Binary tree as Functor

In the last recipe, we have Functor instances defined for Maybe, Either, and List. We even defined the Functor instance. In this recipe, we will create a data type Binary Tree and define a Functor instance for it.

How to do it...

1. Create a new Haskell project binary-tree-functor using the simple Stack template:

        stack new binary-tree-functor simple

2. Open src/Main.hs. This is the file that will be used for our purposes.
3. After adding module definition for Main, add the following import:

        module Main where
        import Data.Functor

4. Define the binary tree and utility functions to create the tree:

        -- The tree can be empty (Leaf) or a node with a 
        -- value, left and right trees.
        data Tree a = Leaf
            | Node (Tree a) a (Tree a) 
            deriving (Show, Eq)

        -- Create a tree given a value, left tree and a right tree
        node :: Tree a -> a -> Tree a -> Tree a
        node l x r = Node l x r

       -- Induct a value...