Combinators defined under Applicative.

skapplicative.hs

module Main where

import Control.Applicative

newtype A = A Integer deriving Show
newtype B = B Integer deriving Show
newtype C = C Integer deriving Show

k :: Applicative f => a -> f a
k = pure

s :: Applicative t => t (a -> b) -> t a -> t b
s = (<*>)

b :: Applicative f => (b -> c) -> f b -> f c
b = s (k s) k

c :: Applicative f => f (a -> b) -> a -> f b
c = s (s (k (s (k s) k)) s) (k k)

h :: (Applicative t, Applicative f) => t (b -> c) -> t (f b) -> t (f c)
h = b s (b b)

pbc :: Integer -> B -> C
pbc x (B y) = C $ x + y

pab :: Integer -> A -> B
pab x (A y) = B $ x * y

main :: IO ()
main = print $ h pbc pab 3 (A 2)