I was confused about what <4> = \lambda ^ 5 4 meant, since it already seemed to have a "4" in it.
The trick is that the 4 seems to be similar to a positional argument index, but numbered inside out.
IOW, in this encoding, <4> is a function that can be called 5 times (the exponent on the lambda) and upon the fifth call will resolve to whatever was passed in 1st (which because of the inside-out ordering is labeled "4").
(For a simpler example, 0 is a function that can be called once and returns its argument.)
So succ is 3-ary; it says, give me a function (index 2, outermost call); next, give me its first argument (index 1, second-outermost call); when you call that (index 0, dropped, innermost call), I'll apply the function to the argument.
But note that if index 2 is a numeral <N>, the outermost call returns a function that will "remember" the next thing passed in and return it after 1 (succ's innermost call) + N + 1 (<N>'s contract) calls.
I think in _Babel_ (and _Katabasis_ as well), Kuang is a bit more prone than Tartt to showing off legit academic tidbits, which gives a nice scholarly glint (the illusion of high-brow? authenticity, dare I say?) to the environment, while not compromising the easy fantasy reading. More details than vibes, perhaps?
(When she gets details wrong, it does break the illusion. Like a small tangent on the etymology of the Greek word for truth in _Katabasis_.)
Oxford also simply has a certain aura for me, being from the US. All in all, I think Kuang's books are great "binge" or "airplane" reads with a smack of academic authenticity.
I saw _Possession_ mentioned elsewhere, which I think does academic vibes _and_ details very and IMO resides in a more refined literary category than either of the two other books. I should reread it!
I was confused about what <4> = \lambda ^ 5 4 meant, since it already seemed to have a "4" in it.
The trick is that the 4 seems to be similar to a positional argument index, but numbered inside out.
IOW, in this encoding, <4> is a function that can be called 5 times (the exponent on the lambda) and upon the fifth call will resolve to whatever was passed in 1st (which because of the inside-out ordering is labeled "4").
(For a simpler example, 0 is a function that can be called once and returns its argument.)
So succ is 3-ary; it says, give me a function (index 2, outermost call); next, give me its first argument (index 1, second-outermost call); when you call that (index 0, dropped, innermost call), I'll apply the function to the argument.
But note that if index 2 is a numeral <N>, the outermost call returns a function that will "remember" the next thing passed in and return it after 1 (succ's innermost call) + N + 1 (<N>'s contract) calls.