(**) Generate-and-test paradigm
Apply the generate-and-test paradigm to construct all symmetric, completely balanced binary trees with a given number of nodes.
An efficient solution, which takes the fact that a tree with an even number of nodes can't be symmetric into consideration:
symCbalTrees n = if n `mod` 2 == 0 then  else [ Branch 'x' t (reverseTree t) | t <- cbalTree (n `div` 2)] reverseTree Empty = Empty reverseTree (Branch x l r) = Branch x (reverseTree r) (reverseTree l)
Or a simple, but less efficient one:
symCbalTrees = filter symmetric . cbalTree