Too many pattern matches to write down for Quadtrees?

Question

Imagine a quadtree defined as follow:

data (Eq a, Show a) => QT a = C a | Q (QT a) (QT a) (QT a) (QT a)
  deriving (Eq, Show)

bad1 = Q u u u u where u = C 255
bad2 = Q (C 0) (C 255) (Q u u u u) (C 64) where u = C 255

The constructor allows you to create not well-formed quadtrees. bad1 should be simply C 255 and bad2 is not valid too because its bottom-right quadtree (for the same reason, it should be Q (C 0) (C 255) (C 244) (C 64).

So far so good. Checking its well-formness is simply a matter of checking its inner quadtrees recursively. The base case is when all inner quadtrees are leafs, whereby all colors shouldn't be all equals.

wellformed :: (Eq a, Show a) => QT a -> Bool
wellformed (Q (C c1) (C c2) (C c3) (C c4)) = any (/= c1) [c2, c3, c4]
wellformed (Q (C c1) (C c2) se (C c4))     = valid se
-- continue defining patters to match e.g Q C C C, C Q Q C, and so on...

Question: Can I avoid typing all matches for all possible combination of leafs and quadtrees?

Please be patient if my question is quite odd, but it's my second-day-Haskell-seamless-learing!

Answer 1

Nevermind...

wellformed :: (Eq a, Show a) => QT a -> Bool
wellformed (C _) = True
wellformed (Q (C c1) (C c2) (C c3) (C c4)) = any (/= c1) [c2, c3, c4]
wellformed (Q nw ne se sw) = wellformed nw && wellformed ne
   && wellformed se && wellformed sw

EDIT: or even better:

wellformed :: (Eq a, Show a) => QT a -> Bool
wellformed (C _) = True
wellformed (Q (C c1) (C c2) (C c3) (C c4)) = any (/= c1) [c2, c3, c4]
wellformed (Q nw ne se sw) = all wellformed [nw, ne, se, sw]

EDIT: note that the bindings are wrong, should be: NW NE SW SE!!!