https://twitter.com/acid2/status/491988232771731456

applicative_traversible_compose_product_sum.hs

module ATComposeProductSum where

import Control.Applicative
import Data.Traversable

import Data.Functor.Compose
import Data.Functor.Product
import Data.Functor.Sum

import Data.Functor.Identity

instance (Applicative f, Applicative g) => Applicative (Sum f g) where
    pure x = InR (pure x)
    InL f <*> InL x = InL (f <*> x)
    InR f <*> InR x = InR (f <*> x)

-- | Applicative Composes
-- >>> pure (+) <*> (Compose (replicate 10 (Just 41))) <*> pure 1
-- Compose [Just 42,Just 42,Just 42,Just 42,Just 42,Just 42,Just 42,Just 42,Just 42,Just 42]
--
-- Traversable Composes
-- >>> traverse (Identity . length) (Compose (replicate 10 (Just "foo")))
-- Identity (Compose [Just 3,Just 3,Just 3,Just 3,Just 3,Just 3,Just 3,Just 3,Just 3,Just 3])
--
-- Applicative Sums
-- >>> pure (+) <*> Pair (Just 41) (replicate 10 41) <*> pure 1
-- Pair (Just 42) [42,42,42,42,42,42,42,42,42,42]
--
-- Traversable Sums
-- >>> traverse (Identity . length) (Pair (Just "foo") (replicate 10 "foo"))
-- Identity (Pair (Just 3) [3,3,3,3,3,3,3,3,3,3])
--
-- Applicative Products
-- >>> (InL (Just (+1))) <*> InL (Just 41) :: Sum Maybe [] Integer
-- InL (Just 42)
-- >>> pure (+1) <*> InR (replicate 10 41) :: Sum Maybe [] Integer
-- InR [42,42,42,42,42,42,42,42,42,42]
--
-- Traversable Products
-- >>> traverse (Identity . (+1)) (InL (Just 41)) :: Identity (Sum Maybe [] Integer)
-- Identity (InL (Just 42))
-- >>> traverse (Identity . (+1)) (InR (replicate 10 41)) :: Identity (Sum Maybe [] Integer)
-- Identity (InR [42,42,42,42,42,42,42,42,42,42])
true = True