Comment by marvinborner
Comment by marvinborner 3 days ago
Fun fact: The nth composition combinator can be created by applying the b combinator to the nth Church numeral:
(1 b) ~> λgfx.(g (f x))
(2 b) ~> λhgfx.(h (g (f x)))
(3 b) ~> λihgfx.(i (h (g (f x))))
...
Furthermore: (X (Y b)) = (X*Y b)
I use these in my bruijn programming language in the form of infix/prefix operators. [1][1] https://bruijn.marvinborner.de/std/Combinator.bruijn.html#b
I think you've got the first claim wrong - for a church numeral N, (N b g f) appears to give the composition of g and f with f taking N arguments.