Explain half-halts transitions and what the purpose is?

The half-halt is one of the most important and most misunderstood concepts in all of riding — misunderstood because the name suggests stopping, when the reality is that a half-halt has nothing to do with stopping and everything to do with reorganizing, rebalancing, and reestablishing communication between horse and rider in the space of a single stride. A full halt brings the horse to a complete stop. A half-halt brings the horse to attention — it asks him to shift his weight slightly rearward, engage his hindquarters more deeply, lift through his back, and rebalance himself onto a lighter forehand — all without losing forward energy or momentum. The purpose of the half-halt is threefold. The first purpose is rebalancing — bringing a horse that has drifted forward and onto his forehand back into a more uphill, self-carrying posture. Every horse gradually shifts forward onto his forehand during the course of work as fatigue accumulates and attention drifts. The half-halt interrupts that gradual drift and restores the balance before it deteriorates into a horse that is heavy, flat, and unresponsive. Used preventively and frequently, the half-halt keeps the horse in balance throughout the entire ride. The second purpose is preparation — alerting the horse that something is about to be asked so that he can organize himself to respond correctly rather than being caught unprepared by a transition, a lateral movement, or a change of direction. A horse that receives a half-halt before a downward transition has been told something is coming, has shifted his weight slightly rearward in preparation, and has his hindquarters engaged and ready to support the deceleration — the result is a smooth, balanced transition that maintains rhythm and throughness. The third purpose is communication — re-establishing the connection between the horse's hindquarters and the rider's hand when the horse has drifted out of the elastic, through contact that correct work requires. The mechanics involve closing both legs simultaneously to maintain impulsion, simultaneously closing the fingers of both hands so the contact firms very slightly and creates a momentary barrier, then releasing the moment you feel the horse shift his weight rearward and lift through his back. The release is what makes the half-halt a communication rather than a constant pressure — a hand that closes and holds is not a half-halt, it is a restriction that the horse braces against.