Home liberachat/#haskell: Logs Calendar

Logs on 2022-07-26 (liberachat/#haskell)

00:07:15 <jackdk> You're welcome. I've only used the lib a little bit but it seems reasonable.
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00:41:44 <Axman6> pavonia: I wrote a fermatFactor function about a week or so ago. if you look in arithmoi and some of its dependencies, you can find functions which can quickly tell you if a^2-n is a square number without having to call isqrt again (it also has an efficient function for finding the integer square root)
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00:43:59 <Axman6> pavonia: https://hackage.haskell.org/package/integer-roots-1.0.2.0/docs/Math-NumberTheory-Roots.html you can use exactSquareRoot
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00:46:28 <Axman6> pavonia: it has a very cool fast function which can eliminate most non-square numbers by just looking at small remainders of the candidate: https://hackage.haskell.org/package/integer-roots-1.0.2.0/docs/src/Math.NumberTheory.Roots.Squares.html#isPossibleSquare
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00:50:31 <pavonia> Axman6: Thanks. My current test is much simpler: (n `mod` 16) `elem` [0,1,4,9]
00:51:28 <Axman6> that last function I linked to essentially does that and some others similar tests
00:51:59 <pavonia> What do you mean by "you can find functions which can quickly tell you if a^2-n is a square number without having to call isqrt again"? I'm only calling it once per candidate
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00:53:22 <pavonia> Ah, without the need to recalculate a*a apparently
00:54:05 <Axman6> well that's one thing, but I mean that calling isqrt and then checking if (isqrt b)^2 == b is a waste.
00:54:53 <Axman6> I had a version that avoided doing a*a every time by instead adding the difference between successive squares, but it ended up slower because it used mor memory I think
00:54:58 <pavonia> Yeah, that's what I meant
00:54:59 <Axman6> only slightly slower though
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00:57:34 <Axman6> if you use case exactSquareRoot (a*a - n) of then it should do the least amount of work, since it first does the efficient check for the posibility of being a square. and then runs integerSquareRootRem' :: Integral a => a -> (a, a)
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01:02:05 <pavonia> "After that, the remainders modulo 9, 25, 7, 11 and 13 are tested to eliminate altogether about 99.436% of all numbers." That's fascinating
01:02:43 <Axman6> the version I had started the recursion with calculating a2 = a^2; a2' = (a+1)^2; diff = a2' - a2; candidate = a2 - n. then passing around diff and candidate, incrementing diff by two, and adding it to candidate. you end up with no multiplications then
01:03:00 <Axman6> but it turned out not to really be worth the extra memory needed I think
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01:07:18 <pavonia> Axman6: Do you by chance know where to find the theory behind those remainder tests? I found the four values mod 16 simply by testing various moduli
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01:12:09 <Axman6> By chance? no. By Duck Duck Go? Possibly: https://www.researchgate.net/publication/337108188_Detecting_square_numbers :P
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01:19:42 <Axman6> looks like that article doesn't talk about those specific constants though
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02:20:30 <naso> is there a way i can write a function with signature e.g. Foldable f => f a -> Set a , that takes a foldable and converts it to a set, but if the input was already a set it does nothing
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02:38:03 <dibblego> Set.fromList . toList
02:38:35 <dibblego> (though Set is not foldable)
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02:45:38 <naso> dibblego: thanks
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02:53:46 <naso> dibblego: if Set is not foldable, why can i apply unions to a set of sets, unions has type unions :: (Foldable f, Ord a) => f (Set a) -> Set a
02:54:21 <dibblego> because in that type, f is foldable
02:54:54 <naso> e.g. i can do : Set.unions (Set.singleton (Set.empty))
02:55:10 <naso> (Set.singleton (Set.empty)) :: Set (Set a)
02:55:19 <naso> ?
02:56:19 <naso> doing :info Set, it says there is a Foldable instance for Set
02:56:26 <naso> instance Foldable Set
02:56:27 <naso> -- Defined in ‘containers-0.6.5.1:Data.Set.Internal’
02:59:37 <jackdk> Wasn't part of the point of splitting classes Foldable and Traversable so that non-functor containers like Set could have Foldable instances?
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03:18:04 <dibblego> ah yeah sorry, I take it back
03:19:28 <naso> all good :)
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05:18:46 <qrpnxz> so it turns out that the Codensity of a MonadReader is also a MonadState. Tried it with ReaderT and indeed works. Unforturnately it uses 2x CPU time, but hey, just 2x not bad for a reader :) I was trying to see why this might be, and i found that a non-transformed reader matches the speed of State exactly. I even tried make a hardcoded ReaderT Codensity and it made no difference. The weird part is
05:18:48 <qrpnxz> that the code is the exact same between the transformed and non-transformed version, so it seems there's some invisible different way that Haskell handles passing around a parameterized type that differs from just a normal value passing. Something about laziness and boxed types breaking tailcalls? Hard to tell. Another interesting result is that ContT StateT was also exactly twice the time, but
05:18:50 <qrpnxz> ContT State was exactly as fast. (With Codensity woth are as fast as just State).
05:19:36 <qrpnxz> s/woth/both
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05:45:12 <Haskelytic> are haskell modules open?
05:45:40 <Haskelytic> as in, can you have 2 source files contributing to the same module namespace?
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05:52:30 <dsal> No.
05:52:39 <dsal> A module can reexport another module, though.
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06:21:22 <Axman6> Haskelytic: if two packages define the same module that you import, you'll fail to compile it. there is an extension, PackageImports, to disambiguate them though (https://ghc.gitlab.haskell.org/ghc/doc/users_guide/exts/package_qualified_imports.html#extension-PackageImports)
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06:23:38 <Haskelytic> thanks!
06:23:56 <Haskelytic> btw, how do I progress further after finishing the haskell book
06:24:30 <dsal> Write lots of code. Read more Haskell books. :)
06:24:31 <Haskelytic> any good intermediate/advanced book recs?
06:25:13 <Haskelytic> dsal: (1) is ongoing :). Need some help with books L(
06:25:37 <dsal> I mostly do the "write lots of code" thing, but there are verticals like "Optics by Example" which I liked and "Thinking With Types"
06:25:52 <dsal> Though I read beginner books now and then just for new perspectives.
06:26:48 <Haskelytic> i'm too fresh out of the HFP book to be revisiting it :)
06:27:01 <Haskelytic> thanks for those ptrs btw, I'll check them out
06:28:09 <jackdk> Haskelytic: http://jackkelly.name/wiki/haskell.html what are you looking for?
06:28:13 <dsal> I've not read haskellbook more than once, but picking up new intro books has occasionally helped.
06:29:56 <Haskelytic> on an unrelated note, I find it absolutely hilarious that c++23 is adding this https://en.cppreference.com/w/cpp/utility/optional/and_then
06:31:00 <Haskelytic> dsal:  skimming the late Richard Bird's haskell books for some mental lubrication :)
06:31:24 <Haskelytic> jackdk: whoooaa...thanks for that!
06:31:36 <dsal> I've not read *all* the books. Just a few.
06:31:53 <dsal> That reading list above looks good. "Parse, Don't Validate" is pretty good life changing stuff.
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06:34:13 <sm> Haskelytic: review source repos of a bunch of interesting packages from hackage, clone and try to build them, try to get a small bugfix accepted
06:34:53 <jackdk> I love reading random packages that appear in the build logs of cabal, like "what on earth is that? I'll look it up while things are building"
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06:35:25 <jackdk> Haskelytic: "What are you looking for?" was not rhetorical -- where do you intend to go with Haskell?
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06:36:33 <jackdk> dsal: I try to curate it fairly carefully, so if you have any suggested additions/removals/replacements I'd be keen to hear them
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06:36:59 <dsal> jackdk: Thanks. I have to look at it a lot more first. There are a few things in there I've not read.
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06:38:16 <Haskelytic> jackdk: I'm learning it on the side so tbh I don't really know. I'm just having a blast finding new ways to write old programs.
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06:39:08 <sm> porting your own programs is another good way
06:39:32 <jackdk> Agreed. I think text-mode games are also a great way to learn a new language, if you're hurting for project ideas
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06:41:56 <Axman6> Haskelytic: the best way to direct your learning is to make things you want to make and find out what you need to know to achieve that
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06:44:49 <Hecate> heya Axman6
06:44:53 <Hecate> how are you doing?
06:45:16 <Axman6> Hey, not too bad my friend, how about you?
06:46:09 <Hecate> hands started to fall apart recently, so I need to stop being so glued to my keyboard
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06:50:29 <Axman6> D:
06:50:42 <Axman6> yeah definitely take care of those, they're pretty... handy
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11:18:50 <bahamas> shouldn't wai-static-middleware set the content type of a js file to text/javascript?
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11:19:18 <bahamas> I see in response headers Content-Type: text/plain
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11:19:46 <bahamas> the file name is "head.3dc67258.js"
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11:42:43 <bahamas> folks who are doing web development in Haskell. how do you serve your static assets in development?
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11:54:39 <sm> I embed them in the executable with file-embed, and serve them with yesod-static
11:56:10 <Franciman> nice solucion
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11:57:57 <bahamas> sm: in development? I don't understand the part about embedding them in the executable
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12:00:33 <sm> as in https://hackage.haskell.org/package/hledger-web-1.26.1/docs/src/Hledger.Web.Settings.StaticFiles.html, if that helps. The package docs have more explanation
12:01:16 <sm> https://hackage.haskell.org/package/file-embed-0.0.15.0/docs/Data-FileEmbed.html eg
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12:37:34 <bahamas> why do I get Unknown field: "extra-source-files" in the cabal file?
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12:50:01 <Axman6> bahamas: we'd need to see how you're using it to know. the docs ar pretty simple https://cabal.readthedocs.io/en/3.6/cabal-package.html#pkg-field-extra-source-files but if you're using it in the wrong placeit'lll be confused
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15:12:22 <matthewmosior> Hello!
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15:19:46 <geekosaur> hello
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15:27:04 <hasbae> import Control.Monad
15:27:09 <hasbae> :t liftM
15:27:10 <lambdabot> Monad m => (a1 -> r) -> m a1 -> m r
15:28:07 <geekosaur> liftM is historical; you probably want fmap
15:28:08 <hasbae> is there some logic for what letters are used for typevars? For example, liftM could be Monad m => (a -> b) -> m a -> m b. But instead it chose a1 and r
15:28:38 <geekosaur> there is logic somewhere but it's not particularly understandable unless you understand the guts of the typechecker
15:29:09 <dolio> That one is written in the source that way, for some reason.
15:29:14 <hasbae> how does one get started in exploring the guts of the typechecker?
15:29:20 <dolio> https://hackage.haskell.org/package/base-4.16.2.0/docs/src/GHC.Base.html#liftM
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15:30:46 <geekosaur> first you go through https://gitlab.haskell.org/ghc/ghc/-/wikis/commentary/compiler/type-checker (and more generally the commentary of which that is a part)
15:30:49 <qrpnxz> hasbae: ik it's informed by whatever name is on the explicit type sigs you write, from there idk, something arbitrary
15:31:54 <hasbae> geekosaur: very cool
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15:33:15 <geekosaur> the commentary is very useful in understanding ghc. but it's not the full story; after going through the commentary you start reading the Notes in the typechecker source (ghc is well supplied with internal source documentation in this form)
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16:38:04 <albet70> how to get current date? like "2022-07-27-12:00:00"
16:38:48 <qrpnxz> albet70: try the time package
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16:40:22 <albet70> yeah, getCurrentTime
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16:52:07 <albet70> import Data.Time.Format.ISO8601 ; do { t <- getCurrentTime; print $ Format t }
16:52:43 <albet70> it tell me Data constructor not in scope: Format :: UTCTime -> a0
16:52:46 <albet70> why?
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16:57:04 <albet70> iso8601Format :: FormatUTCTime
16:57:19 <geekosaur> because Format is a type constructor, not a data constructor
16:57:50 <[exa]> albet70: you might want this instead https://hackage.haskell.org/package/time-1.13/docs/Data-Time-Format.html#v:formatTime
16:58:06 <[exa]> good defaults for the first 2 arguments are below on the same page
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17:05:20 <albet70> I see
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17:40:28 <albet70> https://nliu.net/drafts/2021-09-09-2021-09-09-interview-free.html
17:40:54 <albet70> this code is insane to me, how I can understand it
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17:42:22 <geekosaur> didn't someone (wadler?) also do an embedded basic interpreter in haskell?
17:44:41 <albet70> where's the Free type constructor from
17:45:51 <geekosaur> lennart augustsson, apparently (embedded BASIC)
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17:46:17 <geekosaur> Control.Monad.Free
17:46:28 <geekosaur> it's a free monad, which is commonly used in interpreters
17:47:33 <geekosaur> https://hackage.haskell.org/package/BASIC-0.1.5.0/src/examples/HiLo.hs
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17:48:18 <albet70> thanks
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17:54:20 <megablocks> Hello! I am looking at the GHC code to try to figure out how pinned memory works better. My main question boils down to, is there any benefit to using 16kb vs 32kb chunks when I have large items? Or should it just be a multiple of 4kb?
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17:55:02 <megablocks> My basic understanding is that blocks are 4kb (see https://gitlab.haskell.org/ghc/ghc/-/blob/master/rts/include/rts/Constants.h#L169) but I am not clear on what happens when someone wants a larger chunk.
17:55:18 <geekosaur> that is probably a question for #ghc, but I would assume it's trading off performance against fragmentation
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17:56:50 <geekosaur> (larger blocks mean faster allocation list management but more fragmentation)
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17:57:33 <megablocks> Ah, I just found there's a concept of "block groups" for adjacent blocks! https://gitlab.haskell.org/ghc/ghc/-/blob/master/rts/sm/BlockAlloc.c
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17:58:46 <megablocks> I'll try in #ghc. I didn't know about that channel. Thank you!
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18:05:37 <qrpnxz> i tend to pick memory chunks of 4k or a multiple because that's usually the page size on a linux system, idk if some other metric is relevant to ghc GC or something else
18:06:45 <megablocks> qrpnxz, GHC uses 4kb as well https://gitlab.haskell.org/ghc/ghc/-/blob/master/rts/include/rts/Constants.h#L169
18:06:54 <megablocks> probably for the page size reasons you mention
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19:39:07 <phma> Is it possible to make a type whose parameter is a number, rather than another type?
19:41:47 <geekosaur> there are type level numbers. they are not values
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19:43:10 <phma> What's a type level number?
19:43:16 <geekosaur> > toEnum 1024 :: Data.Fixed.Fixed 2
19:43:18 <lambdabot> 512.0
19:43:48 <geekosaur> 2 there has kind Natural
19:44:00 <geekosaur> and is a type
19:44:49 <geekosaur> the general case of wanting a number a type level requires dependent types, which are not supported in Haskell. Try Idris instead.
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19:45:33 <phma> I've been defining a complex floating point type; I'd like it to have a specifiable number of digits, normally 22 or 44 but could be any positive integer.
19:45:50 <geekosaur> (in particular,m recovering a value-level number from a type level number in Haskell requires a KnownNat constraint)
19:45:58 <phma> So "GosperFloat 22" would be a type.
19:46:12 <geekosaur> that is doable, go look at Data.Fixed
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19:46:37 <geekosaur> > .305 :: Data.Fixed.Fixed 3
19:46:39 <lambdabot> <hint>:1:1: error: parse error on input ‘.’
19:46:46 <geekosaur> > 0.305 :: Data.Fixed.Fixed 3
19:46:47 <lambdabot> 0.0
19:47:03 <geekosaur> hm, I guess I forget how you use them 😕
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19:48:06 <phma> found the hackage page of Fixed
19:48:42 <geekosaur> recent versions claim to support Natural as well as the predefined E<n> type synonyms
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19:49:53 <exarkun> /buffer 12
19:50:32 <geekosaur> oh, I see
19:50:37 <geekosaur> > 0.305 :: Data.Fixed.Fixed 1000
19:50:39 <lambdabot> 0.305
19:51:02 <geekosaur> thought it took number of digits. I think you could define yours that way though
19:53:55 <phma> Another thing: is it permissible for a type that's a member of Ord to have a (<) that has some loops?
19:54:18 <phma> that is, there exist a,b,c such that a<b, b<c, and c<a
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19:57:23 <darkling> I would be very surprised if it were (although I don't know the exact definition of Ord).
19:58:00 <geekosaur> iirc the Report says Ord is a total order, so no
19:59:34 <phma> The GosperInteger type encodes Eisenstein integers (complex numbers in a triangular lattice) in the Gosper base.
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20:00:21 <phma> To decide which of two GosperIntegers has the larger norm, I found it easier to define (<) on them than convert the norm to Integer.
20:01:22 <phma> When comparing norms, the norms are always real numbers, and (<) on GosperIntegers that are real works as expected.
20:01:45 <phma> But near the imaginary axis, you can find numbers which compare circularly.
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20:01:54 <geekosaur> fwiw you will find that Complex Double is not Ord
20:02:16 <phma> but Eisenstein is Ord, which astonished me
20:05:40 <phma> also Double is Ord, but (0/0)==(0/0) is False
20:06:49 <phma> > compare (0/0) (0/0)
20:06:51 <lambdabot> GT
20:07:13 <phma> > (0/0)>(0/0)
20:07:15 <lambdabot> False
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20:07:42 <geekosaur> this gets complained about somewwhat regularly. Double gets to be an exception to the rules because of IEEE arithmetic
20:08:55 <phma> does it cause any problems? do people sort lists with NaN in them?
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20:11:38 <darkling> I'm sure they do somewhere.
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20:13:44 <geekosaur> https://calculist.blogspot.com/2006/02/nancy-typing.html
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20:17:27 <darkling> Nice.
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20:18:26 <geekosaur> anyway Num is a hash of bad abstractions and leaky laws, designed not for coherence but to make it easier for beginners to work with
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21:11:30 <qrpnxz> looks like `text` lost all its hackage docs oops
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21:15:58 <hpc> at least hackage docs didn't lose all their text :P
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21:25:05 <qrpnxz> :P
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21:27:32 <hpc> ah, it was just updated
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21:27:42 <hpc> give it some time for haddock to do its thing on the new code, i guess
21:27:57 <hpc> yeah, status is docs pending at the bottom
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21:29:56 <Cale> (you can also click a previous version to view its docs while you wait)
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21:30:24 <qrpnxz> yes, i also have a system docs in case no internet :)
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21:31:52 <qrpnxz> can't derive semigroup on a newtype over ByteString 😩
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21:36:08 <qrpnxz> guys, what is even the point of text actually. Why not just a newtype wrapper over ByteString? Is it actually doing anything fancy?
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21:37:53 <qrpnxz> the point of whole new underlying implementation that is.
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21:38:21 <geekosaur> text's native representation is utf16 or utf8 depending on version, and includes Unicode support
21:38:34 <geekosaur> ByteString is raw bytes meaning who-knows-what
21:38:38 <hpc> put simply, the difference between text and a simple wrapper is that text works :P
21:39:09 <hpc> it handles encoding and some other assorted stuff for you
21:39:12 <geekosaur> also ByteString is pinned memory for easier interop with FFI
21:39:52 <geekosaur> most people don't understand that there are real differences between byte arrays and proper Unicode
21:40:14 <geekosaur> because most languages make no distinction and let you make huge messes as a result
21:40:48 <qrpnxz> underneath Text is also just "raw bytes" is my point, so really the text api could act on a wrapped bytestring. Or "short"bytestring for unpinned that you point out
21:41:13 <hpc> underneath raw bytes is a pointer and a length
21:41:21 <hpc> so really the text api could act on unsigned integers
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21:43:32 <hpc> blocks of text are a nice logical unit to treat as abstract, since it doesn't really matter what they are implemented as under the hood
21:43:36 <qrpnxz> yes, but that doesn't help, whereas text being just on top ByteString means there's only one implementation of raw bytes to worry about
21:43:49 <hpc> as a bit of a pathological example, imagine having to deal with rust's lifetimes
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21:44:22 <hpc> is your text a string of bytes in the data segment, is it on the heap, what's its encoding, etc
21:44:44 <hpc> or you can just say "it's text, if i say make it utf-8, i don't care what encoding it comes from"
21:44:47 <hpc> and so forth
21:44:58 <hpc> it might be a ByteString now, but it might be some other representation later
21:45:24 <hpc> and in fact, pop quiz: what encoding is the ByteString text uses as its internal representation?
21:45:30 <qrpnxz> yes, i'm proposing why not just have it a bytestring instead of another specialized primitive array implementation in text
21:45:46 <qrpnxz> i'm not proposing a change in the public api
21:46:01 <qrpnxz> ByteString is a Ptr with length
21:46:04 <Profpatsch> NonEmpty defines most of its functions with a lazy pattern match, like uncons ~(a :| as) = (a, nonEmpty as)
21:46:35 <hpc> oh, you're talking about Data.Text.Array?
21:46:48 <Profpatsch> I can understand for a fundamental lib like this, but I feel like doing it for every time you match on (:|) is a bit of a premature optimization?
21:47:07 <hpc> because of what geekosaur mentioned, how it interacts with ffi
21:47:31 <qrpnxz> Profpatsch: you pretty much always want to stream lists as much as possible
21:47:41 <Profpatsch> qrpnxz: yeah that makes sense
21:48:10 <hpc> ByteString uses ForeignPtr, Text uses ByteArray#
21:48:23 <Profpatsch> qrpnxz: do you know if there’s a ZipList1 or something?
21:48:34 <qrpnxz> hpc: ShortByteString also use ByteArray
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21:48:37 <Profpatsch> I want to have zip3 zip4 etc for NonEmpty
21:48:55 <qrpnxz> in base? idk let me check
21:48:58 <Profpatsch> I mean I can just write down the boilerplate but I was surprised by the ~ gotcha
21:49:03 <Profpatsch> qrpnxz: I did check no worries
21:49:12 <qrpnxz> ah, well i guess not
21:49:20 <qrpnxz> but you can make your own
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21:49:32 <Profpatsch> yeah, that’s why I was looking up the definition and was a bit surprised by the ~
21:49:43 <Profpatsch> But it makes sense
21:50:01 <Profpatsch> qrpnxz: on a related note, I’ve been using Validation (NonEmpty _) a lot
21:50:20 <qrpnxz> 👍
21:50:23 <Profpatsch> I’m wondering about the performance of that.
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21:51:20 <qrpnxz> If you are not streaming the lists and using them multiple time you should probably be using an array of some kind
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21:51:30 <Profpatsch> Wouldn’t that be a bit slow, for most cases I do stuff like read from the database and stream back as json
21:51:58 <Profpatsch> I’m not using conduit or similar (yet), so it’s all in memory
21:52:12 <Profpatsch> I guess worrying about that is a bit premature optimization
21:52:18 <Profpatsch> But I wonder if it’s a good pattern.
21:52:32 <qrpnxz> if it's more than a little data you should try to stream it with something like conduit to not waste memory yeah
21:52:43 <Profpatsch> But then error handling becomes hard
21:52:59 <Profpatsch> I mean Validation basically requires to do the whole thing in memory
21:53:18 <Profpatsch> You only know the constructor on the first Failure
21:53:22 <qrpnxz> I think it's a good pattern. I mean, I personally don't mind having a bunch of wrappers if it helps me be able to look at code and say 'yeah, that's a valid whatever for sure'
21:53:24 <Profpatsch> Or at the very end
21:54:15 <Profpatsch> qrpnxz: Validation and These have been a funky improvement to error handling if I’ve ever seen one
21:54:35 <qrpnxz> oh is validation a particular data type you are talking about?
21:54:59 <qrpnxz> ah hadn't heard of that, it's from the either package
21:55:10 <Profpatsch> qrpnxz: Validation is a type isomorphic to Either, but not shortcutting instead it accumulates errors
21:55:36 <qrpnxz> i see
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21:56:34 <qrpnxz> you could be polymorphic on the error monad, then you can choose to shortcut or accumulate or throw io exception. Makes sense.
21:56:38 <Profpatsch> Between Either, Validation and These you basically have all possible error handling behaviours
21:56:52 <Profpatsch> I haven’t seen a case where being polymorphic would make sense
21:57:09 <Profpatsch> (you can also have shortcutting on Success but that is achievable by flipping the Either)
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21:58:04 <Profpatsch> qrpnxz: you can’t really be polymorphic, cause Validation requires the error to be a Semigroup
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21:58:58 <qrpnxz> Either doesn't require it to NOT be semigroup, so that's fine
21:59:35 <Profpatsch> qrpnxz: But usually your error type in Either is something like Text, while for Validation/These it’s a list-like
22:00:22 <qrpnxz> but your function that you want to use with both Validation and Either is of course going to have an error that works with Validation, so if you chose validation that works, and if you choose either that also works.
22:00:27 <Profpatsch> I guess if you have something text-like that concatenates with "\n- " it might make sense
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22:01:24 <Profpatsch> i.e. data ListError = ListError Builder instance Semigroup ListError where (ListError a) <> (ListError b) = a <> "\n- " <> b
22:01:27 <qrpnxz> it's the same thing with IO, if your errors are exception then you can use IO or Either. If the errors are not exceptions, then you can only use either
22:01:48 <Profpatsch> now it’s also somewhat performant
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All times are in UTC on 2022-07-26.