Rose Tree in Haskell -- Finding the Leaves

Question

Please consider the following definition of a rose tree in Haskell

data Rose a = a :> [Rose a]
        deriving (Eq, Show)

root (a :> rs) = a

children (a :> rs) = rs

together with the implementation of the functions to get the root and the children of a rose tree. The bit where I am still struggling is how to implement the functions

size :: Rose a -> Int
leaves :: Rose a -> Int

that count the number of nodes in a rose tree, respectively the number of leaves (nodes without any children). Can anybody help?

Answer 1

size (_ :> ts) = ? + sum ?

leaves (_ :> []) = ?
leaves (_ :> ts) = sum ?

You will need to use recursion to fill in the blanks, and a common higher-order function.