NonEmpty.hs

{-# 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 Fold1_ begin step done <- (toFold_ -> (begin, step, done))
  where Fold1_ begin step done = Fold1 $ \a -> Fold step (begin a) 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_ (Fold1 (f :: a -> Fold a b)) = (begin', step', done')
  where
    done' :: Fold a b -> b
    done' (Fold _step begin done) = done begin

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

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

instance Functor (Fold1 a) where
    fmap f (Fold1 k) = Fold1 (fmap (fmap f) k)
    {-# INLINE fmap #-}

instance Profunctor Fold1 where
    lmap = premap
    {-# INLINE lmap #-}

    rmap = fmap
    {-# INLINE rmap #-}

instance Choice Fold1 where
    right' = nest
    {-# INLINE right' #-}

instance Closed Fold1 where
    closed = nest
    {-# INLINE closed #-}

instance Cosieve Fold1 NonEmpty where
    cosieve = Control.Foldl.NonEmpty.fold1
    {-# INLINE cosieve #-}

instance Applicative (Fold1 a) where
    pure b = Fold1 (pure (pure b))
    {-# INLINE pure #-}

    Fold1 l <*> Fold1 r = Fold1 (liftA2 (<*>) l r)
    {-# INLINE (<*>) #-}

instance Extend (Fold1 a) where
    duplicated (Fold1 f) = Fold1 $ fmap fromFold . duplicated . f
    {-# INLINE duplicated #-}

instance Semigroup b => Semigroup (Fold1 a b) where
    (<>) = liftA2 (<>)
    {-# INLINE (<>) #-}

instance Monoid b => Monoid (Fold1 a b) where
    mempty = pure mempty
    {-# INLINE mempty #-}

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

instance Semigroupoid Fold1 where
    o (Fold1 l1) (Fold1 r1) = Fold1 f1
      where
        f1 a = let r = r1 a
                   l = l1 $ extract r
               in o l r
    {-# INLINE o #-}

instance Category Fold1 where
    (.) = o
    {-# INLINE (.) #-}

    id = last
    {-# INLINE id #-}

instance Strong Fold1 where
    first' f = (,) <$> lmap fst f <*> lmap snd last
    {-# INLINE first' #-}

instance Arrow Fold1 where
    arr f = f <$> last
    {-# INLINE arr #-}

    first = first'
    {-# INLINE first #-}

instance ArrowChoice Fold1 where
    left = left'
    {-# INLINE left #-}

instance Num b => Num (Fold1 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 (Fold1 a b) where
    fromRational = pure . fromRational
    {-# INLINE fromRational #-}

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

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

instance Floating b => Floating (Fold1 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 `Fold1` to a `NonEmpty` list
fold1 :: Foldable1 f => Fold1 a b -> f a -> b
fold1 (Fold1 k) as1 = Foldl.fold (k a) as
  where
    a :| as = toNonEmpty as1
{-# INLINABLE fold1 #-}

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

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

    step (Left' k) a = Right' (k a)
    step (Right' (Fold step' begin' done')) a =
        Right' (Fold step' (step' begin' a) done')

    done (Right' (Fold _ begin' done')) = Just (done' begin')
    done (Left' _) = Nothing
{-# INLINABLE toFold #-}

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

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

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

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

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

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

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

-- | Computes the minimum element with respect to the given comparison function
minimumBy :: (a -> a -> Ordering) -> Fold1 a a
minimumBy cmp = Fold1 (\begin -> Fold min' begin id)
  where
    min' x y = case cmp x y of
        GT -> y
        _  -> 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 f (Fold1_ begin step done) = f begin step 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_ f (Fold1_ begin step done) = done (f begin 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 f (Fold1 k) = Fold1 k'
  where
    k' a = lmap f (k (f a))
{-# INLINABLE premap #-}

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

instance Semigroup (FromMaybe b) where
    FromMaybe f <> FromMaybe g = FromMaybe (f . (Just $!) . 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 k (Fold1_ begin step done) = Fold1_ begin' step' done
  where
    begin' = stepAfromMaybe Nothing
    step' x = stepAfromMaybe (Just $! x)
    stepAfromMaybe = flip (appFromMaybe . getDual . getConst . k (Const . Dual . FromMaybe . flip stepBfromMaybe))
    stepBfromMaybe = maybe begin 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 l (Fold1_ begin step done) =
    done . stepSfromMaybe Nothing
  where
    stepSfromMaybe = flip (appFromMaybe . getDual . getConst . l (Const . Dual . FromMaybe . flip stepAfromMaybe))
    stepAfromMaybe = maybe begin 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 k ts = contramap (\_ -> ()) (traverse1_ k ts)
{-# INLINABLE folded1 #-}

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