Logs on 2025-09-20 (liberachat/#haskell)
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| 08:47:03 | <Enrico63> | Hello there! |
| 08:50:24 | <Rembane> | Hello Enrico63 ! |
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| 08:57:16 | <Enrico63> | I'm going though https://haskell.mooc.fi/part2 and one exercise (https://github.com/moocfi/haskell-mooc/blob/59735e76d37c5470504be4d64206cd49660e1324/exercises/Set9a.hs#L187-L229) consists in implementing a permutation function that works like this: |
| 08:57:17 | <Enrico63> | -- permute [0,1,2,3] "hask" ==> "hask" |
| 08:57:17 | <Enrico63> | -- permute [2,0,1,3] "hask" ==> "ashk" |
| 08:57:18 | <Enrico63> | -- permute [1,2,3,0] "hask" ==> "khas" |
| 08:57:18 | <Enrico63> | Using just lists, I've come up with this solution, which takes O(n log n - i.e. complexity of sorting): |
| 08:57:19 | <Enrico63> | permute :: [Int] -> [a] -> [a] |
| 08:57:19 | <Enrico63> | permute p s = map snd $ sortOn fst $ zip p s |
| 08:57:20 | <Enrico63> | however, if I had used mutable arrays, I could have done something like this, which is just O(n), right? |
| 08:57:20 | <Enrico63> | permute :: [Int] -> [a] -> [a] |
| 08:57:21 | <Enrico63> | permute idxs list = |
| 08:57:21 | <Enrico63> | elems (array (0, n-1) (zip idxs list)) |
| 08:57:22 | <Enrico63> | where n = length list |
| 08:57:22 | <Enrico63> | To me it feels like such a solution requires 2 features: the ability to random access an array with O(1), and mutability. |
| 08:57:23 | <Enrico63> | The solution with sorting doesn't use either of those and indeed it pays with O(n log n) or whatever. |
| 08:57:23 | <Enrico63> | Can anybody suggest some material I could refer to, if I want to better understand the stuff above? |
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| 08:59:49 | <tomsmeding> | Enrico63: the array you used isn't mutable, and doesn't need to be |
| 09:00:35 | <tomsmeding> | I would say that the most straightforward solution is the O(n^2) `permute idxs list = map (list !!) idxs` |
| 09:01:21 | <tomsmeding> | which you can speed up with an array using `permute idxs list = let arr = listArray (0, length list - 1) list in map (arr !) idxs` |
| 09:01:58 | <tomsmeding> | ... apologies, I got the permutation in the wrong direction |
| 09:02:06 | <tomsmeding> | your `array` solution is indeed correct, my suggestions are not |
| 09:02:33 | <tomsmeding> | `array` is indeed implemented using mutation under the hood, but the function as a whole is pure |
| 09:03:06 | <tomsmeding> | and indeed, all of haskell is, necessarily: the underlying hardware can do things only through mutation |
| 09:03:16 | <Enrico63> | Yeah, I know that. But the reason why it is fast is that it uses mutation. |
| 09:03:31 | <tomsmeding> | to an extent |
| 09:03:48 | <tomsmeding> | one thing you could I guess look up in reference to this, is pull arrays vs push arrays |
| 09:03:54 | <Enrico63> | So my question is not about Haskell. It's just that doing this in Haskell forced me to think about something I hadn't thought before. |
| 09:04:09 | <tomsmeding> | what you're being asked here is a forward permutation, which you can do efficiently in push-array style and not in pull-array style |
| 09:04:46 | <tomsmeding> | a backward permutation (which is what I described with `map (list !!) idxs`) can be efficiently implemented using pull arrays, which is more natural in a functional setting |
| 09:04:49 | <Enrico63> | Forward permutation =? I have the list of destination indices of original indices 0,1,2,..? |
| 09:05:12 | <Enrico63> | Ok, I think that's what you mean by forward/backward permutation |
| 09:05:14 | <tomsmeding> | yes |
| 09:07:03 | <Enrico63> | Ok, but backward permutation is a non-problem. I mean, if your original snippet can be even O(n) if `list` gives O(1) `!!`, and requires no mutability to be that fast. |
| 09:07:20 | <tomsmeding> | yes, and that's what I did using listArray |
| 09:07:39 | <tomsmeding> | I'm not sure what kind of theory you're looking for :p |
| 09:07:42 | <Enrico63> | Oh, right, didn't read that. Anyway, that's why I say it's a non-problem |
| 09:08:12 | <tomsmeding> | backward permutation is also easier to parallelise efficiently than forward permutation, especially if the permutation is not required to be bijective |
| 09:08:12 | <Enrico63> | I'm not sure either, ahahah |
| 09:08:41 | <tomsmeding> | having multiple destination elements read from the same source element is... just do that |
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| 09:09:09 | <tomsmeding> | sending multiple source elements to the same destination element using `permute` is suddenly very interesting |
| 09:09:18 | <tomsmeding> | how do you combine multiple elements being sent to the same spot? |
| 09:09:36 | <tomsmeding> | this is why Data.Array.accumArray has a combining function |
| 09:10:41 | <Enrico63> | Why mutiple elements sent to the same spot? That doesn't happen with permutation.. |
| 09:10:50 | <tomsmeding> | but we can generalise the operation to allow that |
| 09:10:57 | <tomsmeding> | well, we can easily generalise backward permutation to allow that |
| 09:11:04 | <tomsmeding> | generalising forward permutation suddenly requires a combining function |
| 09:11:17 | <tomsmeding> | % backpermute idxs list = map (list !!) idxs |
| 09:11:17 | <yahb2> | <no output> |
| 09:11:23 | <tomsmeding> | % backpermute [0,0,0,2] "hask" |
| 09:11:23 | <yahb2> | "hhhs" |
| 09:11:26 | <tomsmeding> | works fine |
| 09:11:41 | <tomsmeding> | % import qualified Data.Array as A |
| 09:11:41 | <yahb2> | <no output> |
| 09:11:59 | <Enrico63> | You're executing Haskell code in here... :O |
| 09:12:18 | <tomsmeding> | % A.accumArray (+) 0 (0,3) (zip [0,0,0,2] [1,2,3,4]) |
| 09:12:18 | <yahb2> | array (0,3) [(0,6),(1,0),(2,4),(3,0)] |
| 09:12:24 | <tomsmeding> | % A.elems $ A.accumArray (+) 0 (0,3) (zip [0,0,0,2] [1,2,3,4]) |
| 09:12:24 | <yahb2> | [6,0,4,0] |
| 09:12:52 | <tomsmeding> | this is a forward permutation with idxs=[0,0,0,2] and list=[1,2,3,4], using the (0, +) monoid |
| 09:13:11 | <tomsmeding> | if the permutation is bijective, i.e. you have no overlap, no monoid is required, as you've seen |
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| 09:13:33 | <tomsmeding> | (1+2+3 = 6) |
| 09:14:05 | <tomsmeding> | @let import qualified Data.Array as A |
| 09:14:06 | <lambdabot> | Defined. |
| 09:14:15 | <tomsmeding> | > A.elems $ A.accumArray (+) 0 (0,3) (zip [0,0,0,2] [a,b,c,d]) |
| 09:14:17 | <lambdabot> | [0 + a + b + c,0,0 + d,0] |
| 09:14:20 | <tomsmeding> | nice |
| 09:14:53 | <Enrico63> | Ok, yes, I see that. I think I just haven't been clear about what is puzzling me. |
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| 09:16:50 | <tomsmeding> | what is puzzling you? :) |
| 09:18:17 | <mauke> | the nature of your game |
| 09:18:19 | <Enrico63> | I guess what I'm saying is that with the example I gave above, I understand that the problem of (backward) permutation is not doable in O(n) unless you have O(1) random access + mutability. And I'd like to understand a bit more about the relation between complexity and .. language features? |
| 09:18:48 | <Enrico63> | I see your point of mutability being an impl. detail, yes. But: |
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| 09:20:16 | <Enrico63> | If I see something like `elems (array (0, n-1) (zip idxs list))`, and one tells me it's happening in O(n), ... then I know that array is allocating an array, doing mutation of that very array, and the passing that very array to elems. |
| 09:20:31 | <tomsmeding> | right |
| 09:21:01 | <Enrico63> | Mutation might be an impl. detail, but it kind leaks out by just knowing the complexity of the algo. If it's O(n), you know it's doing mutability. |
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| 09:21:17 | <tomsmeding> | (in the usual RAM model where memory access is considered O(1), ignoring physical effects that mean memory access is more accurately something like O(sqrt(n)) with a very low constant factor) |
| 09:21:49 | <tomsmeding> | right. It depends mostly on what you consider your "base language" of pure operations |
| 09:22:22 | <tomsmeding> | allocating an array incurs mutation: you mutate the memory allocator's internal data structures and write a bunch of zeros to memory |
| 09:22:41 | <tomsmeding> | but it makes a lot of sense to consider this a pure operation, so we include this, black-box, as a pure operation in our "base language" |
| 09:23:02 | <tomsmeding> | similarly instead of writing zeros, writing elements computed using a pure function is still pure |
| 09:23:26 | <tomsmeding> | ( https://hackage.haskell.org/package/vector-0.13.1.0/docs/Data-Vector.html#v:generate ) |
| 09:23:43 | <tomsmeding> | but somehow it feels wrong for `array` to also be a pure function in our "base language" |
| 09:23:45 | <tomsmeding> | why is that? |
| 09:23:50 | <Enrico63> | Maybe I'm just making confusion between language features and space requirements of an algo, now that I think more about it? |
| 09:24:06 | <tomsmeding> | no I completely get your feeling, I feel the same way about `array` |
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| 09:24:17 | <tomsmeding> | but I do also think that it's a question of perspective |
| 09:24:59 | <tomsmeding> | maybe it's that `array` does not naturally parallelise? |
| 09:25:26 | <tomsmeding> | but it does -- you need an atomic write operation for the elements in case of overlap, but otherwise you're good |
| 09:25:58 | <Enrico63> | What I mean is that backward permutation, from a purely algorithmic perspective, probably requires O(n) space in order to achieve O(n) time. And O(n) space I think assumes that you have O(1) cost for reading-writing anywhere... |
| 09:26:20 | <tomsmeding> | backward permutation is the "easy" one |
| 09:26:33 | <Enrico63> | oh, sorry, then s/back/for/g |
| 09:26:35 | <tomsmeding> | right |
| 09:26:54 | <tomsmeding> | what O(n) space is that? The destination array? |
| 09:26:59 | <Enrico63> | yeah |
| 09:26:59 | <tomsmeding> | you need that anyway |
| 09:27:10 | <tomsmeding> | apart from inputs and outputs, no additional space is needed |
| 09:27:24 | <tomsmeding> | backward permutation (the easy one) also needs space for the input _and_ the output |
| 09:27:31 | <tomsmeding> | can't be done in-place either |
| 09:27:43 | <tomsmeding> | (even if input and output happen to be the same size) |
| 09:28:53 | <Enrico63> | What you mean? Any permutation can be done in-place if you can swap elements, no? |
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| 09:29:03 | <tomsmeding> | from my perspective, the thing that makes `array`/`accumArray` (the forward permutation thing) feel "different" is that we tacitly accept a pull array (Data.Vector.generate) as a basic pure operation, but little more |
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| 09:29:30 | <tomsmeding> | Enrico63: how are you going to do a bijective backward permutation in O(n) time in-place? |
| 09:29:56 | <Enrico63> | Oh, I was lifting the O(n) req |
| 09:30:08 | <tomsmeding> | okay remove the "in O(n) time" then lol |
| 09:30:21 | <Enrico63> | As in, I thought you were saying something general |
| 09:30:25 | <Enrico63> | silly of me thinking so :D |
| 09:30:40 | <tomsmeding> | well, I think of these data movement operations as having a certain expected time complexity |
| 09:30:50 | <tomsmeding> | but in this particular case the time complexity is, I think, irrelevant to my point :p |
| 09:31:09 | <tomsmeding> | I know of a way to do a bijective backward permutation in-place, but it's very sequential and mutation-heavy |
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| 09:31:59 | <tomsmeding> | and moreover, that sequential, mutation-heavy algorithm for a bijective backward permutation can be rather easily modified to do a bijective forward permutation instead |
| 09:32:37 | <tomsmeding> | it's when you lift the requirement of being in-place that the two start to meaningfully differ, as far as I know -- though I may be wrong here, because I've thought very little about the in-place case |
| 09:32:51 | <tomsmeding> | (if you need history: https://ircbrowse.tomsmeding.com/browse/lchaskell?events_page=16546 ) |
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| 09:34:30 | <tomsmeding> | I guess what I'm saying is: do you have a _precise_ way in which forward permutation is "less pure" (for some suitable definition of "less pure" that you can choose) than backward permutation? |
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| 09:41:42 | <Enrico63> | Yes, the way I see it. The solution `permute idxs list = let arr = listArray (0, length list - 1) list in map (arr !) idxs` is fast by being able to read with random access. The ouptut is produced purely, by picking elements from arr while building the new output list. The solution `elems (array (0, n-1) (zip idxs list))` produces the output my |
| 09:41:42 | <Enrico63> | creating the array all at once, and then mutating the elements with random access. |
| 09:42:04 | <Enrico63> | That's probably not _precise_, but I see a difference between the two :D |
| 09:44:36 | <Enrico63> | I see that `listArray (0, lenth list - 1) list` is probably using mutability the same way that `array (0, n-1) (zip idx list))` is using it :/ |
| 09:45:20 | <Enrico63> | well, maybe that's why the two things are not so different :/ |
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| 09:46:05 | <tomsmeding> | Enrico63: your reasoning why `elems (array (0, n-1) (zip idxs list))` is not pure first splits up `array` in two phases: array allocation and then a bunch of writes |
| 09:46:11 | <tomsmeding> | why do you not split up `listArray` similarly? |
| 09:46:26 | <tomsmeding> | right |
| 09:46:48 | <Enrico63> | yeah, I see |
| 09:46:49 | <tomsmeding> | I know they feel different, but indeed the point I'm making is that in terms of _purity_, they aren't necessarily so different |
| 09:47:22 | <tomsmeding> | they generalise differently to non-bijective index mapping functions, and they parallelise somewhat differently, especially in the non-bijective case |
| 09:47:43 | <tomsmeding> | but I don't think there's a robust way you can argue that one is more pure than the other |
| 09:48:01 | <tomsmeding> | without picking an arbitrary "base language" of pure operations that you allow |
| 09:49:16 | <tomsmeding> | also, they're just algorithmically not the same |
| 09:49:48 | <tomsmeding> | but "not the same" doesn't imply an order of preference |
| 09:50:20 | <Enrico63> | Thanks for the discussion! :) |
| 09:50:29 | <tomsmeding> | relevant: https://hackage-content.haskell.org/package/massiv-1.0.5.0/docs/Data-Massiv-Array.html (the `D` representation is a pull array, represented as effectively (Int, Int -> a); the `DL` representation is a push array) |
| 09:50:42 | <Enrico63> | Now that I'm unemployed, I have plenty of time to discuss stuff, ahah |
| 09:50:44 | <tomsmeding> | pull arrays are generally more versatile |
| 09:50:58 | <tomsmeding> | they behave more intuitively under composition of pull-style functions |
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| 19:02:44 | → | Unicorn_Princess joins (~Unicorn_P@user/Unicorn-Princess/x-3540542) |
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| 19:06:36 | × | petrichor quits (~jez@user/petrichor) (Quit: ZNC 1.10.1 - https://znc.in) |
| 19:07:38 | × | merijn quits (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 248 seconds) |
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| 19:15:16 | puke | is now known as Guest2627 |
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| 19:15:16 | × | Guest2627 quits (~puke@user/puke) (Killed (copper.libera.chat (Nickname regained by services))) |
| 19:15:16 | pyooque | is now known as puke |
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| 19:19:08 | Athas_ | is now known as Athas |
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| 19:21:23 | → | dontdieych joins (~dontdieyc@132.226.169.184) |
| 19:22:42 | × | rvalue quits (~rvalue@about/hackers/rvalue) (Quit: bmV2ZXJnb25uYWdpdmV5b3V1cG5ldmVyZ29ubmFsZXR5b3Vkb3du) |
| 19:23:00 | → | rvalue joins (~rvalue@about/hackers/rvalue) |
| 19:23:18 | × | merijn quits (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 260 seconds) |
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| 20:09:31 | × | merijn quits (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 255 seconds) |
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| 20:27:00 | × | merijn quits (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 245 seconds) |
| 20:29:53 | × | tromp quits (~textual@2001:1c00:3487:1b00:5948:8c6b:93fe:bd0a) (Quit: My iMac has gone to sleep. ZZZzzz…) |
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| 20:38:46 | × | merijn quits (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 255 seconds) |
| 20:39:00 | × | Everything quits (~Everythin@88.155.4.6) (Quit: Lost terminal) |
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| 20:57:40 | × | jmcantrell_ quits (~weechat@user/jmcantrell) (Ping timeout: 255 seconds) |
| 21:01:23 | × | chexum quits (~quassel@gateway/tor-sasl/chexum) (Remote host closed the connection) |
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| 21:25:14 | × | merijn quits (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 260 seconds) |
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| 21:41:24 | × | anish quits (~user@52.124.41.233) (Remote host closed the connection) |
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| 21:56:20 | × | CiaoSen quits (~Jura@2a02:8071:64e1:da0:5a47:caff:fe78:33db) (Ping timeout: 244 seconds) |
| 22:00:35 | × | tromp quits (~textual@2001:1c00:3487:1b00:5948:8c6b:93fe:bd0a) (Quit: My iMac has gone to sleep. ZZZzzz…) |
| 22:01:04 | × | takuan quits (~takuan@d8D86B9E9.access.telenet.be) (Remote host closed the connection) |
| 22:02:01 | × | weary-traveler quits (~user@user/user363627) (Ping timeout: 244 seconds) |
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| 22:05:37 | trickard___ | is now known as trickard |
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| 22:10:19 | × | anish quits (~user@52.124.41.233) (Ping timeout: 258 seconds) |
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| 22:14:03 | × | williu5 quits (~williu5@user/williu5) (Client Quit) |
| 22:15:38 | × | Lord_of_Life quits (~Lord@user/lord-of-life/x-2819915) (Quit: Laa shay'a waqi'un moutlaq bale kouloun moumkine) |
| 22:15:59 | → | Lord_of_Life joins (~Lord@user/lord-of-life/x-2819915) |
| 22:16:25 | × | jmcantrell_ quits (~weechat@user/jmcantrell) (Quit: WeeChat 4.7.1) |
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| 22:20:07 | × | Unicorn_Princess quits (~Unicorn_P@user/Unicorn-Princess/x-3540542) (Remote host closed the connection) |
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| 22:52:51 | → | weary-traveler joins (~user@user/user363627) |
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| 22:59:53 | × | merijn quits (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 244 seconds) |
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| 23:23:31 | × | puke quits (~puke@user/puke) (Killed (tantalum.libera.chat (Nickname regained by services))) |
| 23:23:31 | pyooque | is now known as puke |
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| 23:24:53 | × | Jackneill_ quits (~Jackneill@91-83-15-174.pool.digikabel.hu) (Read error: Connection reset by peer) |
| 23:24:54 | × | Digit quits (~user@user/digit) (Remote host closed the connection) |
| 23:24:54 | × | chromoblob quits (~chromoblo@user/chromob1ot1c) (Ping timeout: 256 seconds) |
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| 23:26:01 | YoungFrawg | is now known as YoungFrog |
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| 23:26:19 | × | tzh quits (~tzh@c-76-115-131-146.hsd1.or.comcast.net) (Ping timeout: 256 seconds) |
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| 23:28:41 | × | tzh_ quits (~tzh@c-76-115-131-146.hsd1.or.comcast.net) (Quit: kdjs) |
| 23:31:08 | × | merijn quits (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 256 seconds) |
| 23:31:58 | × | mreh quits (~matthew@host86-146-25-35.range86-146.btcentralplus.com) (Ping timeout: 258 seconds) |
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| 23:44:43 | × | hiredman quits (~hiredman@frontier1.downey.family) (Remote host closed the connection) |
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All times are in UTC on 2025-09-20.