Use cases for functor/applicative/monad instances for functions

Question

Haskell has Functor, Applicative and Monad instances defined for functions (specifically the partially applied type (->) a

Answer 1

Sometimes you want to treat functions of the form a -> m b (where m is an Applicative) as Applicatives themselves. This often happens when writing validators, or parsers.

One way to do this is to use Data.Functor.Compose, which piggybacks on the Applicative instances of (->) a and m to give an Applicative instance for the composition:

import Control.Applicative
import Data.Functor.Compose

type Star m a b = Compose ((->) a) m b

readPrompt :: Star IO String Int
readPrompt = Compose $ \prompt -> do
    putStrLn $ prompt ++ ":"
    readLn

main :: IO ()
main = do
    r <- getCompose (liftA2 (,) readPrompt readPrompt) "write number"
    print r

There are other ways, like creating your own newtype, or using ready-made newtypes from base or other libraries.