[culturedsystems]

You don't need to distinguish KI (the kite) from KI (the kestrel followed by the idiot bird), because they evaluate to the same thing. Kite xy is y, and if you evaluate Kestrel Idiot xy, you get:

    KIxy -> Iy -> y

Similarly, because true is defined as K, and false as KI, if you evaluate Mxy where x and y are K or KI, and keep evaluating, you'll eventually end up with either K or KI, depending on whether (x or y) is true or false. I agree, though, that is confusing that the post didn't explain any of this; I assume it's not finished yet.