1 Even with a fold-based representation of numbers, and pred/equal/subtraction, some computable functions are going to be out of our reach.
3 Fibonacci: doable without Y, but takes some ingenuity
7 Need a general method, where f(n) doesn't just depend on f(n-1) or (f(n-1),f(n-2),..).
9 Looks like Ackermann function is simplest example that MUST be done with Y, Everything simpler could be done using only fixed iteration limits.
12 | when x == 0 -> y + 1
13 | when y == 0 -> A(x-1,1)
14 | _ -> A(x-1, A(x,y-1))
20 A(4,y) = 2^(2^(2^...2)) [y+3 2s] - 3
23 Some algorithms can also be done more efficiently / intelligibly with general mechanism for recursion.
25 How to do recursion with omega.
27 fixed point combinators