haskell - Why is GHC complaining about non-exhaustive patterns?

Question

When I compile the following code with GHC (using the -Wall flag):

module Main where

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

insert :: (Ord a) => a -> Tree a -> Tree a
insert x EmptyTree = Node x EmptyTree EmptyTree
insert x (Node a left right)
    | x == a = Node a left right
    | x < a = Node a (insert x left) right
    | x > a = Node a left (insert x right)

main :: IO()
main = do
    let nums = [1..10]::[Int]
    print . foldr insert EmptyTree $ nums

GHC complains that pattern matching in insert is non-exhaustive:

test.hs|6| 1:
||     Warning: Pattern match(es) are non-exhaustive
||              In an equation for `insert': Patterns not matched: _ (Node _ _ _)

Why is GHC issuing this warning? It is pretty obvious that the pattern GHC complains about is handled in insert x (Node a left right).

Answer 1

It's because the pattern matching is incomplete. There's no guarantee that one of x==a, x<a, or x>a holds. For instance, if the type is Double and x is NaN then none of them are True.