Reader Monad practice

reader.hs

{-# LANGUAGE InstanceSigs #-}

newtype Reader e a = Reader (e -> a)

runReader :: Reader e a -> e -> a
runReader (Reader f) = f

instance Functor (Reader e) where
    fmap :: (a -> b) -> Reader e a -> Reader e b
    fmap a2b (Reader e2a) = Reader (a2b . e2a)

instance Applicative (Reader e) where
    pure :: a -> Reader e a
    pure = Reader . const
    (<*>) :: Reader e (a -> b) -> Reader e a -> Reader e b
    (<*>) (Reader e2a2b) (Reader e2a) = let e2b e = e2a2b e (e2a e) in Reader e2b

instance Monad (Reader e) where
    (>>=) :: Reader e a -> (a -> Reader e b) -> Reader e b
    (>>=) (Reader e2a) a2reb = let e2b e = runReader (a2reb (e2a e)) e in Reader e2b

reader :: (e -> a) -> Reader e a
reader = Reader

ask :: Reader e e
ask = Reader id

local :: (e -> e) -> Reader e a -> Reader e a
local f (Reader e2a) = Reader (e2a . f)