Effective Haskell

Exercises

Flipping the Script

Try to write instances of Functor, Applicative, and Monad for List where Functor is defined in terms of Applicative, and Applicative is defined in terms of Monad. Is this possible? Why or why not?

Not a Functor

Imagine that we’ve created a new type to represent a sorted list of values:

{-# LANGUAGE DerivingStrategies #-}
module SortedListFunctor (SortedList, insertSorted) where

data SortedList a = Empty | Cons a (SortedList a)
  deriving stock (Eq, Show)

insertSorted :: Ord a => a -> SortedList a -> SortedList a
insertSorted a Empty = Cons a Empty
insertSorted a (Cons b bs)
  | a >= b = Cons b (insertSorted a bs)
  | otherwise = Cons a (Cons b bs)

Although ...