As MN Tigerstripes said, I also like to back the horse if you don't get an immediate reaction. A horse needs to know that leg means go and leg means stop at the very basics. If you don't have that understanding then trying to train your horse for other movements and paces is useless in my books.
If the horse is green and genuinely does not understand that I want it to plant its feet and stay there, I'll be patient and just use my seat and close of the hand to ask for halt from walk, allowing the horse to wiggle around while I maintain the pressure. It will soon try to halt as a way of escaping the pressure, and as soon as it does the pressure comes off and I allow it to stand for a few moments. If the horse tries to move off, the pressure is reapplied and the process is repeated.
On the other side of the coin, is the horse that purely acts ignorant to the aids to halt, and either braces the neck/poll/jaw against the aid, or dives onto the forehand and runs through the aid.
With these horses I will be tougher, stop means stop! If the reaction to my aid does not occur within 2 seconds, I will repeat it at the same level and then go to 100% to MAKE that horse stop. So yes, they will cop a pull on the mouth and I will then run them backwards, proceed to walk on 2 steps then ask for halt again. If no reaction, they get run backwards again. Rein back is a forwards movement technically, but to a horse backing up is completely opposite to going forward, so if it's not going to simply stop, it's going to be made mighty uncomfortable by having to back up halfway across the arena.
If you have an 'ignorant' type of horse, just allowing them to figure it out and do it in their own time will not get you anywhere, they have won the battle. A horse needs to react instantaneously to an aid or they are being disobedient. As a dressage rider, if a horse is not 100% with me, waiting for me to ask for a downwards transition with a slight deepening of my seat, or an upwards transition with the lightening of my seat, then I can't to much with that horse until I've got those aids spot on.