Add ‘Compose f g a b’ (= Biff f g Identity a b)

[Icelandjack]

Add Compose f g a b (= Biff f g dentity a b) from Edward's monad homomorphisms

type COMPOSE f g = Biff f g Identity

newtype Compose f g a b = COMPOSE { runCOMPOSE :: COMPOSE f g a b }
  deriving (Functor, Foldable, Traversable, Bifunctor, Bifoldable, Biapplicative)

[Icelandjack]

Also Bitraversable

pattern Compose :: Bifunctor f => f (g a) b -> Compose f g a b
pattern Compose{runCompose} <- (second runIdentity . runBiff . runCOMPOSE -> runCompose)
  where Compose              = COMPOSE . Biff . second Identity

instance (Bitraversable f, Traversable g) => Bitraversable (Compose f g) where
  bitraverse :: Applicative f => (a -> f a') -> (b -> f b') -> ((Tensor f g) a b -> f ((Tensor f g) a' b'))
  bitraverse f g = fmap Tensor . bitraverse (traverse f) g . runTensor

[Icelandjack]

With issue #12369 this becomes an instance of Compose

data family Compose (k -> xx) -> (k' -> k) -> (k' -> xx)

newtype instance Compose f g a     = Compose  (f (g a))
newtype instance Compose f g a b   = Compose2 (f (g a) b)
newtype instance Compose f g a b c = Compose3 (f (g a) b c)