Algorithm to check quadtree horizontal symmetry?

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

Giving the definition as above, write a predicate to check if a given image (coded as a quadtree) is symmetric in respect of vertical axis (horizontal symmetric). Use anonymous function where possible.

Question: How would you implement horizontal symmetry check for a given quadtree?

Well, I was thinking at something like this: when a quadtree is just a leaf, in that case we have horizontal symmetry. Base case is when quadtree has just one level (four leafs) symmetry is just a matter of checking the colors (c1 == c2 && c3 == c4).

In any other case, I might check if this condition is recursive satisfied: nw equals (fliphorizontal(ne)) && sw equals (fliphorizontal(se)), where fliphorizontal flips the quadtree horizontally and equals checks if two quadtrees are equal. However I would like to avoid the use of external function as possible, just anonymous ones if possible.

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

EDIT: fliph example:

fliph :: (Eq a, Show a) => QT a -> QT a
fliph (C a)           = C a
fliph (Q nw ne sw se) = Q (fliph ne) (fliph nw) (fliph se) (fliph sw)

EDIT: final one-function solution (using generalized fold function for quadtrees):

ishsymmetric :: (Eq a, Show a) => QT a -> Bool
ishsymmetric (C _)       = True
ishsymmetric (Q a b c d) = and $ zipWith equals [a,c] [fliph b,fliph d]
    where
        fold f g (C c)       = g c
        fold f g (Q a b c d) = f (fold f g a) (fold f g b)
                                 (fold f g c) (fold f g d)
        fliph q = fold (\a b c d -> Q b a d c) (\c -> C c) q
        equals (C c1) (C c2)           = c1 == c2
        equals (Q a b c d) (Q e f g h) = and $ zipWith equals [a,b,c,d] [e,f,g开发者_如何学JAVA,h]

Something like:

ishsymmetric :: (Eq a, Show a) => QT a -> Bool
ishsymmetric (C _)                           = True
ishsymmetric (Q (C c1) (C c2) (C c3) (C c4)) = c1 == c2 && c3 == c4
ishsymmetric (Q nw ne sw se) = equals nw (fliph ne) && equals sw (fliph se)
    where equals (C a) (C b) = a == b
          equals (Q a b c d) (Q e f g h) = equals a e && equals b f && equals c g && equals d h
          fliph (C a)           = C a
          fliph (Q nw ne sw se) = Q (fliph ne) (fliph nw) (fliph se) (fliph sw)

But syntactic optimizations are possible. :-/

How about

ishsymmetric qt = qt == fliph qt