// The recursive function used by MAP
var make_map =
  next_map =>
    new_list =>
      fn =>
        list =>
          (list_acc =>
            // Have we reached the end of the list?
            (IS_LAST(list)
                     // Yup, so reverse the items in list_acc and
                     // we're done
                     (REVERSE(list_acc))

                     // Nope, so recursively call ourselves passing
                     // in the list accumulator, the function being
                     // applied and whatever is left in the current
                     // list
                     (f => (next_map(list_acc)
                                    (fn)
                                    (TAIL(list)))
                           (f))))
          // Pass the first list item to the function and append the
          // modified value to the start of the new list.  The
          // resulting list becomes the value of the
          // list_acc(umulator) parameter seen above
          (PAIR(fn(HEAD(list)))(new_list));

// Create the MAP function using the Y-Combinator and an initial
// empty list
var MAP = Y(make_map)(EMPTY);