(**) Symmetric binary trees
Let us call a binary tree symmetric if you can draw a vertical line through the root node and then the right subtree is the mirror image of the left subtree. Write a predicate symmetric/1 to check whether a given binary tree is symmetric. Hint: Write a predicate mirror/2 first to check whether one tree is the mirror image of another. We are only interested in the structure, not in the contents of the nodes.
mirror Empty Empty = True mirror (Branch _ a b) (Branch _ x y) = mirror a y && mirror b x mirror _ _ = False symmetric Empty = True symmetric (Branch _ l r) = mirror l r