Binary tree as Applicative

In this example, we will define binary tree and define it as an instance of an Applicative type class. 

How to do it...

1. Create a new project binary-tree-applicative using the simple Stack template.
2. Open src/Main.hs; we will add our recipe to this file.
3. After the initial module definition, add the following imports:

        module Main where

        import Data.Functor
        import Control.Applicative

4. Define the binary tree and add the Functor instance too:

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

        instance Functor Tree where
        fmap _ Leaf = Leaf
        fmap f (Node left value right) = Node (fmap f left) (f value) 
        (fmap f right)

5. Now, define the Applicative instance for the binary tree. Note the recursive definition for pure, producing an infinite tree:

        instance Applicative Tree where
        pure x = let t = Node t x t
           in t

        (<*>) Leaf _ = Leaf
        (&lt...