Question

I’ve a task to write a function with type ‘a btree -> ‘a option list that stores the given tree in a list of elements of type ‘a option in postfix order (postorder).

Internal nodes will be represented by None, external nodes (leaves) with value x will be represented by Some x.

So far it’s easy to do for leaves, but how to put it in an 'a option list?

type 'a btree = L of 'a | N of 'a btree * 'a btree ;;

let rec store t =
    match t with
        | L x -> Some x
        | N (a,b) -> None ???   
;;

The second match case I know is incorrect, but how to solve it?

Answer 1

If you look at your first case, you’ll see it’s also not quite there; it’s returning 'a option, but you want the function to return an 'a option list.

Clearly you’ll be returning a list, so fix that first:

let rec store = function
  | L x -> [Some x]
  | N (a,b) -> [None] (* ??? *)

Now let’s fix the second case; we want to append None to our output, but before that, we want the nodes of our subtrees:

let rec store = function
  | L x -> [Some x]
  | N (a,b) -> (store a) @ (store b) @ [None]

@ has the type

'a list -> 'a list -> 'a list

i.e. it joins lists together. We want to join the list of results from the left subtree, then the right, and then finally the result for this internal node.