Try to visualize with concrete types

data Tree a = NULL | Node (Tree a) a (Tree a) deriving Show

Tree Int    = Node (Tree Int)   Int    (Node Int)       -- OK
Tree String = Node (Tree String) String (Node String) -- OK

f :: Int -> String
f i = show i

and see what you get:

instance Functor Tree where
fmap f NULL = NULL
fmap f (Node left x right)                                                           -- Node (Tree Int)       Int      (Node Int)
    | (left == NULL) && (right == NULL) = Node left (f x) right   -- Node (Tree Int)       String (Node Int)    === Not OK
    | (left /= NULL) = Node (fmap f left) x right                            -- Node (Tree String) Int      (Node Int)       === Not OK
    | (right /= NULL) = Node left x (fmap f right)                           -- Node (Tree Int)      Int      (Node String) === Not OK

-------- Original Message --------
Subject: [Haskell-beginners] Functor on Tree data constructor
From: Nishant <nishantgeek@gmail.com>
To: beginners@haskell.org
Date: 02.04.2014 12:53

instance Functor Tree where

............fmap f NULL = NULL

............fmap f (Node left x right) | (left == NULL) && (right == NULL) = Node left (f x) right

................................................... | (left /= NULL) = Node (fmap f left) x right

................................................... | (right /= NULL) = Node left x (fmap f right)