Haskelliday: A Functor-Applicative-Monad Break from Class. I suggest loading this file into GHCI and exploring the main function and MyTree data type before proceeding to the questions.

week-11b-worksheet.hs

import System.Random (StdGen, randomR, split, newStdGen)

-- main to help debug your Functor, Applicative and Monad instances
-- feel free to edit main!
main :: IO ()
main = do
    treeOne <- generateRandomTree 10 -- tree of ten random nodes
    -- you will end of needing to construct a tree of expressions of some type (a -> a) for the applicative
    -- you can construct that tree manually via value constructors or by creating a new generateTree function
    print treeOne

-- helper function to generate a new tree given a standard gen
-- don't edit this function!
generateTree :: Int -> StdGen -> (MyTree Int, StdGen)
generateTree 0 g = (Nil, g)
generateTree n g = (Node value leftTree rightTree, g3)
    where
        (value, g1) = randomR (1, 100) g
        (g2, g3) = split g1
        n' = (n - 1) `div` 2
        (leftTree, _) = generateTree n' g2
        (rightTree, _) = generateTree (n - 1 - n') g3

-- helper function to build and return a tree with random values
-- don't edit this function!
generateRandomTree :: Int -> IO (MyTree Int)
generateRandomTree n = do
    g <- newStdGen
    let (tree, nextGen) = generateTree n g
    return tree

-- Implement a Functor, Applicative, and Monad instance for the following custom data type:
data MyTree a = Nil | Node a (MyTree a) (MyTree a) deriving Show


-- Question 1 : Functor
-- In the Functor instance for the MyTree data type, 
-- fmap applies a function to each value in the tree while 
-- preserving its structure. The fmap function recursively traverses 
-- the tree and applies the given function to every value it encounters in the tree.

-- Question 2 : Applicative
-- In the Applicative instance for the MyTree data type, 
-- the <*> operator combines two trees by applying a tree of 
-- functions to a tree of values in a pairwise manner. 
-- It recursively traverses both trees and applies each function 
-- from the first tree to the corresponding value in the second tree, 
-- creating a new tree with the results.

-- Question 3 : Monad
-- In the Monad instance for the MyTree data type, 
-- the bind operation (implemented using the >>= operator) is used 
-- to apply a function that returns a MyTree to each value in the input tree, 
-- then merges the resulting trees while preserving the overall structure.