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