I just did a quick youtube search and here is video of the single haul. It is typically done only on the backcast, and the demonstrator uses an exaggerated motion to clearly illustrate it.
I watched another where the guy was actually unconsciously double hauling with a small tug on the forward cast as well as the backcast, and yet another where a guy was hauling on the forward cast, which I would call an atypical, or reverse single haul.
It takes a conscious effort for me also to not give a little tug on the forward cast once I get a fair amount of line in the air - so I can understand why the other two guys on youtube were having trouble on their videos doing the single haul.
The lengths of the haul have nothing to do with whether they are single or double.