Question

How can a value of type:

type Tree =
    | Node of int * Tree list

have a value that references itself generated in a functional way?

The resulting value should be equal to x in the following Python code, for a suitable definition of Tree:

x = Tree()
x.tlist = [x]

Edit: Obviously more explanation is necessary. I am trying to learn F# and functional programming, so I chose to implement the cover tree which I have programmed before in other languages. The relevant thing here is that the points of each level are a subset of those of the level below. The structure conceptually goes to level -infinity.

In imperative languages a node has a list of children which includes itself. I know that this can be done imperatively in F#. And no, it doesn’t create an infinite loop given the cover tree algorithm.

Answer 1

Tomas’s answer suggests two possible ways to create recursive data structures in F#. A third possibility is to take advantage of the fact that record fields support direct recursion (when used in the same assembly that the record is defined in). For instance, the following code works without any problem:

type 'a lst = Nil | NonEmpty of 'a nelst
and 'a nelst = { head : 'a; tail : 'a lst }

let rec infList = NonEmpty { head = 1; tail = infList }

Using this list type instead of the built-in one, we can make your code work:

type Tree = Node of int * Tree lst
let rec x = Node(1, NonEmpty { head = x; tail = Nil })