Fascinating - familiar with basic lambda calculus, but trying to wrap my head around this. Can you link to anything that explains more about how this works?
A more readable form of the program is given at [1].
The tree contains all combinators built up from the single point basis
A = λxλyλz. x z (y (λ_.z)), which is encoded as bit 0 (left branch), while bit 1 (right branch) encodes prefix application.
[1] https://github.com/tromp/AIT/blob/master/ait/allA.lam