #-}

    instance Applicative (Fold a) where
        pure b    = Fold (\() _ -> ()) () (\() -> b)
        {-# INLINE pure #-}

        (Fold stepL beginL doneL) <*> (Fold stepR beginR doneR) =
            let step (Pair xL xR) a = Pair (stepL xL a) (stepR xR a)
                begin = Pair beginL beginR
                done (Pair xL xR) = doneL xL (doneR xR)
            in  Fold step begin done
        {-# INLINE (<*>) #-}

    instance Semigroup b => Semigroup (Fold a b) where
        (<>) = liftA2 (<>)
        {-# INLINE (<>) #-}

    instance Semigroupoid Fold where
        o (Fold step1 begin1 done1) (Fold step2 begin2 done2) = Fold
            step
            (Pair begin1 begin2)
            (\(Pair x _) -> done1 x)
          where
            step (Pair c1 c2) a =
                let c2' = step2 c2 a
                    c1' = step1 c1 (done2 c2')
                in  Pair c1' c2'
        {-# INLINE o #-}

    instance Monoid b => Monoid (Fold a b) where
        mempty = pure mempty
        {-# INLINE mempty #-}

        mappend = liftA2 mappend
        {-# INLINE mappend #-}

    instance Num b => Num (Fold a b) where
        fromInteger = pure . fromInteger
        {-# INLINE fromInteger #-}

        negate = fmap negate
        {-# INLINE negate #-}

        abs = fmap abs
        {-# INLINE abs #-}

        signum = fmap signum
        {-# INLINE signum #-}

        (+) = liftA2 (+)
        {-# INLINE (+) #-}

        (*) = liftA2 (*)
        {-# INLINE (*) #-}

        (-) = liftA2 (-)
        {-# INLINE (-) #-}

    instance Fractional b => Fractional (Fold a b) where
        fromRational = pure . fromRational
        {-# INLINE fromRational #-}

        recip = fmap recip
        {-# INLINE recip #-}

        (/) = liftA2 (/)
        {-# INLINE (/) #-}

    instance Floating b => Floating (Fold a b) where
        pi = pure pi
        {-# INLINE pi #-}

        exp = fmap exp
        {-# INLINE exp #-}

        sqrt = fmap sqrt
        {-# INLINE sqrt #-}

        log = fmap log
        {-# INLINE log #-}

        sin = fmap sin
        {-# INLINE sin #-}

        tan = fmap tan
        {-# INLINE tan #-}

        cos = fmap cos
        {-# INLINE cos #-}

        asin = fmap asin
        {-# INLINE asin #-}

        atan = fmap atan
        {-# INLINE atan #-}

        acos = fmap acos
        {-# INLINE acos #-}

        sinh = fmap sinh
        {-# INLINE sinh #-}

        tanh = fmap tanh
        {-# INLINE tanh #-}

        cosh = fmap cosh
        {-# INLINE cosh #-}

        asinh = fmap asinh
        {-# INLINE asinh #-}

        atanh = fmap atanh
        {-# INLINE atanh #-}

        acosh = fmap acosh
        {-# INLINE acosh #-}

        (**) = liftA2 (**)
        {-# INLINE (**) #-}

        logBase = liftA2 logBase
        {-# INLINE logBase #-}

    {-| Like 'Fold', but monadic.

        A \''FoldM' m a b\' processes elements of type __a__ and
        results in a monadic value of type __m b__.
    -}
    data FoldM m a b =
      -- | @FoldM @ @ step @ @ initial @ @ extract@
      forall x . FoldM (x -> a -> m x) (m x) (x -> m b)

    instance Functor m => Functor (FoldM m a) where
        fmap f (FoldM step start done) = FoldM step start done'
          where
            done' x = fmap f $! done x
        {-# INLINE fmap #-}

    instance Applicative m => Applicative (FoldM m a) where
        pure b = FoldM (\() _ -> pure ()) (pure ()) (\() -> pure b)
        {-# INLINE pure #-}

        (FoldM stepL beginL doneL) <*> (FoldM stepR beginR doneR) =
            let step (Pair xL xR) a = Pair <$> stepL xL a <*> stepR xR a
                begin = Pair <$> beginL <*> beginR
                done (Pair xL xR) = doneL xL <*> doneR xR
            in  FoldM step begin done
        {-# INLINE (<*>) #-}

    instance Functor m => Profunctor (FoldM m) where
        rmap = fmap
        lmap f (FoldM step begin done) = FoldM step' begin done
          where
            step' x a = step x (f a)

    instance (Semigroup b, Monad m) => Semigroup (FoldM m a b) where
        (<>) = liftA2 (<>)
        {-# INLINE (<>) #-}

    instance (Monoid b, Monad m) => Monoid (FoldM m a b) where
        mempty = pure mempty
        {-# INLINE mempty #-}

        mappend = liftA2 mappend
        {-# INLINE mappend #-}

    instance (Monad m, Num b) => Num (FoldM m a b) where
        fromInteger = pure . fromInteger
        {-# INLINE fromInteger #-}

        negate = fmap negate
        {-# INLINE negate #-}

        abs = fmap abs
        {-# INLINE abs #-}

        signum = fmap signum
        {-# INLINE signum #-}

        (+) = liftA2 (+)
        {-# INLINE (+) #-}

        (*) = liftA2 (*)
        {-# INLINE (*) #-}

        (-) = liftA2 (-)
        {-# INLINE (-) #-}

    instance (Monad m, Fractional b) => Fractional (FoldM m a b) where
        fromRational = pure . fromRational
        {-# INLINE fromRational #-}

        recip = fmap recip
        {-# INLINE recip #-}

        (/) = liftA2 (/)
        {-# INLINE (/) #-}

    instance (Monad m, Floating b) => Floating (FoldM m a b) where
        pi = pure pi
        {-# INLINE pi #-}

        exp = fmap exp
        {-# INLINE exp #-}

        sqrt = fmap sqrt
        {-# INLINE sqrt #-}

        log = fmap log
        {-# INLINE log #-}

        sin = fmap sin
        {-# INLINE sin #-}

        tan = fmap tan
        {-# INLINE tan #-}

        cos = fmap cos
        {-# INLINE cos #-}

        asin = fmap asin
        {-# INLINE asin #-}

        atan = fmap atan
        {-# INLINE atan #-}

        acos = fmap acos
        {-# INLINE acos #-}

        sinh = fmap sinh
        {-# INLINE sinh #-}

        tanh = fmap tanh
        {-# INLINE tanh #-}

        cosh = fmap cosh
        {-# INLINE cosh #-}

        asinh = fmap asinh
        {-# INLINE asinh #-}

        atanh = fmap atanh
        {-# INLINE atanh #-}

        acosh = fmap acosh
        {-# INLINE acosh #-}

        (**) = liftA2 (**)
        {-# INLINE (**) #-}

        logBase = liftA2 logBase
        {-# INLINE logBase #-}

    -- | Apply a strict left 'Fold' to a 'Foldable' container
    fold :: Foldable f => Fold a b -> f a -> b
    fold (Fold step begin done) as = F.foldr cons done as begin
      where
        cons a k x = k $! step x a
    {-# INLINE fold #-}

    -- | Like 'fold', but monadic
    foldM :: (Foldable f, Monad m) => FoldM m a b -> f a -> m b
    foldM (FoldM step begin done) as0 = do
        x0 <- begin
        F.foldr step' done as0 $! x0
      where
        step' a k x = do
            x' <- step x a
            k $! x'
    {-# INLINE foldM #-}

    -- | Convert a strict left 'Fold' into a scan
    scan :: Fold a b -> [a] -> [b]
    scan (Fold step begin done) as = foldr cons nil as begin
      where
        nil      x = done x:[]
        cons a k x = done x:(k $! step x a)
    {-# INLINE scan #-}

    {-| Convert a `Fold` into a prescan for any `Traversable` type

        \"Prescan\" means that the last element of the scan is not included
    -}
    prescan :: Traversable t => Fold a b -> t a -> t b
    prescan (Fold step begin done) as = bs
      where
        step' x a = (x', b)
          where
            x' = step x a
            b  = done x
        (_, bs) = mapAccumL step' begin as
    {-# INLINE prescan #-}

    {-| Convert a `Fold` into a postscan for any `Traversable` type

        \"Postscan\" means that the first element of the scan is not included
    -}
    postscan :: Traversable t => Fold a b -> t a -> t b
    postscan (Fold step begin done) as = bs
      where
        step' x a = (x', b)
          where
            x' = step x a
            b  = done x'
        (_, bs) = mapAccumL step' begin as
    {-# INLINE postscan #-}

    -- | Fold all values within a container using 'mappend' and 'mempty'
    mconcat :: Monoid a => Fold a a
    mconcat = Fold mappend mempty id
    {-# INLINABLE mconcat #-}

    -- | Convert a \"@foldMap@\" to a 'Fold'
    foldMap :: Monoid w => (a -> w) -> (w -> b) -> Fold a b
    foldMap to = Fold (\x a -> mappend x (to a)) mempty
    {-# INLINABLE foldMap #-}

    {-| Get the first element of a container or return 'Nothing' if the container is
        empty
    -}
    head :: Fold a (Maybe a)
    head = _Fold1 const
    {-# INLINABLE head #-}

    {-| Get the last element of a container or return 'Nothing' if the container is
        empty
    -}
    last :: Fold a (Maybe a)
    last = _Fold1 (flip const)
    {-# INLINABLE last #-}

    {-| Get the last element of a container or return a default value if the container
        is empty
    -}
    lastDef :: a -> Fold a a
    lastDef a = Fold (\_ a' -> a') a id
    {-# INLINABLE lastDef #-}

    {-| Return the last N elements

    -}
    lastN :: Int -> Fold a [a]
    lastN n = Fold step begin done
      where
        step s a = s' |> a
          where
            s' =
                if Seq.length s < n
                then s
                else Seq.drop 1 s
        begin = Seq.empty
        done  = F.toList
    {-# INLINABLE lastN #-}

    -- | Returns 'True' if the container is empty, 'False' otherwise
    null :: Fold a Bool
    null = Fold (\_ _ -> False) True id
    {-# INLINABLE null #-}

    -- | Return the length of the container
    length :: Fold a Int
    length = genericLength
    {- Technically, 'length' is just 'genericLength' specialized to 'Int's.  I keep
       the two separate so that I can later provide an 'Int'-specialized
       implementation of 'length' for performance reasons like "GHC.List" does
       without breaking backwards compatibility.
    -}
    {-# INLINABLE length #-}

    -- | Returns 'True' if all elements are 'True', 'False' otherwise
    and :: Fold Bool Bool
    and = Fold (&&) True id
    {-# INLINABLE and #-}

    -- | Returns 'True' if any element is 'True', 'False' otherwise
    or :: Fold Bool Bool
    or = Fold (||) False id
    {-# INLINABLE or #-}

    {-| @(all predicate)@ returns 'True' if all elements satisfy the predicate,
        'False' otherwise
    -}
    all :: (a -> Bool) -> Fold a Bool
    all predicate = Fold (\x a -> x && predicate a) True id
    {-# INLINABLE all #-}

    {-| @(any predicate)@ returns 'True' if any element satisfies the predicate,
        'False' otherwise
    -}
    any :: (a -> Bool) -> Fold a Bool
    any predicate = Fold (\x a -> x || predicate a) False id
    {-# INLINABLE any #-}

    -- | Computes the sum of all elements
    sum :: Num a => Fold a a
    sum = Fold (+) 0 id
    {-# INLINABLE sum #-}

    -- | Computes the product of all elements
    product :: Num a => Fold a a
    product = Fold (*) 1 id
    {-# INLINABLE product #-}

    -- | Compute a numerically stable arithmetic mean of all elements
    mean :: Fractional a => Fold a a
    mean = Fold step begin done
      where
        begin = Pair 0 0
        step (Pair x n) y = let n' = n+1 in Pair (x + (y - x) /n') n'
        done (Pair x _) = x
    {-# INLINABLE mean #-}

    -- | Compute a numerically stable (population) variance over all elements
    variance :: Fractional a => Fold a a
    variance = Fold step begin done
      where
        begin = Pair3 0 0 0

        step (Pair3 n mean_ m2) x = Pair3 n' mean' m2'
          where
            n'     = n + 1
            mean'  = (n * mean_ + x) / (n + 1)
            delta  = x - mean_
            m2'    = m2 + delta * delta * n / (n + 1)

        done (Pair3 n _ m2) = m2 / n
    {-# INLINABLE variance #-}

    {-| Compute a numerically stable (population) standard deviation over all
        elements
    -}
    std :: Floating a => Fold a a
    std = sqrt variance
    {-# INLINABLE std #-}

    -- | Computes the maximum element
    maximum :: Ord a => Fold a (Maybe a)
    maximum = _Fold1 max
    {-# INLINABLE maximum #-}

    {-| Computes the maximum element with respect to the given comparison
        function
    -}
    maximumBy :: (a -> a -> Ordering) -> Fold a (Maybe a)
    maximumBy cmp = _Fold1 max'
      where
        max' x y = case cmp x y of
            GT -> x
            _  -> y
    {-# INLINABLE maximumBy #-}

    -- | Computes the minimum element
    minimum :: Ord a => Fold a (Maybe a)
    minimum = _Fold1 min
    {-# INLINABLE minimum #-}

    {-| Computes the minimum element with respect to the given comparison
        function
    -}
    minimumBy :: (a -> a -> Ordering) -> Fold a (Maybe a)
    minimumBy cmp = _Fold1 min'
      where
        min' x y = case cmp x y of
            GT -> y
            _  -> x
    {-# INLINABLE minimumBy #-}

    {-| @(elem a)@ returns 'True' if the container has an element equal to @a@,
        'False' otherwise
    -}
    elem :: Eq a => a -> Fold a Bool
    elem a = any (a ==)
    {-# INLINABLE elem #-}

    {-| @(notElem a)@ returns 'False' if the container has an element equal to @a@,
        'True' otherwise
    -}
    notElem :: Eq a => a -> Fold a Bool
    notElem a = all (a /=)
    {-# INLINABLE notElem #-}

    {-| @(find predicate)@ returns the first element that satisfies the predicate or
        'Nothing' if no element satisfies the predicate
    -}
    find :: (a -> Bool) -> Fold a (Maybe a)
    find predicate = Fold step Nothing' lazy
      where
        step x a = case x of
            Nothing' -> if predicate a then Just' a else Nothing'
            _        -> x
    {-# INLINABLE find #-}

    {-| @(index n)@ returns the @n@th element of the container, or 'Nothing' if the
        container has an insufficient number of elements
    -}
    index :: Int -> Fold a (Maybe a)
    index = genericIndex
    {-# INLINABLE index #-}

    {-| @(elemIndex a)@ returns the index of the first element that equals @a@, or
        'Nothing' if no element matches
    -}
    elemIndex :: Eq a => a -> Fold a (Maybe Int)
    elemIndex a = findIndex (a ==)
    {-# INLINABLE elemIndex #-}

    {-| @(findIndex predicate)@ returns the index of the first element that
        satisfies the predicate, or 'Nothing' if no element satisfies the predicate
    -}
    findIndex :: (a -> Bool) -> Fold a (Maybe Int)
    findIndex predicate = Fold step (Left' 0) hush
      where
        step x a = case x of
            Left' i ->
                if predicate a
                then Right' i
                else Left' (i + 1)
            _       -> x
    {-# INLINABLE findIndex #-}

    {-| @(lookup a)@ returns the element paired with the first matching item, or
        'Nothing' if none matches
    -}
    lookup :: Eq a => a -> Fold (a,b) (Maybe b)
    lookup a0 = Fold step Nothing' lazy
      where
        step x (a,b) = case x of
          Nothing' -> if a == a0
            then Just' b
            else Nothing'
          _ -> x
    {-# INLINABLE lookup #-}

    data Pair3 a b c = Pair3 !a !b !c

    -- | Pick a random element, using reservoir sampling
    random :: FoldM IO a (Maybe a)
    random = FoldM step begin done
      where
        begin = do
            g <- createSystemRandom
            return $! Pair3 g Nothing' (1 :: Int)

        step (Pair3 g Nothing'  _) a = return $! Pair3 g (Just' a) 2
        step (Pair3 g (Just' a) m) b = do
            n <- uniformR (1, m) g
            let c = if n == 1 then b else a
            return $! Pair3 g (Just' c) (m + 1)

        done (Pair3 _ ma _) = return (lazy ma)
    {-# INLINABLE random #-}

    data VectorState = Incomplete {-# UNPACK #-} !Int | Complete

    data RandomNState v a = RandomNState
        { _size      ::                !VectorState
        , _reservoir ::                !(Mutable v RealWorld a)
        , _position  :: {-# UNPACK #-} !Int
        , _gen       :: {-# UNPACK #-} !GenIO
        }

    -- | Pick several random elements, using reservoir sampling
    randomN :: Vector v a => Int -> FoldM IO a (Maybe (v a))
    randomN n = FoldM step begin done
      where
        step
            :: MVector (Mutable v) a
            => RandomNState v a -> a -> IO (RandomNState v a)
        step (RandomNState (Incomplete m) mv i g) a = do
            M.write mv m a
            let m' = m + 1
            let s  = if n <= m' then Complete else Incomplete m'
            return $! RandomNState s mv (i + 1) g
        step (RandomNState  Complete      mv i g) a = do
            r <- uniformR (0, i - 1) g
            if r < n
                then M.unsafeWrite mv r a
                else return ()
            return (RandomNState Complete mv (i + 1) g)

        begin = do
            mv  <- M.new n
            gen <- createSystemRandom
            let s = if n <= 0 then Complete else Incomplete 0
            return (RandomNState s mv 1 gen)

        done :: Vector v a => RandomNState v a -> IO (Maybe (v a))
        done (RandomNState (Incomplete _) _  _ _) = return Nothing
        done (RandomNState  Complete      mv _ _) = do
            v <- V.freeze mv
            return (Just v)

    -- | Converts an effectful function to a fold. Specialized version of 'sink'.
    mapM_ :: Monad m => (a -> m ()) -> FoldM m a ()
    mapM_ = sink
    {-# INLINABLE mapM_ #-}

    {-| Converts an effectful function to a fold

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

    sink ::  (Monoid w, Monad m) => (a -> m w) -> FoldM m a w
    sink act = FoldM step begin done  where
      done = return
      begin = return mempty
      step m a = do
        m' <- act a
        return $! mappend m m'
    {-# INLINABLE sink #-}

    -- | Like 'length', except with a more general 'Num' return value
    genericLength :: Num b => Fold a b
    genericLength = Fold (\n _ -> n + 1) 0 id
    {-# INLINABLE genericLength #-}

    -- | Like 'index', except with a more general 'Integral' argument
    genericIndex :: Integral i => i -> Fold a (Maybe a)
    genericIndex i = Fold step (Left' 0) done
      where
        step x a = case x of
            Left'  j -> if i == j then Right' a else Left' (j + 1)
            _        -> x
        done x = case x of
            Left'  _ -> Nothing
            Right' a -> Just a
    {-# INLINABLE genericIndex #-}

    -- | Fold all values into a list
    list :: Fold a [a]
    list = Fold (\x a -> x . (a:)) id ($ [])
    {-# INLINABLE list #-}

    -- | Fold all values into a list, in reverse order
    revList :: Fold a [a]
    revList = Fold (\x a -> a:x) [] id
    {-# INLINABLE revList #-}

    {-| /O(n log n)/.  Fold values into a list with duplicates removed, while
        preserving their first occurrences
    -}
    nub :: Ord a => Fold a [a]
    nub = Fold step (Pair Set.empty id) fin
      where
        step (Pair s r) a = if Set.member a s
          then Pair s r
          else Pair (Set.insert a s) (r . (a :))
        fin (Pair _ r) = r []
    {-# INLINABLE nub #-}

    {-| /O(n^2)/.  Fold values into a list with duplicates removed, while preserving
        their first occurrences
    -}
    eqNub :: Eq a => Fold a [a]
    eqNub = Fold step (Pair [] id) fin
      where
        step (Pair known r) a = if List.elem a known
          then Pair known r
          else Pair (a : known) (r . (a :))
        fin (Pair _ r) = r []
    {-# INLINABLE eqNub #-}

    -- | Fold values into a set
    set :: Ord a => Fold a (Set.Set a)
    set = Fold (flip Set.insert) Set.empty id
    {-# INLINABLE set #-}

    -- | Fold values into a hash-set
    hashSet :: (Eq a, Hashable a) => Fold a (HashSet.HashSet a)
    hashSet = Fold (flip HashSet.insert) HashSet.empty id
    {-# INLINABLE hashSet #-}

    {-|
    Fold pairs into a map.
    -}
    map :: Ord a => Fold (a, b) (Map.Map a b)
    map = Fold step begin done
      where
        begin = mempty
        step m (k, v) = Map.insert k v m
        done = id
    {-# INLINABLE map #-}

    {-|
    Fold pairs into a hash-map.
    -}
    hashMap :: (Eq a, Hashable a) => Fold (a, b) (HashMap.HashMap a b)
    hashMap = Fold step begin done
      where
        begin = mempty
        step m (k, v) = HashMap.insert k v m
        done = id
    {-# INLINABLE hashMap #-}

    -- | Fold all values into a vector
    vector :: Vector v a => Fold a (v a)
    vector = Fold step begin done
      where
        begin = VectorBuilder.Builder.empty

        step x a = x <> VectorBuilder.Builder.singleton a

        done = VectorBuilder.Vector.build
    {-# INLINABLE vector #-}

    maxChunkSize :: Int
    maxChunkSize = 8 * 1024 * 1024

    {-| Fold all values into a vector

        This is more efficient than `vector` but is impure
    -}
    vectorM :: (PrimMonad m, Vector v a) => FoldM m a (v a)
    vectorM = FoldM step begin done
      where
        begin = do
            mv <- M.unsafeNew 10
            return (Pair mv 0)
        step (Pair mv idx) a = do
            let len = M.length mv
            mv' <- if idx >= len
                then M.unsafeGrow mv (min len maxChunkSize)
                else return mv
            M.unsafeWrite mv' idx a
            return (Pair mv' (idx + 1))
        done (Pair mv idx) = do
            v <- V.freeze mv
            return (V.unsafeTake idx v)
    {-# INLINABLE vectorM #-}

    {- $utilities
        'purely' and 'impurely' allow you to write folds compatible with the @foldl@
        library without incurring a @foldl@ dependency.  Write your fold to accept
        three parameters corresponding to the step function, initial
        accumulator, and extraction function and then users can upgrade your
        function to accept a 'Fold' or 'FoldM' using the 'purely' or 'impurely'
        combinators.

        For example, the @pipes@ library implements @fold@ and @foldM@ functions in
        @Pipes.Prelude@ with the following type:

    > Pipes.Prelude.fold
    >     :: Monad m
    >     -> (x -> a -> x) -> x -> (x -> b) -> Producer a m () -> m b
    >
    > Pipes.Prelude.foldM
    >     :: Monad m
    >     => (x -> a -> m x) -> m x -> (x -> m b) -> Producer a m () -> m b

        Both @fold@ and @foldM@ is set up so that you can wrap them with either
        'purely' or 'impurely' to accept a 'Fold' or 'FoldM', respectively:

    > purely Pipes.Prelude.fold
    >     :: Monad m => Fold a b -> Producer a m () -> m b
    >
    > impurely Pipes.Prelude.foldM
    >     :: Monad m => FoldM m a b -> Producer a m () -> m b

        Other streaming libraries supporting 'purely' and 'impurely' include @io-streams@ and @streaming@.
        So for example we have:

    > purely System.IO.Streams.fold_
    >     :: Fold a b -> Streams.InputStream a -> IO b
    >
    > impurely System.IO.Streams.foldM_
    >     :: FoldM IO a b -> Streams.InputStream a -> IO b

        The @monotraversable@ package makes it convenient to apply a
        'Fold' or 'FoldM' to pure containers that do not allow
        a general 'Foldable' instance, like unboxed vectors:

    > purely ofoldlUnwrap
    >     :: MonoFoldable mono
    >     => Fold (Element mono) b -> mono -> b
    >
    > impurely ofoldMUnwrap
    >     :: MonoFoldable mono
    >     => FoldM m (Element mono) b -> mono -> m b
    -}

    -- | Upgrade a fold to accept the 'Fold' type
    purely :: (forall x . (x -> a -> x) -> x -> (x -> b) -> r) -> Fold a b -> r
    purely f (Fold step begin done) = f step begin done
    {-# INLINABLE purely #-}

    -- | Upgrade a more traditional fold to accept the `Fold` type
    purely_ :: (forall x . (x -> a -> x) -> x -> x) -> Fold a b -> b
    purely_ f (Fold step begin done) = done (f step begin)
    {-# INLINABLE purely_ #-}

    -- | Upgrade a monadic fold to accept the 'FoldM' type
    impurely
        :: (forall x . (x -> a -> m x) -> m x -> (x -> m b) -> r)
        -> FoldM m a b
        -> r
    impurely f (FoldM step begin done) = f step begin done
    {-# INLINABLE impurely #-}

    -- | Upgrade a more traditional monadic fold to accept the `FoldM` type
    impurely_
        :: Monad m
        => (forall x . (x -> a -> m x) -> m x -> m x) -> FoldM m a b -> m b
    impurely_ f (FoldM step begin done) = do
        x <- f step begin
        done x
    {-# INLINABLE impurely_ #-}

    {-| Generalize a `Fold` to a `FoldM`

    > generalize (pure r) = pure r
    >
    > generalize (f <*> x) = generalize f <*> generalize x
    -}
    generalize :: Monad m => Fold a b -> FoldM m a b
    generalize (Fold step begin done) = FoldM step' begin' done'
      where
        step' x a = return (step x a)
        begin'    = return  begin
        done' x   = return (done x)
    {-# INLINABLE generalize #-}

    {-| Simplify a pure `FoldM` to a `Fold`

    > simplify (pure r) = pure r
    >
    > simplify (f <*> x) = simplify f <*> simplify x
    -}
    simplify :: FoldM Identity a b -> Fold a b
    simplify (FoldM step begin done) = Fold step' begin' done'
      where
        step' x a = runIdentity (step x a)
        begin'    = runIdentity  begin
        done' x   = runIdentity (done x)
    {-# INLINABLE simplify #-}

    {- | Shift a 'FoldM' from one monad to another with a morphism such as 'lift' or 'liftIO';
         the effect is the same as 'Control.Monad.Morph.hoist'.
    -}
    hoists :: (forall x . m x -> n x) -> FoldM m a b -> FoldM n a b
    hoists phi (FoldM step begin done) = FoldM (\a b -> phi (step a b)) (phi begin) (phi . done)
    {-# INLINABLE hoists #-}

    {-| Allows to continue feeding a 'FoldM' even after passing it to a function
    that closes it.

    For pure 'Fold's, this is provided by the 'Control.Comonad.Comonad' instance.
    -}
    duplicateM :: Applicative m => FoldM m a b -> FoldM m a (FoldM m a b)
    duplicateM (FoldM step begin done) =
        FoldM step begin (\x -> pure (FoldM step (pure x) done))
    {-# INLINABLE duplicateM #-}

    {-| @_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.
     -}
    _Fold1 :: (a -> a -> a) -> Fold a (Maybe a)
    _Fold1 step = Fold step_ Nothing' lazy
      where
        step_ mx a = Just' (case mx of
            Nothing' -> a
            Just' x -> step x a)
    {-# INLINABLE _Fold1 #-}

    {-| @(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
    -}
    premap :: (a -> b) -> Fold b r -> Fold a r
    premap f (Fold step begin done) = Fold step' begin done
      where
        step' x a = step x (f a)
    {-# INLINABLE premap #-}

    {-| @(premapM f folder)@ returns a new 'FoldM' where f is applied to each input
        element

    > premapM return = id
    >
    > premapM (f <=< g) = premap g . premap f

    > premapM k (pure r) = pure r
    >
    > premapM k (f <*> x) = premapM k f <*> premapM k x
    -}
    premapM :: Monad m => (a -> m b) -> FoldM m b r -> FoldM m a r
    premapM f (FoldM step begin done) = FoldM step' begin done
      where
        step' x a = f a >>= step x
    {-# INLINABLE premapM #-}

    {-| @(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.

    > fold (prefilter p folder) list = fold folder (filter p list)

    >>> fold (prefilter (>5) Control.Foldl.sum) [1..10]
    40

    >>> fold Control.Foldl.sum (filter (>5) [1..10])
    40
    -}
    prefilter :: (a -> Bool) -> Fold a r -> Fold a r
    prefilter f (Fold step begin done) = Fold step' begin done
      where
        step' x a = if f a then step x a else x
    {-# INLINABLE prefilter #-}

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

    > foldM (prefilterM p folder) list = foldM folder (filter p list)
    -}
    prefilterM :: (Monad m) => (a -> m Bool) -> FoldM m a r -> FoldM m a r
    prefilterM f (FoldM step begin done) = FoldM step' begin done
      where
        step' x a = do
          use <- f a
          if use then step x a else return x
    {-# INLINABLE prefilterM #-}

    {-| A handler for the upstream input of a `Fold`

        Any lens, traversal, or prism will type-check as a `Handler`
    -}
    type Handler a b =
        forall x . (b -> Const (Dual (Endo x)) b) -> a -> Const (Dual (Endo x)) a

    {-| @(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
    -}
    handles :: Handler a b -> Fold b r -> Fold a r
    handles k (Fold step begin done) = Fold step' begin done
      where
        step' = flip (appEndo . getDual . getConst . k (Const . Dual . Endo . flip step))
    {-# INLINABLE handles #-}

    {- | @(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

    -}
    foldOver :: Handler s a -> Fold a b -> s -> b
    foldOver l (Fold step begin done) =
      done . flip appEndo begin . getDual . getConst . l (Const . Dual . Endo . flip step)
    {-# INLINABLE foldOver #-}

    {-|
    > instance Monad m => Monoid (EndoM m a) where
    >     mempty = EndoM return
    >     mappend (EndoM f) (EndoM g) = EndoM (f <=< g)
    -}
    newtype EndoM m a = EndoM { appEndoM :: a -> m a }

    instance Monad m => Semigroup (EndoM m a) where
        (EndoM f) <> (EndoM g) = EndoM (f <=< g)
        {-# INLINE (<>) #-}

    instance Monad m => Monoid (EndoM m a) where
        mempty = EndoM return
        {-# INLINE mempty #-}

        mappend = (<>)
        {-# INLINE mappend #-}

    {-| A Handler for the upstream input of `FoldM`

        Any lens, traversal, or prism will type-check as a `HandlerM`
    -}
    type HandlerM m a b =
        forall x . (b -> Const (Dual (EndoM m x)) b) -> a -> Const (Dual (EndoM m x)) a

    {-| @(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
    -}
    handlesM :: HandlerM m a b -> FoldM m b r -> FoldM m a r
    handlesM k (FoldM step begin done) = FoldM step' begin done
      where
        step' = flip (appEndoM . getDual . getConst . k (Const . Dual . EndoM . flip step))
    {-# INLINABLE handlesM #-}

    {- | @(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

    -}
    foldOverM :: Monad m => HandlerM m s a -> FoldM m a b -> s -> m b
    foldOverM l (FoldM step begin done) s = do
      b <- begin
      r <- (flip appEndoM b . getDual . getConst . l (Const . Dual . EndoM . flip step)) s
      done r
    {-# INLINABLE foldOverM #-}

    {-|
    > folded :: Foldable t => Fold (t a) a
    >
    > handles folded :: Foldable t => Fold a r -> Fold (t a) r
    -}
    folded
        :: (Contravariant f, Applicative f, Foldable t)
        => (a -> f a) -> (t a -> f (t a))
    folded k ts = contramap (\_ -> ()) (F.traverse_ k ts)
    {-# INLINABLE folded #-}

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

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

    -}
    filtered :: Monoid m => (a -> Bool) -> (a -> m) -> a -> m
    filtered p k x
        | p x = k x
        | otherwise = mempty
    {-# INLINABLE filtered #-}

    {-| Perform a 'Fold' while grouping the data according to a specified group
    projection function. Returns the folded result grouped as a map keyed by the
    group.

    -}
    groupBy :: Ord g => (a -> g) -> Fold a r -> Fold a (Map g r)
    groupBy grouper (Fold f i e) = Fold f' mempty (fmap e)
      where
        f' !m !a = alter (\o -> Just (f (fromMaybe i o) a)) (grouper a) m
    {-# INLINABLE groupBy #-}

    {-| Combine two folds into a fold over inputs for either of them.
    -}
    either :: Fold a1 b1 -> Fold a2 b2 -> Fold (Either a1 a2) (b1, b2)
    either l r = (,) <$> handles _Left l <*> handles _Right r
    {-# INLINABLE either #-}

    {-| Combine two monadic folds into a fold over inputs for either of them.
    -}
    eitherM :: Monad m => FoldM m a1 b1 -> FoldM m a2 b2 -> FoldM m (Either a1 a2) (b1, b2)
    eitherM l r = (,) <$> handlesM _Left l <*> handlesM _Right r
    {-# INLINABLE eitherM #-}

    {- $reexports
        @Control.Monad.Primitive@ re-exports the 'PrimMonad' type class

        @Data.Foldable@ re-exports the 'Foldable' type class

        @Data.Vector.Generic@ re-exports the 'Vector' type class
    -}