Well... since I am learning more and more about half halts everyday, I guess I should join this discussion.
In my opinion, half halts come a rider working effectively with his/her horse and has a solid connection with their legs and a looser connection with their hands. Not loose, but a squeeze and soften kinda thing.
Half halts should'nt really result in a faster tempo, they should result in relaxation and collection... which generally makes the horses rhythm slower. I have to disagree with that other forum because where I come from, we use half halts to bring our horse back and collect them, not send them forward. Take and release, Squeeze and soften whatever. When you are riding with a solid foundation you can create engament or collection or different tempo. Just because you are riding "in sync" it doesnt mean your half halt creates engagement. If your half halt sends your horse on... then you did something wrong.