In that case, AFAIK the mamluks never developped half-swording.
The mamluks fought as horse-archers/heavy cavalry. they would soften up their enemies from a distance using composite bows on horseback bows mongol-style, then once the enemy was sufficiently weakened they would charge with their lances. for close quarters work they would use maces and warhammers. In the 13th century the main sword used by mamluks was a straight double-edged sword. During the course of the 14th century they gradually adopted kilij-style sabres.
Their main enemies in the 14th-15th centuries, apart from each other, were the Mongols, The Aq-Qoyonlu Turcomans and the Ottomans, all of who would have been similarly equiped and (initially at least with regards to the Ottomans, they adopted field artillary and muskets in the late 15th century) would have used similar tactics.
Mamluk words:
As you can see, non are particularly suited to half-swording. All are meant for use on horseback.