{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE CPP #-}
{-# LANGUAGE MultiParamTypeClasses #-}

{-| This module provides a `Fold1` type that is a \"non-empty\" analog of the
    `Fold` type, meaning that it requires at least one input element in order to
    produce a result

    This module does not provide all of the same utilities as the
    "Control.Foldl" module.  Instead, this module only provides the utilities
    which can make use of the non-empty input guarantee (e.g. `head`).  For
    all other utilities you can convert them from the equivalent `Fold` using
    `fromFold`.

    Import this module qualified to avoid clashing with the Prelude:

>>> import qualified Control.Foldl.NonEmpty as Foldl1

    Use 'fold1' to apply a 'Fold1' to a non-empty list:

>>> Foldl1.fold1 Foldl1.last (1 :| [2..10])
10

-}

module Control.Foldl.NonEmpty (
    -- * Fold Types
      Fold1(.., Fold1_)

    -- * Folding
    , Control.Foldl.NonEmpty.fold1

    -- * Conversion between Fold and Fold1
    , fromFold
    , toFold

    -- * Folds
    , sconcat
    , head
    , last
    , maximum
    , maximumBy
    , minimum
    , minimumBy

    -- ** Non-empty Container Folds
    , nonEmpty

    -- * Utilities
    , purely
    , purely_
    , premap
    , FromMaybe(..)
    , Handler1
    , handles
    , foldOver
    , folded1
    , nest
    ) where

import Control.Applicative (liftA2, Const(..))
import Control.Arrow (Arrow (..), ArrowChoice (..))
import Control.Category (Category ())
import qualified Control.Category
import Control.Comonad (Comonad(..))
import Control.Foldl (Fold(..))
import Control.Foldl.Internal (Either'(..))
import Data.List.NonEmpty (NonEmpty(..))
import Data.Monoid (Dual(..))
import Data.Functor.Apply (Apply (..))
import Data.Functor.Extend (Extend (..))
import Data.Profunctor
import Data.Profunctor.Sieve (Cosieve(..))
import Data.Semigroup.Foldable (Foldable1(..), traverse1_)
import Data.Semigroupoid (Semigroupoid (..))
import Data.Functor.Contravariant (Contravariant(..))

import Prelude hiding (head, last, minimum, maximum)

import qualified Control.Foldl as Foldl

{- $setup

>>> import qualified Control.Foldl.NonEmpty as Foldl1
>>> import qualified Data.List.NonEmpty as NonEmpty
>>> import Data.Functor.Apply (Apply(..))
>>> import Data.Semigroup.Traversable (Traversable1(..))
>>> import Data.Monoid (Sum(..))

>>> _2 f (x, y) = fmap (\i -> (x, i)) (f y)

>>> both1 f (x, y) = (,) <$> f x <.> f y

-}

{-| A `Fold1` is like a `Fold` except that it consumes at least one input
    element
-}
data Fold1 a b = Fold1 (a -> Fold a b)

{-| @Fold1_@ is an alternative to the @Fold1@ constructor if you need to
    explicitly work with an initial, step and extraction function.

    @Fold1_@ is similar to the @Fold@ constructor, which also works with an
    initial, step and extraction function. However, note that @Fold@ takes the
    step function as the first argument and the initial accumulator as the
    second argument, whereas @Fold1_@ takes them in swapped order:

    @Fold1_ @ @ initial @ @ step @ @ extract@

    While @Fold@ resembles 'Prelude.foldl', @Fold1_@ resembles
    'Data.Foldable1.foldlMap1'.
-}
pattern Fold1_ :: forall a b. forall x. (a -> x) -> (x -> a -> x) -> (x -> b) -> Fold1 a b
pattern $mFold1_ :: forall {r} {a} {b}.
Fold1 a b
-> (forall {x}. (a -> x) -> (x -> a -> x) -> (x -> b) -> r)
-> ((# #) -> r)
-> r
$bFold1_ :: forall a b x. (a -> x) -> (x -> a -> x) -> (x -> b) -> Fold1 a b
Fold1_ begin step done <- (toFold_ -> (begin, step, done))
  where Fold1_ a -> x
begin x -> a -> x
step x -> b
done = (a -> Fold a b) -> Fold1 a b
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 ((a -> Fold a b) -> Fold1 a b) -> (a -> Fold a b) -> Fold1 a b
forall a b. (a -> b) -> a -> b
$ \a
a -> (x -> a -> x) -> x -> (x -> b) -> Fold a b
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold x -> a -> x
step (a -> x
begin a
a) x -> b
done
#if __GLASGOW_HASKELL__ >= 902
{-# INLINABLE Fold1_ #-}
#endif
{-# COMPLETE Fold1_ :: Fold1 #-}

toFold_ :: Fold1 a b -> (a -> Fold a b, Fold a b -> a -> Fold a b, Fold a b -> b)
toFold_ :: forall a b.
Fold1 a b
-> (a -> Fold a b, Fold a b -> a -> Fold a b, Fold a b -> b)
toFold_ (Fold1 (a -> Fold a b
f :: a -> Fold a b)) = (a -> Fold a b
begin', Fold a b -> a -> Fold a b
step', Fold a b -> b
done')
  where
    done' :: Fold a b -> b
    done' :: Fold a b -> b
done' (Fold x -> a -> x
_step x
begin x -> b
done) = x -> b
done x
begin

    step' :: Fold a b -> a -> Fold a b
    step' :: Fold a b -> a -> Fold a b
step' (Fold x -> a -> x
step x
begin x -> b
done) a
a = (x -> a -> x) -> x -> (x -> b) -> Fold a b
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold x -> a -> x
step (x -> a -> x
step x
begin a
a) x -> b
done

    begin' :: a -> Fold a b
    begin' :: a -> Fold a b
begin' = a -> Fold a b
f
{-# INLINABLE toFold_ #-}

instance Functor (Fold1 a) where
    fmap :: forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
fmap a -> b
f (Fold1 a -> Fold a a
k) = (a -> Fold a b) -> Fold1 a b
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 ((Fold a a -> Fold a b) -> (a -> Fold a a) -> a -> Fold a b
forall a b. (a -> b) -> (a -> a) -> a -> b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((a -> b) -> Fold a a -> Fold a b
forall a b. (a -> b) -> Fold a a -> Fold a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f) a -> Fold a a
k)
    {-# INLINE fmap #-}

instance Profunctor Fold1 where
    lmap :: forall a b c. (a -> b) -> Fold1 b c -> Fold1 a c
lmap = (a -> b) -> Fold1 b c -> Fold1 a c
forall a b c. (a -> b) -> Fold1 b c -> Fold1 a c
premap
    {-# INLINE lmap #-}

    rmap :: forall b c a. (b -> c) -> Fold1 a b -> Fold1 a c
rmap = (b -> c) -> Fold1 a b -> Fold1 a c
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap
    {-# INLINE rmap #-}

instance Choice Fold1 where
    right' :: forall a b c. Fold1 a b -> Fold1 (Either c a) (Either c b)
right' = Fold1 a b -> Fold1 (Either c a) (Either c b)
forall (f :: * -> *) a b. Apply f => Fold1 a b -> Fold1 (f a) (f b)
nest
    {-# INLINE right' #-}

instance Closed Fold1 where
    closed :: forall a b x. Fold1 a b -> Fold1 (x -> a) (x -> b)
closed = Fold1 a b -> Fold1 (x -> a) (x -> b)
forall (f :: * -> *) a b. Apply f => Fold1 a b -> Fold1 (f a) (f b)
nest
    {-# INLINE closed #-}

instance Cosieve Fold1 NonEmpty where
    cosieve :: forall a b. Fold1 a b -> NonEmpty a -> b
cosieve = Fold1 a b -> NonEmpty a -> b
forall (f :: * -> *) a b. Foldable1 f => Fold1 a b -> f a -> b
Control.Foldl.NonEmpty.fold1
    {-# INLINE cosieve #-}

instance Applicative (Fold1 a) where
    pure :: forall a. a -> Fold1 a a
pure a
b = (a -> Fold a a) -> Fold1 a a
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (Fold a a -> a -> Fold a a
forall a. a -> a -> a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> Fold a a
forall a. a -> Fold a a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
b))
    {-# INLINE pure #-}

    Fold1 a -> Fold a (a -> b)
l <*> :: forall a b. Fold1 a (a -> b) -> Fold1 a a -> Fold1 a b
<*> Fold1 a -> Fold a a
r = (a -> Fold a b) -> Fold1 a b
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 ((Fold a (a -> b) -> Fold a a -> Fold a b)
-> (a -> Fold a (a -> b)) -> (a -> Fold a a) -> a -> Fold a b
forall a b c. (a -> b -> c) -> (a -> a) -> (a -> b) -> a -> c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 Fold a (a -> b) -> Fold a a -> Fold a b
forall a b. Fold a (a -> b) -> Fold a a -> Fold a b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
(<*>) a -> Fold a (a -> b)
l a -> Fold a a
r)
    {-# INLINE (<*>) #-}

instance Extend (Fold1 a) where
    duplicated :: forall a. Fold1 a a -> Fold1 a (Fold1 a a)
duplicated (Fold1 a -> Fold a a
f) = (a -> Fold a (Fold1 a a)) -> Fold1 a (Fold1 a a)
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 ((a -> Fold a (Fold1 a a)) -> Fold1 a (Fold1 a a))
-> (a -> Fold a (Fold1 a a)) -> Fold1 a (Fold1 a a)
forall a b. (a -> b) -> a -> b
$ (Fold a a -> Fold1 a a) -> Fold a (Fold a a) -> Fold a (Fold1 a a)
forall a b. (a -> b) -> Fold a a -> Fold a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Fold a a -> Fold1 a a
forall a b. Fold a b -> Fold1 a b
fromFold (Fold a (Fold a a) -> Fold a (Fold1 a a))
-> (a -> Fold a (Fold a a)) -> a -> Fold a (Fold1 a a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Fold a a -> Fold a (Fold a a)
forall a. Fold a a -> Fold a (Fold a a)
forall (w :: * -> *) a. Extend w => w a -> w (w a)
duplicated (Fold a a -> Fold a (Fold a a))
-> (a -> Fold a a) -> a -> Fold a (Fold a a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Fold a a
f
    {-# INLINE duplicated #-}

instance Semigroup b => Semigroup (Fold1 a b) where
    <> :: Fold1 a b -> Fold1 a b -> Fold1 a b
(<>) = (b -> b -> b) -> Fold1 a b -> Fold1 a b -> Fold1 a b
forall a b c. (a -> b -> c) -> Fold1 a a -> Fold1 a b -> Fold1 a c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 b -> b -> b
forall a. Semigroup a => a -> a -> a
(<>)
    {-# INLINE (<>) #-}

instance Monoid b => Monoid (Fold1 a b) where
    mempty :: Fold1 a b
mempty = b -> Fold1 a b
forall a. a -> Fold1 a a
forall (f :: * -> *) a. Applicative f => a -> f a
pure b
forall a. Monoid a => a
mempty
    {-# INLINE mempty #-}

    mappend :: Fold1 a b -> Fold1 a b -> Fold1 a b
mappend = Fold1 a b -> Fold1 a b -> Fold1 a b
forall a. Semigroup a => a -> a -> a
(<>)
    {-# INLINE mappend #-}

instance Semigroupoid Fold1 where
    o :: forall j k1 i. Fold1 j k1 -> Fold1 i j -> Fold1 i k1
o (Fold1 j -> Fold j k1
l1) (Fold1 i -> Fold i j
r1) = (i -> Fold i k1) -> Fold1 i k1
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 i -> Fold i k1
f1
      where
        f1 :: i -> Fold i k1
f1 i
a = let r :: Fold i j
r = i -> Fold i j
r1 i
a
                   l :: Fold j k1
l = j -> Fold j k1
l1 (j -> Fold j k1) -> j -> Fold j k1
forall a b. (a -> b) -> a -> b
$ Fold i j -> j
forall a. Fold i a -> a
forall (w :: * -> *) a. Comonad w => w a -> a
extract Fold i j
r
               in Fold j k1 -> Fold i j -> Fold i k1
forall j k1 i. Fold j k1 -> Fold i j -> Fold i k1
forall {k} (c :: k -> k -> *) (j :: k) (k1 :: k) (i :: k).
Semigroupoid c =>
c j k1 -> c i j -> c i k1
o Fold j k1
l Fold i j
r
    {-# INLINE o #-}

instance Category Fold1 where
    . :: forall j k1 i. Fold1 j k1 -> Fold1 i j -> Fold1 i k1
(.) = Fold1 b c -> Fold1 a b -> Fold1 a c
forall j k1 i. Fold1 j k1 -> Fold1 i j -> Fold1 i k1
forall {k} (c :: k -> k -> *) (j :: k) (k1 :: k) (i :: k).
Semigroupoid c =>
c j k1 -> c i j -> c i k1
o
    {-# INLINE (.) #-}

    id :: forall a. Fold1 a a
id = Fold1 a a
forall a. Fold1 a a
last
    {-# INLINE id #-}

instance Strong Fold1 where
    first' :: forall a b c. Fold1 a b -> Fold1 (a, c) (b, c)
first' Fold1 a b
f = (,) (b -> c -> (b, c)) -> Fold1 (a, c) b -> Fold1 (a, c) (c -> (b, c))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> ((a, c) -> a) -> Fold1 a b -> Fold1 (a, c) b
forall a b c. (a -> b) -> Fold1 b c -> Fold1 a c
forall (p :: * -> * -> *) a b c.
Profunctor p =>
(a -> b) -> p b c -> p a c
lmap (a, c) -> a
forall a b. (a, b) -> a
fst Fold1 a b
f Fold1 (a, c) (c -> (b, c)) -> Fold1 (a, c) c -> Fold1 (a, c) (b, c)
forall a b.
Fold1 (a, c) (a -> b) -> Fold1 (a, c) a -> Fold1 (a, c) b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> ((a, c) -> c) -> Fold1 c c -> Fold1 (a, c) c
forall a b c. (a -> b) -> Fold1 b c -> Fold1 a c
forall (p :: * -> * -> *) a b c.
Profunctor p =>
(a -> b) -> p b c -> p a c
lmap (a, c) -> c
forall a b. (a, b) -> b
snd Fold1 c c
forall a. Fold1 a a
last
    {-# INLINE first' #-}

instance Arrow Fold1 where
    arr :: forall b c. (b -> c) -> Fold1 b c
arr b -> c
f = b -> c
f (b -> c) -> Fold1 b b -> Fold1 b c
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Fold1 b b
forall a. Fold1 a a
last
    {-# INLINE arr #-}

    first :: forall a b c. Fold1 a b -> Fold1 (a, c) (b, c)
first = Fold1 b c -> Fold1 (b, d) (c, d)
forall a b c. Fold1 a b -> Fold1 (a, c) (b, c)
forall (p :: * -> * -> *) a b c.
Strong p =>
p a b -> p (a, c) (b, c)
first'
    {-# INLINE first #-}

instance ArrowChoice Fold1 where
    left :: forall a b c. Fold1 a b -> Fold1 (Either a c) (Either b c)
left = Fold1 b c -> Fold1 (Either b d) (Either c d)
forall a b c. Fold1 a b -> Fold1 (Either a c) (Either b c)
forall (p :: * -> * -> *) a b c.
Choice p =>
p a b -> p (Either a c) (Either b c)
left'
    {-# INLINE left #-}

instance Num b => Num (Fold1 a b) where
    fromInteger :: Integer -> Fold1 a b
fromInteger = b -> Fold1 a b
forall a. a -> Fold1 a a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (b -> Fold1 a b) -> (Integer -> b) -> Integer -> Fold1 a b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Integer -> b
forall a. Num a => Integer -> a
fromInteger
    {-# INLINE fromInteger #-}

    negate :: Fold1 a b -> Fold1 a b
negate = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Num a => a -> a
negate
    {-# INLINE negate #-}

    abs :: Fold1 a b -> Fold1 a b
abs = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Num a => a -> a
abs
    {-# INLINE abs #-}

    signum :: Fold1 a b -> Fold1 a b
signum = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Num a => a -> a
signum
    {-# INLINE signum #-}

    + :: Fold1 a b -> Fold1 a b -> Fold1 a b
(+) = (b -> b -> b) -> Fold1 a b -> Fold1 a b -> Fold1 a b
forall a b c. (a -> b -> c) -> Fold1 a a -> Fold1 a b -> Fold1 a c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 b -> b -> b
forall a. Num a => a -> a -> a
(+)
    {-# INLINE (+) #-}

    * :: Fold1 a b -> Fold1 a b -> Fold1 a b
(*) = (b -> b -> b) -> Fold1 a b -> Fold1 a b -> Fold1 a b
forall a b c. (a -> b -> c) -> Fold1 a a -> Fold1 a b -> Fold1 a c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 b -> b -> b
forall a. Num a => a -> a -> a
(*)
    {-# INLINE (*) #-}

    (-) = (b -> b -> b) -> Fold1 a b -> Fold1 a b -> Fold1 a b
forall a b c. (a -> b -> c) -> Fold1 a a -> Fold1 a b -> Fold1 a c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (-)
    {-# INLINE (-) #-}

instance Fractional b => Fractional (Fold1 a b) where
    fromRational :: Rational -> Fold1 a b
fromRational = b -> Fold1 a b
forall a. a -> Fold1 a a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (b -> Fold1 a b) -> (Rational -> b) -> Rational -> Fold1 a b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Rational -> b
forall a. Fractional a => Rational -> a
fromRational
    {-# INLINE fromRational #-}

    recip :: Fold1 a b -> Fold1 a b
recip = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Fractional a => a -> a
recip
    {-# INLINE recip #-}

    / :: Fold1 a b -> Fold1 a b -> Fold1 a b
(/) = (b -> b -> b) -> Fold1 a b -> Fold1 a b -> Fold1 a b
forall a b c. (a -> b -> c) -> Fold1 a a -> Fold1 a b -> Fold1 a c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 b -> b -> b
forall a. Fractional a => a -> a -> a
(/)
    {-# INLINE (/) #-}

instance Floating b => Floating (Fold1 a b) where
    pi :: Fold1 a b
pi = b -> Fold1 a b
forall a. a -> Fold1 a a
forall (f :: * -> *) a. Applicative f => a -> f a
pure b
forall a. Floating a => a
pi
    {-# INLINE pi #-}

    exp :: Fold1 a b -> Fold1 a b
exp = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
exp
    {-# INLINE exp #-}

    sqrt :: Fold1 a b -> Fold1 a b
sqrt = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
sqrt
    {-# INLINE sqrt #-}

    log :: Fold1 a b -> Fold1 a b
log = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
log
    {-# INLINE log #-}

    sin :: Fold1 a b -> Fold1 a b
sin = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
sin
    {-# INLINE sin #-}

    tan :: Fold1 a b -> Fold1 a b
tan = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
tan
    {-# INLINE tan #-}

    cos :: Fold1 a b -> Fold1 a b
cos = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
cos
    {-# INLINE cos #-}

    asin :: Fold1 a b -> Fold1 a b
asin = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
asin
    {-# INLINE asin #-}

    atan :: Fold1 a b -> Fold1 a b
atan = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
atan
    {-# INLINE atan #-}

    acos :: Fold1 a b -> Fold1 a b
acos = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
acos
    {-# INLINE acos #-}

    sinh :: Fold1 a b -> Fold1 a b
sinh = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
sinh
    {-# INLINE sinh #-}

    tanh :: Fold1 a b -> Fold1 a b
tanh = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
tanh
    {-# INLINE tanh #-}

    cosh :: Fold1 a b -> Fold1 a b
cosh = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
cosh
    {-# INLINE cosh #-}

    asinh :: Fold1 a b -> Fold1 a b
asinh = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
asinh
    {-# INLINE asinh #-}

    atanh :: Fold1 a b -> Fold1 a b
atanh = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
atanh
    {-# INLINE atanh #-}

    acosh :: Fold1 a b -> Fold1 a b
acosh = (b -> b) -> Fold1 a b -> Fold1 a b
forall a b. (a -> b) -> Fold1 a a -> Fold1 a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap b -> b
forall a. Floating a => a -> a
acosh
    {-# INLINE acosh #-}

    ** :: Fold1 a b -> Fold1 a b -> Fold1 a b
(**) = (b -> b -> b) -> Fold1 a b -> Fold1 a b -> Fold1 a b
forall a b c. (a -> b -> c) -> Fold1 a a -> Fold1 a b -> Fold1 a c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 b -> b -> b
forall a. Floating a => a -> a -> a
(**)
    {-# INLINE (**) #-}

    logBase :: Fold1 a b -> Fold1 a b -> Fold1 a b
logBase = (b -> b -> b) -> Fold1 a b -> Fold1 a b -> Fold1 a b
forall a b c. (a -> b -> c) -> Fold1 a a -> Fold1 a b -> Fold1 a c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 b -> b -> b
forall a. Floating a => a -> a -> a
logBase
    {-# INLINE logBase #-}

-- | Apply a strict left `Fold1` to a `NonEmpty` list
fold1 :: Foldable1 f => Fold1 a b -> f a -> b
fold1 :: forall (f :: * -> *) a b. Foldable1 f => Fold1 a b -> f a -> b
fold1 (Fold1 a -> Fold a b
k) f a
as1 = Fold a b -> [a] -> b
forall (f :: * -> *) a b. Foldable f => Fold a b -> f a -> b
Foldl.fold (a -> Fold a b
k a
a) [a]
as
  where
    a
a :| [a]
as = f a -> NonEmpty a
forall a. f a -> NonEmpty a
forall (t :: * -> *) a. Foldable1 t => t a -> NonEmpty a
toNonEmpty f a
as1
{-# INLINABLE fold1 #-}

-- | Promote any `Fold` to an equivalent `Fold1`
fromFold :: Fold a b -> Fold1 a b
fromFold :: forall a b. Fold a b -> Fold1 a b
fromFold (Fold x -> a -> x
step x
begin x -> b
done) = (a -> Fold a b) -> Fold1 a b
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (\a
a -> (x -> a -> x) -> x -> (x -> b) -> Fold a b
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold x -> a -> x
step (x -> a -> x
step x
begin a
a) x -> b
done)
{-# INLINABLE fromFold #-}

-- | Promote any `Fold1` to an equivalent `Fold`
toFold :: Fold1 a b -> Fold a (Maybe b)
toFold :: forall a b. Fold1 a b -> Fold a (Maybe b)
toFold (Fold1 a -> Fold a b
k0) = (Either' (a -> Fold a b) (Fold a b)
 -> a -> Either' (a -> Fold a b) (Fold a b))
-> Either' (a -> Fold a b) (Fold a b)
-> (Either' (a -> Fold a b) (Fold a b) -> Maybe b)
-> Fold a (Maybe b)
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold Either' (a -> Fold a b) (Fold a b)
-> a -> Either' (a -> Fold a b) (Fold a b)
forall {a} {b} {a}.
Either' (a -> Fold a b) (Fold a b) -> a -> Either' a (Fold a b)
step Either' (a -> Fold a b) (Fold a b)
forall {b}. Either' (a -> Fold a b) b
begin Either' (a -> Fold a b) (Fold a b) -> Maybe b
forall {a} {a} {a}. Either' a (Fold a a) -> Maybe a
done
  where
    begin :: Either' (a -> Fold a b) b
begin = (a -> Fold a b) -> Either' (a -> Fold a b) b
forall a b. a -> Either' a b
Left' a -> Fold a b
k0

    step :: Either' (a -> Fold a b) (Fold a b) -> a -> Either' a (Fold a b)
step (Left' a -> Fold a b
k) a
a = Fold a b -> Either' a (Fold a b)
forall a b. b -> Either' a b
Right' (a -> Fold a b
k a
a)
    step (Right' (Fold x -> a -> x
step' x
begin' x -> b
done')) a
a =
        Fold a b -> Either' a (Fold a b)
forall a b. b -> Either' a b
Right' ((x -> a -> x) -> x -> (x -> b) -> Fold a b
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold x -> a -> x
step' (x -> a -> x
step' x
begin' a
a) x -> b
done')

    done :: Either' a (Fold a a) -> Maybe a
done (Right' (Fold x -> a -> x
_ x
begin' x -> a
done')) = a -> Maybe a
forall a. a -> Maybe a
Just (x -> a
done' x
begin')
    done (Left' a
_) = Maybe a
forall a. Maybe a
Nothing
{-# INLINABLE toFold #-}

-- | Fold all values within a non-empty container into a `NonEmpty` list
nonEmpty :: Fold1 a (NonEmpty a)
nonEmpty :: forall a. Fold1 a (NonEmpty a)
nonEmpty = (a -> Fold a (NonEmpty a)) -> Fold1 a (NonEmpty a)
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (\a
a -> ([a] -> NonEmpty a) -> Fold a [a] -> Fold a (NonEmpty a)
forall a b. (a -> b) -> Fold a a -> Fold a b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (a
a a -> [a] -> NonEmpty a
forall a. a -> [a] -> NonEmpty a
:|) Fold a [a]
forall a. Fold a [a]
Foldl.list)
{-# INLINEABLE nonEmpty #-}

-- | Fold all values within a non-empty container using (`<>`)
sconcat :: Semigroup a => Fold1 a a
sconcat :: forall a. Semigroup a => Fold1 a a
sconcat = (a -> Fold a a) -> Fold1 a a
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (\a
begin -> (a -> a -> a) -> a -> (a -> a) -> Fold a a
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold a -> a -> a
forall a. Semigroup a => a -> a -> a
(<>) a
begin a -> a
forall a. a -> a
id)
{-# INLINABLE sconcat #-}

-- | Get the first element of a non-empty container
head :: Fold1 a a
head :: forall a. Fold1 a a
head = (a -> Fold a a) -> Fold1 a a
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (\a
begin -> (a -> a -> a) -> a -> (a -> a) -> Fold a a
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold a -> a -> a
forall {p} {p}. p -> p -> p
step a
begin a -> a
forall a. a -> a
id)
  where
    step :: p -> p -> p
step p
a p
_ = p
a
{-# INLINABLE head #-}

-- | Get the last element of a non-empty container
last :: Fold1 a a
last :: forall a. Fold1 a a
last = (a -> Fold a a) -> Fold1 a a
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (\a
begin -> (a -> a -> a) -> a -> (a -> a) -> Fold a a
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold a -> a -> a
forall {p} {p}. p -> p -> p
step a
begin a -> a
forall a. a -> a
id)
  where
    step :: p -> p -> p
step p
_ p
a = p
a
{-# INLINABLE last #-}

-- | Computes the maximum element
maximum :: Ord a => Fold1 a a
maximum :: forall a. Ord a => Fold1 a a
maximum = (a -> Fold a a) -> Fold1 a a
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (\a
begin -> (a -> a -> a) -> a -> (a -> a) -> Fold a a
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold a -> a -> a
forall a. Ord a => a -> a -> a
max a
begin a -> a
forall a. a -> a
id)
{-# INLINABLE maximum #-}

-- | Computes the maximum element with respect to the given comparison function
maximumBy :: (a -> a -> Ordering) -> Fold1 a a
maximumBy :: forall a. (a -> a -> Ordering) -> Fold1 a a
maximumBy a -> a -> Ordering
cmp = (a -> Fold a a) -> Fold1 a a
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (\a
begin -> (a -> a -> a) -> a -> (a -> a) -> Fold a a
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold a -> a -> a
max' a
begin a -> a
forall a. a -> a
id)
  where
    max' :: a -> a -> a
max' a
x a
y = case a -> a -> Ordering
cmp a
x a
y of
        Ordering
GT -> a
x
        Ordering
_  -> a
y
{-# INLINABLE maximumBy #-}

-- | Computes the minimum element
minimum :: Ord a => Fold1 a a
minimum :: forall a. Ord a => Fold1 a a
minimum = (a -> Fold a a) -> Fold1 a a
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (\a
begin -> (a -> a -> a) -> a -> (a -> a) -> Fold a a
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold a -> a -> a
forall a. Ord a => a -> a -> a
min a
begin a -> a
forall a. a -> a
id)
{-# INLINABLE minimum #-}

-- | Computes the minimum element with respect to the given comparison function
minimumBy :: (a -> a -> Ordering) -> Fold1 a a
minimumBy :: forall a. (a -> a -> Ordering) -> Fold1 a a
minimumBy a -> a -> Ordering
cmp = (a -> Fold a a) -> Fold1 a a
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 (\a
begin -> (a -> a -> a) -> a -> (a -> a) -> Fold a a
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
Fold a -> a -> a
min' a
begin a -> a
forall a. a -> a
id)
  where
    min' :: a -> a -> a
min' a
x a
y = case a -> a -> Ordering
cmp a
x a
y of
        Ordering
GT -> a
y
        Ordering
_  -> a
x
{-# INLINABLE minimumBy #-}

-- | Upgrade a fold to accept the 'Fold1' type
purely :: (forall x . (a -> x) -> (x -> a -> x) -> (x -> b) -> r) -> Fold1 a b -> r
purely :: forall a b r.
(forall x. (a -> x) -> (x -> a -> x) -> (x -> b) -> r)
-> Fold1 a b -> r
purely forall x. (a -> x) -> (x -> a -> x) -> (x -> b) -> r
f (Fold1_ a -> x
begin x -> a -> x
step x -> b
done) = (a -> x) -> (x -> a -> x) -> (x -> b) -> r
forall x. (a -> x) -> (x -> a -> x) -> (x -> b) -> r
f a -> x
begin x -> a -> x
step x -> b
done
{-# INLINABLE purely #-}

-- | Upgrade a more traditional fold to accept the `Fold1` type
purely_ :: (forall x . (a -> x) -> (x -> a -> x) -> x) -> Fold1 a b -> b
purely_ :: forall a b.
(forall x. (a -> x) -> (x -> a -> x) -> x) -> Fold1 a b -> b
purely_ forall x. (a -> x) -> (x -> a -> x) -> x
f (Fold1_ a -> x
begin x -> a -> x
step x -> b
done) = x -> b
done ((a -> x) -> (x -> a -> x) -> x
forall x. (a -> x) -> (x -> a -> x) -> x
f a -> x
begin x -> a -> x
step)
{-# INLINABLE purely_ #-}

{-| @(premap f folder)@ returns a new 'Fold1' where f is applied at each step

> Foldl1.fold1 (premap f folder) list = Foldl1.fold1 folder (NonEmpty.map f list)

>>> Foldl1.fold1 (premap Sum Foldl1.sconcat) (1 :| [2..10])
Sum {getSum = 55}

>>> Foldl1.fold1 Foldl1.sconcat $ NonEmpty.map Sum (1 :| [2..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) -> Fold1 b r -> Fold1 a r
premap :: forall a b c. (a -> b) -> Fold1 b c -> Fold1 a c
premap a -> b
f (Fold1 b -> Fold b r
k) = (a -> Fold a r) -> Fold1 a r
forall a b. (a -> Fold a b) -> Fold1 a b
Fold1 a -> Fold a r
k'
  where
    k' :: a -> Fold a r
k' a
a = (a -> b) -> Fold b r -> Fold a r
forall a b c. (a -> b) -> Fold b c -> Fold a c
forall (p :: * -> * -> *) a b c.
Profunctor p =>
(a -> b) -> p b c -> p a c
lmap a -> b
f (b -> Fold b r
k (a -> b
f a
a))
{-# INLINABLE premap #-}

{-|
> instance Monad m => Semigroup (FromMaybe m a) where
>     mappend (FromMaybe f) (FromMaybe g) = FromMaybeM (f . Just . g)
-}
newtype FromMaybe b = FromMaybe { forall b. FromMaybe b -> Maybe b -> b
appFromMaybe :: Maybe b -> b }

instance Semigroup (FromMaybe b) where
    FromMaybe Maybe b -> b
f <> :: FromMaybe b -> FromMaybe b -> FromMaybe b
<> FromMaybe Maybe b -> b
g = (Maybe b -> b) -> FromMaybe b
forall b. (Maybe b -> b) -> FromMaybe b
FromMaybe (Maybe b -> b
f (Maybe b -> b) -> (Maybe b -> Maybe b) -> Maybe b -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (b -> Maybe b
forall a. a -> Maybe a
Just (b -> Maybe b) -> b -> Maybe b
forall a b. (a -> b) -> a -> b
$!) (b -> Maybe b) -> (Maybe b -> b) -> Maybe b -> Maybe b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Maybe b -> b
g)
    {-# INLINE (<>) #-}

{-| A handler for the upstream input of a `Fold1`

    This is compatible with van Laarhoven optics as defined in the lens package.
    Any lens, fold1 or traversal1 will type-check as a `Handler1`.
-}
type Handler1 a b =
    forall x. (b -> Const (Dual (FromMaybe x)) b) -> a -> Const (Dual (FromMaybe x)) a

{-| @(handles t folder)@ transforms the input of a `Fold1` using a Lens,
    Traversal1, or Fold1 optic:

> handles _1        :: Fold1 a r -> Fold1 (a, b) r
> handles traverse1 :: Traversable1 t => Fold1 a r -> Fold1 (t a) r
> handles folded1   :: Foldable1    t => Fold1 a r -> Fold1 (t a) r

>>> Foldl1.fold1 (handles traverse1 Foldl1.nonEmpty) $ (1 :| [2..4]) :| [ 5 :| [6,7], 8 :| [9,10] ]
1 :| [2,3,4,5,6,7,8,9,10]

>>> Foldl1.fold1 (handles _2 Foldl1.sconcat) $ (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 :: forall a b r. Handler1 a b -> Fold1 b r -> Fold1 a r
handles :: forall a b r. Handler1 a b -> Fold1 b r -> Fold1 a r
handles Handler1 a b
k (Fold1_ b -> x
begin x -> b -> x
step x -> r
done) = (a -> x) -> (x -> a -> x) -> (x -> r) -> Fold1 a r
forall a b x. (a -> x) -> (x -> a -> x) -> (x -> b) -> Fold1 a b
Fold1_ a -> x
begin' x -> a -> x
step' x -> r
done
  where
    begin' :: a -> x
begin' = Maybe x -> a -> x
stepAfromMaybe Maybe x
forall a. Maybe a
Nothing
    step' :: x -> a -> x
step' x
x = Maybe x -> a -> x
stepAfromMaybe (x -> Maybe x
forall a. a -> Maybe a
Just (x -> Maybe x) -> x -> Maybe x
forall a b. (a -> b) -> a -> b
$! x
x)
    stepAfromMaybe :: Maybe x -> a -> x
stepAfromMaybe = (a -> Maybe x -> x) -> Maybe x -> a -> x
forall a b c. (a -> b -> c) -> b -> a -> c
flip (FromMaybe x -> Maybe x -> x
forall b. FromMaybe b -> Maybe b -> b
appFromMaybe (FromMaybe x -> Maybe x -> x)
-> (a -> FromMaybe x) -> a -> Maybe x -> x
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Dual (FromMaybe x) -> FromMaybe x
forall a. Dual a -> a
getDual (Dual (FromMaybe x) -> FromMaybe x)
-> (a -> Dual (FromMaybe x)) -> a -> FromMaybe x
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Const (Dual (FromMaybe x)) a -> Dual (FromMaybe x)
forall {k} a (b :: k). Const a b -> a
getConst (Const (Dual (FromMaybe x)) a -> Dual (FromMaybe x))
-> (a -> Const (Dual (FromMaybe x)) a) -> a -> Dual (FromMaybe x)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (b -> Const (Dual (FromMaybe x)) b)
-> a -> Const (Dual (FromMaybe x)) a
Handler1 a b
k (Dual (FromMaybe x) -> Const (Dual (FromMaybe x)) b
forall {k} a (b :: k). a -> Const a b
Const (Dual (FromMaybe x) -> Const (Dual (FromMaybe x)) b)
-> (b -> Dual (FromMaybe x)) -> b -> Const (Dual (FromMaybe x)) b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FromMaybe x -> Dual (FromMaybe x)
forall a. a -> Dual a
Dual (FromMaybe x -> Dual (FromMaybe x))
-> (b -> FromMaybe x) -> b -> Dual (FromMaybe x)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Maybe x -> x) -> FromMaybe x
forall b. (Maybe b -> b) -> FromMaybe b
FromMaybe ((Maybe x -> x) -> FromMaybe x)
-> (b -> Maybe x -> x) -> b -> FromMaybe x
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Maybe x -> b -> x) -> b -> Maybe x -> x
forall a b c. (a -> b -> c) -> b -> a -> c
flip Maybe x -> b -> x
stepBfromMaybe))
    stepBfromMaybe :: Maybe x -> b -> x
stepBfromMaybe = (b -> x) -> (x -> b -> x) -> Maybe x -> b -> x
forall b a. b -> (a -> b) -> Maybe a -> b
maybe b -> x
begin x -> b -> x
step
{-# INLINABLE handles #-}

{- | @(foldOver f folder xs)@ folds all values from a Lens, Traversal1 or Fold1 optic with the given folder

>>> foldOver (_2 . both1) Foldl1.nonEmpty (1, (2, 3))
2 :| [3]

> Foldl1.foldOver f folder xs == Foldl1.fold1 folder (xs ^.. f)

> Foldl1.foldOver (folded1 . f) folder == Foldl1.fold1 (Foldl1.handles f folder)

> Foldl1.foldOver folded1 == Foldl1.fold1

-}
foldOver :: Handler1 s a -> Fold1 a b -> s -> b
foldOver :: forall s a b. Handler1 s a -> Fold1 a b -> s -> b
foldOver Handler1 s a
l (Fold1_ a -> x
begin x -> a -> x
step x -> b
done) =
    x -> b
done (x -> b) -> (s -> x) -> s -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Maybe x -> s -> x
stepSfromMaybe Maybe x
forall a. Maybe a
Nothing
  where
    stepSfromMaybe :: Maybe x -> s -> x
stepSfromMaybe = (s -> Maybe x -> x) -> Maybe x -> s -> x
forall a b c. (a -> b -> c) -> b -> a -> c
flip (FromMaybe x -> Maybe x -> x
forall b. FromMaybe b -> Maybe b -> b
appFromMaybe (FromMaybe x -> Maybe x -> x)
-> (s -> FromMaybe x) -> s -> Maybe x -> x
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Dual (FromMaybe x) -> FromMaybe x
forall a. Dual a -> a
getDual (Dual (FromMaybe x) -> FromMaybe x)
-> (s -> Dual (FromMaybe x)) -> s -> FromMaybe x
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Const (Dual (FromMaybe x)) s -> Dual (FromMaybe x)
forall {k} a (b :: k). Const a b -> a
getConst (Const (Dual (FromMaybe x)) s -> Dual (FromMaybe x))
-> (s -> Const (Dual (FromMaybe x)) s) -> s -> Dual (FromMaybe x)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Const (Dual (FromMaybe x)) a)
-> s -> Const (Dual (FromMaybe x)) s
Handler1 s a
l (Dual (FromMaybe x) -> Const (Dual (FromMaybe x)) a
forall {k} a (b :: k). a -> Const a b
Const (Dual (FromMaybe x) -> Const (Dual (FromMaybe x)) a)
-> (a -> Dual (FromMaybe x)) -> a -> Const (Dual (FromMaybe x)) a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. FromMaybe x -> Dual (FromMaybe x)
forall a. a -> Dual a
Dual (FromMaybe x -> Dual (FromMaybe x))
-> (a -> FromMaybe x) -> a -> Dual (FromMaybe x)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Maybe x -> x) -> FromMaybe x
forall b. (Maybe b -> b) -> FromMaybe b
FromMaybe ((Maybe x -> x) -> FromMaybe x)
-> (a -> Maybe x -> x) -> a -> FromMaybe x
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Maybe x -> a -> x) -> a -> Maybe x -> x
forall a b c. (a -> b -> c) -> b -> a -> c
flip Maybe x -> a -> x
stepAfromMaybe))
    stepAfromMaybe :: Maybe x -> a -> x
stepAfromMaybe = (a -> x) -> (x -> a -> x) -> Maybe x -> a -> x
forall b a. b -> (a -> b) -> Maybe a -> b
maybe a -> x
begin x -> a -> x
step
{-# INLINABLE foldOver #-}

{-|
> handles folded1 :: Foldable1 t => Fold1 a r -> Fold1 (t a) r
-}
folded1
    :: (Contravariant f, Apply f, Foldable1 t)
    => (a -> f a) -> (t a -> f (t a))
folded1 :: forall (f :: * -> *) (t :: * -> *) a.
(Contravariant f, Apply f, Foldable1 t) =>
(a -> f a) -> t a -> f (t a)
folded1 a -> f a
k t a
ts = (t a -> ()) -> f () -> f (t a)
forall a' a. (a' -> a) -> f a -> f a'
forall (f :: * -> *) a' a.
Contravariant f =>
(a' -> a) -> f a -> f a'
contramap (\t a
_ -> ()) ((a -> f a) -> t a -> f ()
forall (t :: * -> *) (f :: * -> *) a b.
(Foldable1 t, Apply f) =>
(a -> f b) -> t a -> f ()
traverse1_ a -> f a
k t a
ts)
{-# INLINABLE folded1 #-}

{-| Nest a fold in an Apply.
-}
nest :: Apply f => Fold1 a b -> Fold1 (f a) (f b)
nest :: forall (f :: * -> *) a b. Apply f => Fold1 a b -> Fold1 (f a) (f b)
nest (Fold1_ a -> x
i x -> a -> x
s x -> b
e) =
    (f a -> f x)
-> (f x -> f a -> f x) -> (f x -> f b) -> Fold1 (f a) (f b)
forall a b x. (a -> x) -> (x -> a -> x) -> (x -> b) -> Fold1 a b
Fold1_
        ((a -> x) -> f a -> f x
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> x
i)
        ((x -> a -> x) -> f x -> f a -> f x
forall a b c. (a -> b -> c) -> f a -> f b -> f c
forall (f :: * -> *) a b c.
Apply f =>
(a -> b -> c) -> f a -> f b -> f c
liftF2 x -> a -> x
s)
        ((x -> b) -> f x -> f b
forall a b. (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap x -> b
e)
{-# INLINABLE nest #-}