Comment by marvinborner

Comment by marvinborner 2 days ago

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Ah yes, you're right. I messed up the associativity in the reductions.

  (2 b) ~> λhgfx.(h ((g f) x))
  (3 b) ~> λihgfx.(i (((h g) f) x))
  ...
It still does what most interpretations would consider the "nth composition combinator":

  (1 b f g) x = f (g x)
  (2 b f g) x y = f (g x y)
  (3 b f g) x y z = f (g x y z)
  ...
marvinborner 2 days ago

Okay, you've definitely nerd-sniped me here. Actually producing my initial reductions is not as trivial as I thought. Still, I came up with a solution that works for n>2:

  d = λλλλ(3 2 (1 0)) # common
  d' = λλλλλ(4 3 2 (1 0)) # common
  weird = λλλλλ(4 (d (3 2)) 1 0)
Here I use de Bruijn indices instead of named variables and write Church numerals as <n>.

Then,

  (<n-3> weird d' b) ~> λ^{n+1}(n (n-1 (n-2 ... (1 0)..)))
I could explain it in detail if anyone's interested. There should be some more elegant solutions though, so give it a try!
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