How to represent tree with sharing in Haskell

Question

I would like to represent a \"tree\" of the following shape in Haskell:

   /\\                            
  /\\/\\
 /\\/\\/\\
/\\/\\/\\/\\
` ` ` ` `
         


        

Answer 1

Perhaps you can represent it simply as a list of leaves and apply the function level by level until you're down to one value, i.e. something like this:

type Tree a = [a]

propagate :: (a -> a -> a) -> Tree a -> a
propagate f xs =
  case zipWith f xs (tail xs) of
    [x] -> x
    xs' -> propagate f xs'