Tail-recursion on trees

Question

I have a data structure,

datatype \'a tree = Leaf | Branch of \'a tree * \'a * \'a tree

and I want to write a function that traverses this tr

Answer 1

Like @seanmcl writes, the systematic way to convert a function to be tail-recursive is to use continuation-passing style.

After that you probably want to reify your continuations and use a more concrete data type, like a list for instance:

fun treefoldL f init tree =
    let fun loop Leaf acc [] = acc
          | loop Leaf acc ((x, right) :: stack) =
            loop right (f(x,acc)) stack
          | loop (Branch (left, x, right)) acc stack =
            loop left acc ((x, right) :: stack)
    in  loop tree init [] end