Algorithm for checking quadrant horizontal symmetry?

Question

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

Defining as described above, write a predicate to check if a given image (encoded as a quadrant) is symmetric about the vertical axis (horizontal symmetric). Use an anonymous function if possible.

Question . How would you implement a horizontal symmetry check for a given quadrant?

Well, I was thinking of something like this: when a square is just a leaf , in this case we have horizontal symmetry. The basic case is that quadtree has only one level (four sheets) of symmetry - it's just a color check (c1 == c2 && c3 == c4).

In any other case, I can check if this condition is satisfied: nw equals (fliphorizontal(ne)) && sw equals (fliphorizontal(se))where it fliphorizontalflips the quadrants horizontally, and equalschecks if the two quadrants are equal. However, I would like to avoid using an external function as much as possible, just anonymous 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 : The ultimate single-function solution (using the generic fold function for quadrants):

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,h]

Answer 1

Sort of:

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 syntax optimizations are possible .: - /

Answer 2

What about

ishsymmetric qt = qt == fliph qt