3,354 karma · joined June 23, 2014
Suppose we have foldr as in [A] -> B -> ((A, B) -> B) -> B, foldl as in [A] -> B -> ((B, A) -> B) -> B, and reduce as in [A] -> ((A, A) -> A) -> A.
Then we have foldr list value operator = reduce [\b -> operator a b | a <- list] (.), foldl list value operator = foldr (reverse list) value (flip operator), and in the case of a finite non-empty list and associative operator, we have reduce list operator = foldr (tail list) (head list) operator = foldl (init list) (last list) operator.
So these are all basically slight re-parametrizations of each other.
Gödelian incompleteness is the specific kind established by Gödel's proof, where theory T can't prove Con(T) without being inconsistent. But the inability of ZFC to consistently decide the Continuum Hypothesis is established in a completely different manner, with the Continuum Hypothesis not consistently decided by ZFC + Con(ZFC) either, or any such thing.
Yes, these problems are systematic. That is what I am saying. That doesn't make it any nicer.
(So what is this article talking about? I guess it's talking mainly about "Write programs to handle text streams, because that is a universal interface".)