dolio 2017-02-24 09:45:52
EvanR: Anyhow, you need to nail down what stuff like "repeat that indefinitely" means.
EvanR 2017-02-24 09:46:59
unfoldr
EvanR 2017-02-24 09:47:05
iterate
dolio 2017-02-24 09:47:39
That gives you a list of things.
Tuplanolla 2017-02-24 09:47:43
It seems dubious that you could generate the reals with a countable process, EvanR.
dolio 2017-02-24 09:47:58
Each one of those things will have a finite number of constructions on your input.
dolio 2017-02-24 09:48:40
And if they're things subject to the diagonal argument each time, of course each one won't be complete.
EvanR 2017-02-24 09:51:11
yes, if the question is if the result is complete, were back to the beginning
GusCE6 2017-02-24 09:51:43
Is this a place for help with programming?
EvanR 2017-02-24 09:51:47
yes it seems dubious
EvanR 2017-02-24 09:52:04
but it seems interesting that i can seem to use the construction to get "even more reals" than before
monochrom 2017-02-24 09:52:06
No.
EvanR 2017-02-24 09:52:18
then refold the result, then do it again
EvanR 2017-02-24 09:52:21
and iterate that
dolio 2017-02-24 09:52:22
You already listed countably many reals.
dolio 2017-02-24 09:52:38
Why are you surprised that you can generate countably many more?
dolio 2017-02-24 09:52:47
And still not have all uncountably many of them?
EvanR 2017-02-24 09:52:49
how many times do i need to iterate that before something different happens
EvanR 2017-02-24 09:53:20
countable x countable is still countable
EvanR 2017-02-24 09:53:36
i mean, i guess, i vaguely remember
GusCE6 2017-02-24 09:53:45
Basically I'm trying to get started programming applications. I do understand basic website programming.
int-e 2017-02-24 09:53:47
GusCE6: if it's related to the Haskell programming language...
monochrom 2017-02-24 09:54:29
10000 to 1 it is not.
GusCE6 2017-02-24 09:55:13
Oh- Do you know a chat room that can help me out here?
monochrom 2017-02-24 09:57:27
There is none.
Tuplanolla 2017-02-24 09:59:31
This is one, but you need to install GHC first, GusCE6.
GusCE6 2017-02-24 09:59:31
Actually, I'm trying to do so on a Windows CE6 ARM 8505 device...
Tuplanolla 2017-02-24 09:59:31
Forget what I said.
sveit 2017-02-24 09:59:31
in a functional heap/priority queue, is there a way around doing breadth-first search to find the node at which to insert an element?
EvanR 2017-02-24 09:59:31
i found this paper on the subject... "How Real are Real Numbers" by Gregory Chaitin https://www.cs.auckland.ac.nz/~chaitin/olympia.pdf
GusCE6 2017-02-24 09:59:31
It's a long story, but it boils down to an effort to keep weak outdated devices from becoming useless.
sveit 2017-02-24 09:59:31
of course i mean so that the heap stays balanced
flxw 2017-02-24 09:59:31
just to report back: Thanks for the input to my free theorems question. I was watching the wadler talk and indeed is beginning to help clear things up! ;)
Tuplanolla 2017-02-24 09:59:31
Freenode is not the best place to look for Windows support, GusCE6.
monochrom 2017-02-24 10:11:32
Or rather, by binary floating point.
dolio 2017-02-24 10:11:58
nshepperd_: Right, the question would then be what it means to 'iterate' that many times.
dolio 2017-02-24 10:12:51
And it's still not clear that the diagonalization process wouldn't miss things.
dolio 2017-02-24 10:13:30
If you could even define it sensibly.
nshepperd_ 2017-02-24 10:17:14
sdrodge: don't know anything about it
ongy 2017-02-24 10:18:58
monochrom: countable^countable? I thought it's just squared?
ongy 2017-02-24 10:19:44
oh it's 2^countable_infinity if I see this correctly
sdrodge 2017-02-24 10:20:46
There's not much significance to that notation other than the fact that a finite powerset of P has size 2^(size P).
sdrodge 2017-02-24 10:22:17
So since the cardinality of reals is equal to the cardinality of the powerset of naturals, we keep using that notation.
sveit 2017-02-24 10:22:51
is it a cause for worry in the community that many data structures typically used in non-trivial algorithms have worse asymptotic and constant factors when implemented functionally? i'm not trying to be a troll, i'm asking if this is seen as a serious obstacle or (hopefully) there is some reason this concern is unfounded.
Tuplanolla 2017-02-24 10:23:25
It's a deterrent for some applications, sveit.
Cale 2017-02-24 10:26:24
sveit: Well, if it ever matters, you can still do all the imperative stuff.
Cale 2017-02-24 10:26:24
sveit: However, it really tends not to be a big deal in practice.
sdrodge 2017-02-24 10:26:24
sveit: It's not unfounded at all, and Haskell has a lot of ways to enter impurity land for when you actually need performance characteristics that only destructive mutability can provide.
ezyang 2017-02-24 10:26:24
To people who use lens out there: is there any practical utility to being able to swap out lens implementation?
Cale 2017-02-24 10:26:24
There are a few places where we have data structures that are implemented via various degrees of cheating and which present a purely functional interface.
Tuplanolla 2017-02-24 10:26:24
We don't have enough number crunching scientists here.
ezyang 2017-02-24 10:26:24
(I'm asking because type synonym lenses actually need a new feature that we have thought about, but didn't implement because we couldn't think of a good use case for)
Cale 2017-02-24 10:26:24
e.g. ByteString and Vector and Text and various other array libraries all use various low level hackery to implement the operations
