Bifoldable

class Bifoldable p where

  bifold :: Monoid m => p m m -> m

  bifold = bifoldMap id id

  bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> p a b -> m

  bifoldMap f g = bifoldr (mappend . f) (mappend . g) mempty

  bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c

  bifoldr f g z t = appEndo (bifoldMap (Endo #. f) (Endo #. g) t) z

  bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c

  bifoldl f g z t = appEndo (getDual (bifoldMap (Dual . Endo . flip f) (Dual . Endo . flip g) t)) z

Bifoldable 是个类型类。主要用于折叠二元数据结构。

Bifoldable 的法则

bifold ≡ bifoldMap id id

bifoldMap f g ≡ bifoldr (mappend . f) (mappend . g) mempty

bifoldr f g z t ≡ appEndo (bifoldMap (Endo . f) (Endo . g) t) z

Either 是个 Bifoldable

instance Bifoldable Either where

  bifoldMap f _ (Left a) = f a

  bifoldMap _ g (Right b) = g b

(,) 是个 Bifoldable

instance Bifoldable (,) where

  bifoldMap f g ~(a, b) = f a `mappend` g b

Const 是个 Bifoldable

instance Bifoldable Const where

  bifoldMap f _ (Const a) = f a

应用 Bifoldable

Prelude Data.Bifoldable> bifoldr (^) (-) 2 (Left 2)

4

Prelude Data.Bifoldable> bifoldr (^) (-) 2 (Right 3)

1

Prelude Data.Bifoldable> bifoldr (^) (-) 2 (2,3)

2

Prelude Data.Bifoldable Control.Applicative> bifoldr (^) (-) 2 (Const 2)

4

Prelude Data.Bifoldable> bifoldl (^) (-) 4 (Left 2)

16

Prelude Data.Bifoldable> bifoldl (^) (-) 4 (Right 3)

1

Prelude Data.Bifoldable> bifoldl (^) (-) 4 (2,3)

13

Prelude Data.Bifoldable Control.Applicative> bifoldl (^) (-) 4 (Const 2)

16

手动计算

bifoldr (^) (-) 1 (2,3)

= appEndo (bifoldMap (Endo #. (^)) (Endo #. (-)) (2,3)) 1

= appEndo ((Endo #. (^) $ 2) (Endo #. (-) $ 3)) 1

= appEndo ((Endo (2^)) `mappend` (Endo (3-))) $ 1

= (2^) . (3-) $ 1

= 2 ^ (3 - 1) = 4

bifoldl (^) (-) 4 (2,3)

= appEndo (getDual (bifoldMap (Dual . Endo . flip (^)) (Dual . Endo . flip (-)) (2,3))) 4

= appEndo (getDual ((Dual . Endo . flip (^) $ 2)  `mappend` (Dual . Endo . flip (-) $ 3))) 4

= appEndo (getDual ((Dual $ Endo (^2)) `mappend` (Dual $ Endo (subtract 3)))) 4

= (subtract 3) . (^2) $ 4

= (4 ^ 2) - 3 = 13

Bifoldable 其他函数

bifoldrM :: (Bifoldable t, Monad m) => (a -> c -> m c) -> (b -> c -> m c) -> c -> t a b -> m c

bifoldrM f g z0 xs = bifoldl f' g' return xs z0 where

  f' k x z = f x z >>= k

  g' k x z = g x z >>= k

bifoldlM :: (Bifoldable t, Monad m) => (a -> b -> m a) -> (a -> c -> m a) -> a -> t b c -> m a

bifoldlM f g z0 xs = bifoldr f' g' return xs z0 where

  f' x k z = f z x >>= k

  g' x k z = g z x >>= k

bitraverse_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f ()

bitraverse_ f g = bifoldr ((*>) . f) ((*>) . g) (pure ())

bimapM_:: (Bifoldable t, Monad m) => (a -> m c) -> (b -> m d) -> t a b -> m ()

bimapM_ f g = bifoldr ((>>) . f) ((>>) . g) (return ())

biforM_ :: (Bifoldable t, Monad m) => t a b ->  (a -> m c) -> (b -> m d) -> m ()

biforM_ t f g = bimapM_ f g t

bisequenceA_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()

bisequenceA_ = bifoldr (*>) (*>) (pure ())

bisequence_ :: (Bifoldable t, Monad m) => t (m a) (m b) -> m ()

bisequence_ = bifoldr (>>) (>>) (return ())

biList :: Bifoldable t => t a a -> [a]

biList = bifoldr (:) (:) []

biconcat :: Bifoldable t => t [a] [a] -> [a]

biconcat = bifold

biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c]

biconcatMap = bifoldMap

biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool

biany p q = getAny . bifoldMap (Any . p) (Any . q)

biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool

biall p q = getAll . bifoldMap (All . p) (All . q)

Prelude Data.Bifoldable> bifoldrM (\x y -> [x+y]) (\x y -> [x*y]) 4 (2,3)

[14]

Prelude Data.Bifoldable> bifoldrM (\x y -> [x+y, x+y+1]) (\x y -> [x*y, x*y*2]) 4 (2,3)

[14,15,26,27]

Prelude Data.Bifoldable> bifoldlM (\x y -> [x+y]) (\x y -> [x*y]) 4 (2,3)

[18]

Prelude Data.Bifoldable> bifoldlM (\x y -> [x+y, x+y+1]) (\x y -> [x*y, x*y*2]) 4 (2,3)

[18,36,21,42]

Prelude Data.Bifoldable> bitraverse_ print print ("hello", "world")

"hello"

"world"

Prelude Data.Bifoldable> bimapM_ print print ("hello", "world")

"hello"

"world"

Prelude Data.Bifoldable> biforM_ ("hello", "world") print print

"hello"

"world"

Prelude Data.Bifoldable> bisequenceA_ (print "hello", print "world")

"hello"

"world"

Prelude Data.Bifoldable> bisequence_ (print "hello", print "world")

"hello"

"world"

Prelude Data.Bifoldable> biList ("hello","world")

["hello","world"]

Prelude Data.Bifoldable> biconcat (["hello"],["world"])

["hello","world"]

Prelude Data.Bifoldable> biconcatMap (++",")(++"!") ("hello","world")

"hello,world!"

Prelude Data.Bifoldable> biany ('e' `elem`)('e' `elem`) ("hello","world")

True

Prelude Data.Bifoldable> biall ('e' `elem`)('e' `elem`) ("hello","world")

False