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| 2024-10-08 03:28:54 +0200 | <haskellbridge> | <thirdofmay18081814goya> what are some useful coinductive types? |
| 2024-10-08 03:29:09 +0200 | troojg | (~troojg@user/troojg) troojg |
| 2024-10-08 03:29:17 +0200 | morb | (~morb@pool-108-41-100-120.nycmny.fios.verizon.net) |
| 2024-10-08 03:29:43 +0200 | <monochrom> | Infinite lists. Infinite free monads. |
| 2024-10-08 03:30:14 +0200 | <haskellbridge> | <thirdofmay18081814goya> hm right i see ty |
| 2024-10-08 03:31:06 +0200 | <talismanick> | infinite (nonempty) lists are often referred to in literature as streams |
| 2024-10-08 03:31:13 +0200 | <talismanick> | you can even do calculus on them: https://www.cs.ox.ac.uk/people/ralf.hinze/publications/CSC.pdf |
| 2024-10-08 03:32:01 +0200 | <haskellbridge> | <thirdofmay18081814goya> are these the streams you usually encounter in programming? |
| 2024-10-08 03:33:35 +0200 | <geekosaur> | I think mathematical streams are used to model those streams, since their size is from the standpoint of programs "infinite" or at least indeterminate? |
| 2024-10-08 03:34:17 +0200 | <EvanR> | object oriented programming via copatterns |
| 2024-10-08 03:34:18 +0200 | <geekosaur> | for example, a network stream could hypothetically last forever, although in practice something will cause the remote to close the connection or be lost or etc. |
| 2024-10-08 03:34:33 +0200 | <monochrom> | I didn't think of the elegant "join s = head (head s) : join (tail (tail s))". (I only knew to wrote it as [s !! i !! i | i <- [0..]]) |
| 2024-10-08 03:35:05 +0200 | <talismanick> | there are types which are isomorphic to streams (can be exchanged one-for-one); these are given a `Comonad` instance, which lets them use any operation defined on comonads (generalized from the case specialized to the stream type given in the paper) |
| 2024-10-08 03:35:14 +0200 | <EvanR> | chalk up remote host closed connection to "thread died" xD |
| 2024-10-08 03:35:26 +0200 | <EvanR> | thread's code itself has no idea |
| 2024-10-08 03:35:44 +0200 | <EvanR> | it never observed the end of the stream so it's still infinite xD |
| 2024-10-08 03:35:57 +0200 | <talismanick> | https://hackage.haskell.org/package/comonad-5.0.8/ shows 164 reverse dependencies and 8416 indirect |
| 2024-10-08 03:36:15 +0200 | <talismanick> | so there are few cases :D |
| 2024-10-08 03:36:31 +0200 | <haskellbridge> | <thirdofmay18081814goya> i see thanks for comments! |
| 2024-10-08 03:37:12 +0200 | <geekosaur> | fwiw what I am aiming for is "the size isn't defined statically by your program, but by something synamic / outside of it" |
| 2024-10-08 03:37:45 +0200 | <geekosaur> | *dynamic |
| 2024-10-08 03:38:58 +0200 | morb | (~morb@pool-108-41-100-120.nycmny.fios.verizon.net) (Remote host closed the connection) |
| 2024-10-08 03:39:07 +0200 | <EvanR> | the basic haskell list type really is a conundrum for ultrafinitists right |
| 2024-10-08 03:39:09 +0200 | <monochrom> | It is the same as "unbounded" Integer where there is a bound but it's outside of your model. |
| 2024-10-08 03:39:23 +0200 | <EvanR> | if all haskell lists are "really" finite, then what is the answer to length (repeat ()) |
| 2024-10-08 03:39:54 +0200 | <EvanR> | or is the length function broken |
| 2024-10-08 03:40:11 +0200 | <geekosaur> | ⊥ because `length` breaks when it hits `maxBound :: Int` |
| 2024-10-08 03:40:28 +0200 | <EvanR> | >_< |
| 2024-10-08 03:41:35 +0200 | youthlic | (~Thunderbi@user/youthlic) youthlic |
| 2024-10-08 03:41:58 +0200 | <haskellbridge> | <thirdofmay18081814goya> hm can we not do induction on coinductive structures or does coinduction capture something completely different? |
| 2024-10-08 03:42:12 +0200 | <haskellbridge> | <thirdofmay18081814goya> (is coinduction the type eliminator for coinductive types?) |
| 2024-10-08 03:43:42 +0200 | raehik | (~raehik@rdng-25-b2-v4wan-169990-cust1344.vm39.cable.virginm.net) (Ping timeout: 252 seconds) |
| 2024-10-08 03:45:53 +0200 | geekosaur | is wondering if it would be a type introducer |
| 2024-10-08 03:46:34 +0200 | <geekosaur> | (or "co-eliminator", whatever that works out to be) |
| 2024-10-08 03:48:24 +0200 | xff0x | (~xff0x@fsb6a9491c.tkyc517.ap.nuro.jp) |
| 2024-10-08 03:51:04 +0200 | <EvanR> | the only reason you can do induction on an inductive type is because it comes with an induction rule |
| 2024-10-08 03:51:59 +0200 | <EvanR> | unless you can figure out how to synthesize one as a theorem |
| 2024-10-08 03:52:09 +0200 | <haskellbridge> | <thirdofmay18081814goya> yeah the induction rule associated to a particular inductive type is the elimination rule for that type |
| 2024-10-08 03:54:08 +0200 | <monochrom> | induction rule is part of what "inductive type" means. What does "coinductive type" mean? Perhaps it contains the coinduction rule. |
| 2024-10-08 03:54:31 +0200 | <EvanR> | you can probably come up with a coinductive type which it is possible to derive a synthetic induction rule |
| 2024-10-08 03:54:35 +0200 | <EvanR> | for |
| 2024-10-08 03:54:56 +0200 | <EvanR> | like one that doesn't lead to infinite data |
| 2024-10-08 03:56:22 +0200 | <EvanR> | but if you look at another example, the potentially infinite natural number type... you can see how induction would fail |
| 2024-10-08 03:57:38 +0200 | raehik | (~raehik@rdng-25-b2-v4wan-169990-cust1344.vm39.cable.virginm.net) raehik |
| 2024-10-08 03:57:59 +0200 | <EvanR> | to prove something for all potentially infinite natural numbers, can you just prove it for 0 and assuming P for n prove it for n+1 |
| 2024-10-08 03:58:04 +0200 | <EvanR> | no |
| 2024-10-08 03:59:20 +0200 | <haskellbridge> | <thirdofmay18081814goya> if you use a set-theoretic semantics any natural number is a finite set the only infinite set is the set of natural numbers itself, proofs on the set of all natural numbers use that method yeah |
| 2024-10-08 03:59:47 +0200 | <EvanR> | specifically define the potentially infinite natural numbers using the coinductive style |
| 2024-10-08 03:59:59 +0200 | <EvanR> | not set theory |
| 2024-10-08 03:59:59 +0200 | <haskellbridge> | <thirdofmay18081814goya> oh |
| 2024-10-08 04:00:08 +0200 | <haskellbridge> | <thirdofmay18081814goya> ok i see |
| 2024-10-08 04:00:28 +0200 | <EvanR> | though I'm not sure set theory would fix it |
| 2024-10-08 04:01:09 +0200 | <monochrom> | You can do it in set theory. It is just not called "the natural numbers" there. |
| 2024-10-08 04:01:26 +0200 | <EvanR> | ordinals? xD |
| 2024-10-08 04:01:40 +0200 | <EvanR> | that comes with its own induction rule |
| 2024-10-08 04:01:57 +0200 | <monochrom> | But we also say "lazy Krivine machine" where Krivine only wrote an eager machine and it was Sestoft who modified it to make a lazy machine. |
| 2024-10-08 04:02:39 +0200 | <monochrom> | We also say "make a Xerox copy" and then go on to use a Konica photocopier. |
| 2024-10-08 04:02:59 +0200 | <EvanR> | thirdofmayyaddayaddagoya: if you do classic induction to prove something, you proved it for all finite natural numbers, and that's it |
| 2024-10-08 04:03:01 +0200 | <monochrom> | so I guess "infinite natural" and even "uncountable natural" can be legit names. |
| 2024-10-08 04:03:31 +0200 | <EvanR> | it misses something |
| 2024-10-08 04:05:08 +0200 | <EvanR> | a related phenomenon, if you write a recursive algorithm to process a natural number and it recurses on something smaller than its argument, you can be sure it terminates. But then that fails if someone gives you an infinite number |
| 2024-10-08 04:05:34 +0200 | <EvanR> | it's illogical! |
| 2024-10-08 04:06:54 +0200 | <monochrom> | It's even the same phenomenon. The termination proof assumes induction, so it only covers what induction reaches. |
| 2024-10-08 04:07:01 +0200 | <haskellbridge> | <thirdofmay18081814goya> hm looks like coalgebras sort disassemble things |
| 2024-10-08 04:07:09 +0200 | <haskellbridge> | <thirdofmay18081814goya> sort of disassemble things |
| 2024-10-08 04:08:29 +0200 | <haskellbridge> | <thirdofmay18081814goya> hm so then in a sense the final coalgebra gives you a canonical way to disassemble a thing |
| 2024-10-08 04:08:41 +0200 | <monochrom> | On recent exams I became careful to write "Prove by induction: For all finite lists xs, ..." :) |
| 2024-10-08 04:12:37 +0200 | <EvanR> | is final coalgebra the categorical wonkery for coinductive types? |
| 2024-10-08 04:12:40 +0200 | <monochrom> | Hagino says "co-natural number" instead of "infinite natural number". :) |
| 2024-10-08 04:12:54 +0200 | <haskellbridge> | <thirdofmay18081814goya> EvanR: yes |
| 2024-10-08 04:13:33 +0200 | td_ | (~td@i5387091A.versanet.de) (Ping timeout: 246 seconds) |
| 2024-10-08 04:13:58 +0200 | <monochrom> | Hagino's thesis has a toy language that lets you declare inductive types and coinductive types. (Or more accurately, initial algebra types and final coalgebra types.) You may find many answers there. You can just google "Hagino thesis". (I just did.) |
| 2024-10-08 04:14:45 +0200 | <haskellbridge> | <thirdofmay18081814goya> monochrom: was planning to return to his thesis after foray into coinduction |
| 2024-10-08 04:14:56 +0200 | <EvanR> | disassemble might give you the wrong idea |
| 2024-10-08 04:15:11 +0200 | <haskellbridge> | <thirdofmay18081814goya> monochrom: by any chance do you know how Hagino's type formation through adjunction works? |
| 2024-10-08 04:15:17 +0200 | <monochrom> | And if that is not enough, look for "Bart Jacobs coalgebra". He's the coalgebra guy. |
| 2024-10-08 04:15:28 +0200 | <EvanR> | the coinductive style gives you options for how to observe a value of the type, if you could ever obtain one to start with |
| 2024-10-08 04:15:36 +0200 | <monochrom> | I don't, I didn't really read it. |
| 2024-10-08 04:15:39 +0200 | td_ | (~td@i5387092D.versanet.de) td_ |
| 2024-10-08 04:16:02 +0200 | athan | (~athan@syn-098-153-145-140.biz.spectrum.com) (Quit: Konversation terminated!) |
| 2024-10-08 04:16:30 +0200 | <EvanR> | so if the value was assembled somehow yeah you could diassemble it, but it might just have multiple ways to proceed to the next observation which for all you know is unrelated to any construction sequence |
| 2024-10-08 04:17:41 +0200 | <EvanR> | and in the case of infinite data, assembling from the ground up is impossible |
| 2024-10-08 04:18:52 +0200 | <EvanR> | but maybe that's just prejudice leaking through from "a monad is this thing you wrap like a burrito" PTSD |
| 2024-10-08 04:19:25 +0200 | <dolio> | To build codata, you say what happens for all the ways of observing it, corecursively. |
| 2024-10-08 04:21:28 +0200 | <dolio> | Like unfoldr, but that only has one thing to observe. |
| 2024-10-08 04:26:10 +0200 | <dolio> | It's nicer when the outermost level is a product, so there are multiple observations, like when data is a sum, with multiple constructors. |
| 2024-10-08 04:27:08 +0200 | <haskellbridge> | <thirdofmay18081814goya> ty for comments helpful stuff |
| 2024-10-08 04:29:21 +0200 | LukeHoersten | (~LukeHoers@user/lukehoersten) LukeHoersten |
| 2024-10-08 04:31:07 +0200 | identity | (~identity@user/ZharMeny) (Quit: ERC 5.6.0.30.1 (IRC client for GNU Emacs 30.0.91)) |
| 2024-10-08 04:36:59 +0200 | raehik | (~raehik@rdng-25-b2-v4wan-169990-cust1344.vm39.cable.virginm.net) (Ping timeout: 260 seconds) |
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| 2024-10-08 04:52:51 +0200 | athan | (~athan@syn-098-153-145-140.biz.spectrum.com) athan |
| 2024-10-08 04:59:04 +0200 | vanishingideal | (~vanishing@user/vanishingideal) (Ping timeout: 272 seconds) |
| 2024-10-08 05:01:04 +0200 | sourcetarius | (~sourcetar@user/sourcetarius) (Quit: sourcetarius) |
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| 2024-10-08 05:22:21 +0200 | motherfsck | (~motherfsc@user/motherfsck) motherfsck |
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| 2024-10-08 05:29:52 +0200 | youthlic | (~Thunderbi@user/youthlic) youthlic |
| 2024-10-08 05:31:20 +0200 | ethantwardy | (user@user/ethantwardy) ethantwardy |
| 2024-10-08 05:43:38 +0200 | floyza | (~gavin@h69-11-148-150.kndrid.broadband.dynamic.tds.net) (Remote host closed the connection) |
| 2024-10-08 05:43:57 +0200 | floyza | (~gavin@h69-11-148-150.kndrid.broadband.dynamic.tds.net) gdown |
| 2024-10-08 05:44:40 +0200 | infinity0 | (~infinity0@pwned.gg) (Ping timeout: 272 seconds) |
| 2024-10-08 05:46:59 +0200 | Lord_of_Life | (~Lord@user/lord-of-life/x-2819915) (Ping timeout: 260 seconds) |
| 2024-10-08 05:49:41 +0200 | Lord_of_Life | (~Lord@user/lord-of-life/x-2819915) Lord_of_Life |
| 2024-10-08 06:04:53 +0200 | infinity0 | (~infinity0@pwned.gg) infinity0 |
| 2024-10-08 06:07:51 +0200 | talismanick | (~user@2601:644:937c:ed10::ae5) (Remote host closed the connection) |
| 2024-10-08 06:08:05 +0200 | talismanick | (~user@2601:644:937c:ed10::ae5) talismanick |
| 2024-10-08 06:15:45 +0200 | vanishingideal | (~vanishing@user/vanishingideal) vanishingideal |
| 2024-10-08 06:19:30 +0200 | _d0t | (~{-d0t-}@user/-d0t-/x-7915216) (Ping timeout: 265 seconds) |
| 2024-10-08 06:24:28 +0200 | _d0t | (~{-d0t-}@user/-d0t-/x-7915216) {-d0t-} |
| 2024-10-08 06:34:45 +0200 | <Axman6> | I'm forgetting the name of something; "a finger-tree is an example of a non-??? recursive structure", I want to say ??? = uniform but I don't think that's right |
| 2024-10-08 06:39:57 +0200 | simendsjo | (~user@84.211.91.108) (Ping timeout: 276 seconds) |
| 2024-10-08 06:45:50 +0200 | <jackdk> | Axman6: Is this about how finger trees use polymorphic recursion? |
| 2024-10-08 06:45:56 +0200 | LukeHoersten | (~LukeHoers@user/lukehoersten) (Quit: My MacBook has gone to sleep. ZZZzzz…) |
| 2024-10-08 06:55:47 +0200 | <mauke> | Axman6: non-regular? nested type? |
| 2024-10-08 06:57:53 +0200 | michalz | (~michalz@185.246.207.222) |
| 2024-10-08 07:03:41 +0200 | astra | amish |
| 2024-10-08 07:03:44 +0200 | amish | (sid289983@id-289983.hampstead.irccloud.com) (Changing host) |
| 2024-10-08 07:03:44 +0200 | amish | (sid289983@user/amish) amish |
| 2024-10-08 07:04:04 +0200 | amish | astra |
| 2024-10-08 07:08:47 +0200 | st_aldini1 | (~Thunderbi@136.48.22.91) st_aldini |
| 2024-10-08 07:09:05 +0200 | euphores | (~SASL_euph@user/euphores) euphores |
| 2024-10-08 07:10:13 +0200 | st_aldini | (~Thunderbi@136.48.22.91) (Ping timeout: 248 seconds) |
| 2024-10-08 07:10:13 +0200 | st_aldini1 | st_aldini |
| 2024-10-08 07:12:38 +0200 | takuan | (~takuan@178-116-218-225.access.telenet.be) |
| 2024-10-08 07:21:51 +0200 | dtman34 | (~dtman34@2601:447:d080:1a3c:e9e9:5bc8:51:a5ea) (Quit: ZNC 1.8.2+deb3.1 - https://znc.in) |
| 2024-10-08 07:22:12 +0200 | dtman34 | (~dtman34@c-174-53-203-90.hsd1.mn.comcast.net) dtman34 |
| 2024-10-08 07:23:01 +0200 | jinsun | (~jinsun@user/jinsun) (Ping timeout: 248 seconds) |
| 2024-10-08 07:32:01 +0200 | weary-traveler | (~user@user/user363627) (Remote host closed the connection) |
| 2024-10-08 07:38:13 +0200 | <Axman6> | yeah I think both of those work |
| 2024-10-08 07:53:12 +0200 | acidjnk | (~acidjnk@p200300d6e72cfb34519e9ca14c5ce943.dip0.t-ipconnect.de) acidjnk |
| 2024-10-08 07:57:33 +0200 | ubert | (~Thunderbi@178.165.187.120.wireless.dyn.drei.com) ubert |
| 2024-10-08 08:04:00 +0200 | vanishingideal | (~vanishing@user/vanishingideal) (Ping timeout: 272 seconds) |
| 2024-10-08 08:08:25 +0200 | euleritian | (~euleritia@ip4d16fc38.dynamic.kabel-deutschland.de) (Read error: Connection reset by peer) |
| 2024-10-08 08:08:38 +0200 | euleritian | (~euleritia@ip4d16fc38.dynamic.kabel-deutschland.de) |
| 2024-10-08 08:09:11 +0200 | euleritian | (~euleritia@ip4d16fc38.dynamic.kabel-deutschland.de) (Remote host closed the connection) |
| 2024-10-08 08:09:33 +0200 | euleritian | (~euleritia@ip4d16fc38.dynamic.kabel-deutschland.de) |
| 2024-10-08 08:10:24 +0200 | vanishingideal | (~vanishing@user/vanishingideal) vanishingideal |
| 2024-10-08 08:10:57 +0200 | mari-estel | (~mari-este@185.238.219.10) |
| 2024-10-08 08:11:38 +0200 | mari77696 | (~mari-este@185.238.219.10) |
| 2024-10-08 08:14:05 +0200 | foul_owl | (~kerry@185.219.141.162) (Ping timeout: 255 seconds) |
| 2024-10-08 08:17:16 +0200 | sord937 | (~sord937@gateway/tor-sasl/sord937) sord937 |
| 2024-10-08 08:32:05 +0200 | Sgeo | (~Sgeo@user/sgeo) (Read error: Connection reset by peer) |
| 2024-10-08 08:32:17 +0200 | mari77696 | (~mari-este@185.238.219.10) (Ping timeout: 248 seconds) |
| 2024-10-08 08:32:49 +0200 | mari-estel | (~mari-este@185.238.219.10) (Ping timeout: 248 seconds) |
| 2024-10-08 08:42:16 +0200 | rosco | (~rosco@175.136.22.30) rosco |
| 2024-10-08 08:44:10 +0200 | tromp | (~textual@92-110-219-57.cable.dynamic.v4.ziggo.nl) |