Example of extending a type with an interface in F#

ExtInterface.fs

type MyType() =
    member x.Stuff = 1
    member x.DoStuff() = x.Stuff

type IListLike<'T> =
    abstract Enumerate : unit -> seq<'T>

type MyType with
    member x.DoMore() = x.DoStuff() + 1 // this works
    interface IListLike<int> with       // this doesn't: All implemented interfaces should be declared on the initial declaration of the type
        member x.Enumerate() = seq { yield 1; yield 2 }

[<EntryPoint>]
let main argv = 
    let t = new MyType()
    printfn "%A" (t.DoMore())
    System.Console.ReadKey() |> ignore
    0 // return an integer exit code

http://research.microsoft.com/en-us/um/cambridge/projects/fsharp/manual/spec.html#_Toc335818946

Extensions may not define fields, interfaces, abstract slots, inherit declarations, or dispatch slot (interface and override) implementations.

In particular I think the fundamental reason is this: Extension members are compiled as CLI static members with encoded names.

Which obviously can't allow you to augment the type with a new interface.