F# Search Up Data Tree and Update - f#

Question

UPDATE:
Pavel correctly answered the original question and made me realize I left out an important detail - the search is on the nth parent. I'm curious if there's a more elegant solution, but at least I got something that works.
type searchf =
| None of None: unit
| CountUp of CountUp: int
| ParentNode of ParentNode: Node
let search (nthParent: int) (tree: Node) (child: Node): Node =
if (nthParent = -1) //-1 Top, 0 Current, 1 Parent, 2 Grandparent
then tree
else
let rec f (t: Node): searchf =
match t = child with
| true when nthParent = 0 -> ParentNode t
| true -> CountUp nthParent
| _ ->
let foldSubs (acc: searchf) (xy: Node): searchf =
match acc with
| CountUp i -> CountUp i
| _ -> f xy
let acc =
match t.ChildNode with
| [] -> None ()
| x -> x |> List.fold foldSubs (None ())
match acc with
| CountUp x when x = 1 -> ParentNode t //parent found in sub list, so this is it
| CountUp x -> CountUp (x - 1)
| _ -> acc
match (f tree) with
| ParentNode t -> t
| _ -> tree
ORIGINAL QUESTION:
I have a small tree, usually 2-5 nodes per branch, max depth of 4. I'm stuck trying to figure out the functional way of searching the tree for a node and returning updated trees.
//I'm not opposed to adding a key field, but my tree does not have one naturally.
type Node = { Name: string; ChildNode: Node list; }
let newNode (name: string)(childNode: Node list) =
{Name=name; ChildNode=childNode;}
let tree =
newNode
"Main" [
newNode "File" [
newNode "Open" [];
newNode "Close" [];
newNode "Print" [
newNode "Preview" [];
newNode "Settings" [];
]
];
newNode "Edit" [
newNode "Cut" [];
newNode "Copy" [];
newNode "Paste" [];
newNode "Preferences" [
newNode "User" [];
newNode "System" [];
]
]
]
let updateTree (tree: Node ) (oldNode: Node ) (newNode: Node ): Node =
//??
tree
let randomNode = tree.ChildNode.[1].ChildNode.[3]
let newRandomNode = { randomNode with Name = "Options"}
let updatedTree = updateTree tree randomNode newRandomNode

Answer 1

Here's a simple example.
let rec updateTree tree oldNode newNode =
if tree = oldNode
then newNode
else { tree with ChildNode = [for a in tree.ChildNode -> updateTree a oldNode newNode]}
UPD:
With the update of the question here's another solution.
To find nth parent of node you can use something like this.
type SearchResult =
| Failure
| Incomplete of int
| Complete of Node
let searchNthParent nthParent node target =
if nthParent < 0
then Complete node
else
// You can just use this function if you
// don't need check on nthParent < 0
let rec inFunc left node target =
if node = target
then
if left > 0
then Incomplete left
else Complete node
else
let rec iterateWhileFailure f list =
match list with
| [] -> Failure
| h::t ->
match f left h target with
| Failure -> iterateWhileFailure f t
| a -> a
match iterateWhileFailure inFunc node.ChildNode with
| Incomplete left when left > 1 -> Incomplete (left - 1)
| Incomplete _ -> Complete node
| a -> a
inFunc nthParent node target