Haskell help, /prog/!


-- create a random tree.
randomTree :: Random r => IO (BinaryTree r)
randomTree =
     -- randomly pick the left and right sides.
  do leftIO  <- pick(randomLeaf, randomBranch)
     rightIO <- pick(randomLeaf, randomBranch)
     -- "un-IO" the sides.
     left    <- leftIO
     right   <- rightIO
     -- get a random value for the top of the branch/tree.
     value   <- randomIO
     -- create branch and return.
     return (Branch left value right)
  where
    -- return left or right at random.
    pick (left, right) =
      do useLeft <- randomRIO(True, False)
         if useLeft then return left else return right
    -- create a random leaf.
    randomLeaf =
      do value <- randomIO
         let leaf = Leaf value
         return leaf
    -- setup an alias.
    randomBranch = randomTree

This code actually works fine, but I'm wondering if there's a way to simplify the "leftIO/rightIO" stuff. Is there some sort of "double arrow" that will un-Monad twice, or is this verbosity unavoidable?

... which is part of it, but the reason some people need to go back to probabilities and statistics is because they are caught in the gambler's fallacy that "random" means "average" or "fair".  Each flip of a coin has a 50% chance for that flip and has no relation to any previous flips.