I couldn't think of a better name...
Anyway, when this player type presses a button (walk button, maybe?) in conjunction with a movement key, the player dives in the direction that corresponds to the key they pressed. Diving forwards would play the crouch animation and diving backwards would play the sit animation, but I'm not sure how the side-dives would work.
Diving is faster than jumping and you can shoot while diving, but after hitting the ground, there is a short recovery time where the player has to get up.
And yes, I've been playing a lot of Max Payne and Action Half-Life.