Failing to write async recursive iteration function

Question

I'm trying to write a recursion method to retrieve the parent of a object (and that parent etc). This in itself isn't a problem but the calls are async which result in the following error:

The body of '.....Recursive(string)' cannot be an iterator block because 'Task<IEnumerable>' is not an iterator interface type [...]csharp(CS1624)

The code:

private async Task<IEnumerable<string>> Recursive(string objectId)
{
    var result = await GetParent(objectId);
    if (result?.Length > 0)
    {
        yield return result;
        await Recursive(objectId);
    }
}

private async Task<string> GetParent(string objectId)
{
    await Task.Run(() => { return $"{objectId}/parent"; });
}

I have also tried IAsyncEnumerable but that resulted in the folllowing error:

'IAsyncEnumerable' does not contain a definition for 'GetAwaiter' and no accessible extension method 'GetAwaiter' accepting a first argument of type 'IAsyncEnumerable' could be found (are you missing a using directive or an assembly reference?) [...]csharp(CS1061)

private async IAsyncEnumerable<string> Recursive(string objectId)
{
    var result = await GetParent(objectId);
    if (result?.Length > 0)
    {
        yield return result;
        await Recursive(objectId);
    }
}

private async Task<string> GetParent(string objectId)
{
    await Task.Run(() => { return $"{objectId}/parent"; });
}

I'm going to write a while loop to get this to work. But I'm interested if this is possible at all.

Update 2: Ok, I think I got it. Thanks guys.

private async IAsyncEnumerable<string> Recursive(string objectId)
{
    var result = await GetParent(objectId);
    if (result?.Length > 0)
    {
        yield return result;
        await foreach (var r2 in Recursive(objectId))
        {
            yield return r2;
        }
    }
}

private async Task<string> GetParent(string objectId)
{
    await Task.Run(() => { return $"{objectId}/parent"; });
}

Answer 1

The current code wouldn't compile even if it was synchronous, and the result was IEnumerable<string>. The results of Recursive are never returned. It's not possible to just return an IEnumerable from an iterator either.

This code would work. Whether it does anything useful is another matter :

private IEnumerable<string> Recursive(string objectId)
{
    var result = GetParent(objectId);
    if (!string.IsNullOrEmpty(result))
    {
        yield return result;
        foreach(var r in Recursive(result))
        {
            yield return r;
        }
    }
}

private string GetParent(string objectId)
{
    return $"{objectId}/parent";
    
}

Getting it to work asynchronously only needs changing to IAsyncEnumerable and using await:

private async IAsyncEnumerable<string> Recursive(string objectId)
{
    var result = await GetParent(objectId);
    if (!string.IsNullOrEmpty(result))
    {
        yield return result;
        await foreach(var r in Recursive(result))
        {
            yield return r;
        }
    }
}

private  Task<string> GetParent(string objectId)
{
    return Task.FromResult($"{objectId}/parent");
}