Are Infinite Types (aka Recursive Types) not possible in F#?

Question

I was chatting with Sadek Drobi on twitter when be brought up that F# didn\'t seem to support Infinite Types. It turns out that in C# you can do something along these lines

Answer 1

Recursive record types should work as well.

type A = { A : A }
let rec a : A = { A = a }

I'd be interested in a practical application. Or even an impractical one :)

Answer 2

type d<'T> = delegate of 'T -> d<'T>  //'
let del : d<int> = null
let anotherDel = del.Invoke(1).Invoke(2).Invoke(3)

I think you need a named type that is representable directly in CLI to break the recursion, so in F# this means you need an actual delegate type as well.

Answer 3

You can also do something like

type 'a RecType = RecType of ('a -> 'a RecType)

to create a named type through which to perform the recursion. Now this works:

let rec specialF = RecType (fun _ -> specialF)