Chapter_12.hs

{-# LANGUAGE InstanceSigs #-}
{-# LANGUAGE DeriveGeneric #-}

module Chapter_12 where

import Prelude hiding (Maybe, Nothing, Just)
import GHC.Generics

-- Exercise 12.WarmUp1
-- Consider following type:

data Maybe a = Nothing | Just a
  deriving (Eq, Ord, Show, Read)

-- Provide instance definitions to make this type into instances of the Functor, Applicative and Monad classes.

-- Here are some examples of how these instance definitions can be used: 

-- >>> fmap (+1) Nothing
-- Nothing

-- >>> fmap (+1) (Just 1)
-- Just 2

-- >>> pure (+1) <*> Just 1
-- Just 2

-- >>> pure (+) <*> Just 1 <*> Just 3
-- Just 4

-- >>> pure (+) <*> Nothing <*> Just 2
-- Nothing

-- >>> safediv n m = if (m == 0) then Nothing else (Just (div n m))
-- >>> do {n <- pure 10; m <- pure 2; safediv n m}
-- Just 5

-- >>> safediv n m = if (m == 0) then Nothing else (Just (div n m))
-- >>> do {n <- pure 10; m <- pure 0; safediv n m}
-- Nothing



instance Functor Maybe where
  -- fmap :: ???
  fmap = undefined
instance Applicative Maybe where
  -- pure :: ???
  pure = undefined
  -- (<*>) :: ???
  (<*>) = undefined
instance Monad Maybe where
  -- (>>=) :: ???
  (>>=) = undefined





-- Exercise 12.1 (*)
-- Define an instance of the Functor class for the following type of binary trees that have data in their nodes:

data Tree a = Leaf | Node (Tree a) a (Tree a) 
    deriving (Read, Show, Eq, Generic)

instance Functor Tree where
    -- fmap :: ???
    fmap = undefined


-- Note: Just in case you are wondering, this type of tree does not have an appropriate instance of the Applicative or Monar class. Take a look at https://dkalemis.wordpress.com/2014/03/22/trees-as-monads/ for an explanation.