Applicative Notes - from Graham Hutton's _Programming in Haskell_

applicative-notes.hs

-- the class of functors which support <*> and pure are called 
-- applicative functors or applicatives

-- class Functor f => Applicative f where 
--   pure :: a -> f a 
--   <*>  :: f (a -> b) -> f a -> f b

-- generalise the idea of mapping to functions with multiple arguments

-- associates to the left
-- ((g <*> x) <*> y) <*> z

import Control.Applicative

instance Applicative [] where
  pure x = [x]
  fs <*> xs = [f x | f <- fs, x <- xs]

[(+),(*)] <*> [10] <*> [10] -- [20, 100]
liftA2 (*) [10] [10]  -- [100]

let func x y z = x * y * z
Just func <*> Just 1 <*> Just 10 <*> Just 100 -- Just 1000
pure (Just 10)                                -- Just 10
pure func <*> Just 1 <*> Just 10 <*> Just 100 -- Just 1000
liftA3 func (Just 1) (Just 10) (Just 100)     -- Just 1000
func <$> Just 1 <*> Just 10 <*> Just 100      -- Just 1000

Just (.) <*> Just (+ 1) <*> Just (* 2) <*> Just 10 -- 1 + (2 * 10)
Just (.) <*> Just (+ 1) <*> Just (* 2) <*> Just 10
func <$> Just 1 <*> Just 10 <*> Just 100 -- Just 1000