Logs on 2025-03-30 (liberachat/#haskell)
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| 00:12:05 | <haskellbridge> | <thirdofmay18081814goya> does anyone know of an invertible coding function "Int -> Int" for a value of type "Tree Int"? i.e., translate a value "Tree Int" into a value "Int" and have a unique way to translate an "Int" back into a "Tree Int" |
| 00:12:26 | <haskellbridge> | <thirdofmay18081814goya> does anyone know of an invertible coding function "Tree Int -> Int"* |
| 00:13:09 | <haskellbridge> | <thirdofmay18081814goya> suppose specifically a rose tree with values "Int" |
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| 00:16:30 | <haskellbridge> | <dmjio> thirdofmay18081814goya did you tree "foldTree" and "unfoldTree" |
| 00:16:43 | <haskellbridge> | <dmjio> * try |
| 00:18:29 | <haskellbridge> | <Bowuigi> thirdofmay18081814goya I don't see how that could be total, since you have to fit many values of Int in a single one, any of which can be as large as INT_MAX |
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| 00:18:37 | <Leary> | thirdofmay: Impossible; |Tree Int| > |Int|. If you wanted an invertible `Tree Integer -> Integer`, then you're essentially doing de/serialisation. |
| 00:20:45 | <haskellbridge> | <Bowuigi> If you ignore size concerns and want an invertible "Tree Integer -> Integer", you can get one by treating the output integer as a binary file |
| 00:20:56 | <geekosaur> | gödel coding /s |
| 00:21:36 | <haskellbridge> | <thirdofmay18081814goya> Leary: this is not the case, note that any element of "Tree Int" is constructible in a finite number of steps, so can be encoded by a function "Nat -> Tree Int", and therefore "Tree Int" has the same size as "Int" (since "| Int | = | Nat |") |
| 00:22:57 | <haskellbridge> | <Bowuigi> Wouldn't that mean that it's possible to encode its zipper instead of the actual tree? |
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| 00:25:30 | <haskellbridge> | <thirdofmay18081814goya> Bowuigi: yeah, am just looking for any function that can uniquely specify a tree + an ordering on "Tree Int" that we can use this function with |
| 00:26:04 | <haskellbridge> | <Bowuigi> Also note that finite doesn't mean it's inside an Int's bounds |
| 00:29:34 | <__monty__> | Int is not Integer. And neither is the same as the mathematical concept. |
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| 00:32:35 | <Leary> | thirdofmay: |Int| = 2^64 |
| 00:33:33 | <Leary> | (or 2^32 if you live in the past) |
| 00:34:11 | <haskellbridge> | <thirdofmay18081814goya> Leary: oh you're fully right then |
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| 00:35:05 | <haskellbridge> | <thirdofmay18081814goya> didn't realize "Int" was finite, I thought it was the type of Nat + (Nat - 1) |
| 00:35:32 | <haskellbridge> | <thirdofmay18081814goya> * { 0 }) |
| 00:36:05 | <haskellbridge> | <thirdofmay18081814goya> a type isomorphic to "Nat + (Nat - { 0 })"* |
| 00:38:34 | <haskellbridge> | <thirdofmay18081814goya> then as a matter of fact, "Int !! (| Int | + 1)" will not be a value of type "Int", correct? |
| 00:38:59 | <monochrom> | Actually in Haskell we don't have a "Nat", we have Word (Data.Word) and Natural (Numeric.Natural). |
| 00:39:30 | <monochrom> | Unpopular opinion: It is more consistent to s/Word/Nat/ because Int : Nat :: Integer :: Natural |
| 00:39:31 | <haskellbridge> | <Bowuigi> It would overflow I think, in C it is UB but not sure about it in Haskell |
| 00:40:53 | <Leary> | > maxBound + (1 :: Int) == minBound |
| 00:40:54 | <lambdabot> | True |
| 00:41:01 | <haskellbridge> | <Bowuigi> Word kinda makes sense because of machine words, but UInt or Nat would make more sense |
| 00:41:05 | <Leary> | > (succ maxBound :: Int) == minBound |
| 00:41:07 | <lambdabot> | *Exception: Prelude.Enum.succ{Int}: tried to take `succ' of maxBound |
| 00:41:29 | <monochrom> | You can always try maxBound + 1 |
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| 00:43:47 | <haskellbridge> | <thirdofmay18081814goya> hm so there's an invertible serialization/deserialization function for "Tree Natural"? (or "Tree Word", assuming I understand correctly that "| Word | = | Natural |"?) |
| 00:44:11 | <haskellbridge> | <thirdofmay18081814goya> and "| Natural | = | Set of natural numbers |" |
| 00:44:15 | <haskellbridge> | <Bowuigi> No, Natural is Integer but unsigned |
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| 00:44:26 | <monochrom> | In Haskell2010 it's simulataneously "UB" and "implementation-defined". The exact quote: "The results of exceptional conditions (such as overflow or underflow) on the fixed-precision numeric types are undefined; an implementation may choose error (⊥, semantically), a truncated value, or a special value such as infinity, indefinite, etc." |
| 00:45:56 | <haskellbridge> | <Bowuigi> Also is Natural the same size as the set of natural numbers? It has bottoms too |
| 00:46:53 | <haskellbridge> | <thirdofmay18081814goya> no it seems, assuming "Natural" has the size of the set of unsigned integers, it is a finite set too |
| 00:47:06 | <haskellbridge> | <Bowuigi> Not only implementation-wise, but also because every computation of type Natural is a Natural, including "1 + undefined" |
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| 00:48:23 | <haskellbridge> | <thirdofmay18081814goya> so is there no type that has the size of the set of natural numbers in haskell? |
| 00:48:30 | <monochrom> | > 10^100 :: Natural |
| 00:48:31 | <lambdabot> | 1000000000000000000000000000000000000000000000000000000000000000000000000000... |
| 00:48:33 | <Leary> | thirdofmay: |Word| = |Int|; |Natural| = |Integer| = omega |
| 00:48:49 | <haskellbridge> | <thirdofmay18081814goya> ah that clears it up, ty |
| 00:50:32 | <haskellbridge> | <thirdofmay18081814goya> so rephrasing: there is an invertible serialization function for "Tree Natural", correct? |
| 00:51:12 | <haskellbridge> | <thirdofmay18081814goya> what would be the API to access it? |
| 00:55:26 | <geekosaur> | that's a somewhat weird way to put it. I would say that you can define such a function, not that one exists with a particular API |
| 00:55:38 | <geekosaur> | how you define it would depend on what you intend to do with it |
| 00:56:20 | <geekosaur> | (My comment about Gödel coding was only half a joke; it would certainly work but would be overkill and probably extremely inefficient for your purpose) |
| 00:58:14 | <haskellbridge> | <thirdofmay18081814goya> wrt Godel coding, beginning to read http://foibg.com/ijita/vol17/ijita17-1-p02.pdf |
| 00:58:23 | <haskellbridge> | <thirdofmay18081814goya> not terribly preoccupied with efficiency atm |
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| 01:03:53 | <monochrom> | Unpopular opinion: But Gödel numbers is terribly preoccupied with gross inefficiency. |
| 01:04:49 | <geekosaur> | ^ |
| 01:05:43 | <haskellbridge> | <thirdofmay18081814goya> monochrom: what's an alternative? |
| 01:05:52 | <haskellbridge> | <thirdofmay18081814goya> any alternative |
| 01:06:13 | <monochrom> | You should look at the binary package and what it does to "instance Binary (Tree e)" |
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| 01:06:42 | <haskellbridge> | <thirdofmay18081814goya> "Data.Binary" that is? |
| 01:07:23 | <monochrom> | Sure, if module names are still unambiguous like 20 years ago. |
| 01:07:53 | <haskellbridge> | <thirdofmay18081814goya> will do, thanks a lot for the reference. am literally looking for anything that works lol |
| 01:11:28 | <geekosaur> | heh. let's put it this way: countably infinite Gödel numbers are considered a feature for their use case |
| 01:11:51 | <geekosaur> | (only a slight overstatement) |
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| 01:12:28 | <geekosaur> | well, arguably so are uncountably infinite ones, at least as results 🙂 |
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| 01:25:46 | <haskellbridge> | <jv> 'd |
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| 01:48:18 | <EvanR> | thirdofmay18081814goya, data Nat = Z | S !Nat |
| 01:49:01 | <EvanR> | ignoring bottoms |
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| 01:49:10 | <haskellbridge> | <thirdofmay18081814goya> right |
| 01:50:48 | <EvanR> | data Int = Nat :- Nat |
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| 02:00:40 | <EvanR> | data Rat = Over { numer :: Int, denomMinusOne :: Nat } |
| 02:01:46 | <geekosaur> | I was going to say you got that backwards, but in hindsight I guess it depends on how you interpret that name |
| 02:02:18 | <EvanR> | data Real = Rat Rat | Lim (Rat -> Real) |
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| 02:07:23 | <EvanR> | data Surreal = Cut (Tree Surreal) (Tree Surreal) |
| 02:11:44 | <JuanDaugherty> | issat knuth's? |
| 02:12:51 | <JuanDaugherty> | https://en.wikipedia.org/wiki/Surreal_number confirmed |
| 02:13:11 | <JuanDaugherty> | (and credit where credit due to Conway) |
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| 02:15:08 | <EvanR> | I will gratefully deposit 0x$1.00 ($2.56) to the account of the first person who finds and reports anything that remains technically, historically, typographically, or politically incorrect. -- knuth |
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| 02:56:57 | <EvanR> | thirdofmay18081814goya, "any element of Tree Int can be constructed in a finite number of steps" ... |
| 02:57:16 | <EvanR> | what's a step |
| 02:58:15 | <monochrom> | A step is a finite number of substeps. >:) |
| 02:59:23 | <EvanR> | did I construct let xs = 1 : xs in xs in a finite number of steps, or is it even successfully constructed |
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| 03:03:06 | <haskellbridge> | <thirdofmay18081814goya> EvanR: a step is a natural number that designates a pair, given by a natural number and its successor, such that when fed into a function "Nat -> Tree Int", produce a tree that is at most different by a single application of the datatype constructor |
| 03:03:35 | <haskellbridge> | <thirdofmay18081814goya> (tentative definition) |
| 03:03:49 | <EvanR> | what |
| 03:04:26 | <haskellbridge> | <thirdofmay18081814goya> replace "at most one application of the datatype constructor" by "exactly one application" |
| 03:04:28 | <EvanR> | are you only allowing finite trees |
| 03:04:44 | <haskellbridge> | <thirdofmay18081814goya> yeah in this case, only inductively defined trees |
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| 03:05:14 | <EvanR> | alright so a step is a constructor |
| 03:05:38 | <EvanR> | and there's only finitely many of them |
| 03:05:50 | <EvanR> | based |
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| 03:08:00 | <haskellbridge> | <thirdofmay18081814goya> EvanR: well, I think we need the whole thing: 1. a natural number 2. designating a natural number and its succesor 3. such that fed to a function that indexes constructor applications, 4. produce a tree different by exactly a single application of the "Branch" constructor (if our tree datatype is defined by a "Node" and "Branch" constructor) |
| 03:09:35 | <EvanR> | isn't the result of Branch t1 t2 always "a tree different by exactly a single application of the Branch constructor" |
| 03:10:10 | <EvanR> | from the pair of trees |
| 03:12:24 | <haskellbridge> | <thirdofmay18081814goya> hm true, but supposing the function indexing applications is "ITA" (abbreviating "IndexedTreeApplication"), we want a step to designate the difference between "Branch (ITA n) (ITA m)" and "ITA n", where "m" is strictly smaller than "n" |
| 03:13:12 | <haskellbridge> | <thirdofmay18081814goya> or analogously the difference between "Branch (ITA m) (ITA n)" |
| 03:13:19 | <haskellbridge> | <thirdofmay18081814goya> and "ITA n" |
| 03:13:41 | <EvanR> | I have no idea what the objective was, I just cherry picked this one idea of getting any "Tree Int" in a finite number of steps, which didn't make sense to me in general, but now it does since finite |
| 03:14:05 | <haskellbridge> | <thirdofmay18081814goya> heheh right |
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| 03:18:21 | <EvanR> | true or false: any geometric diagram can be constructed in a finite number of steps |
| 03:19:44 | <haskellbridge> | <thirdofmay18081814goya> can we specify the geometric diagram as "[(Integer, Integer)]"? |
| 03:20:07 | <haskellbridge> | <thirdofmay18081814goya> in that case I would think so |
| 03:20:08 | <EvanR> | a linked list of coordinates? no |
| 03:20:20 | <haskellbridge> | <thirdofmay18081814goya> why not |
| 03:20:31 | <EvanR> | you could even draw a line that way |
| 03:20:33 | <EvanR> | couldn't |
| 03:20:56 | <haskellbridge> | <thirdofmay18081814goya> well yeah: the ordering of the linked list specifies which lines exist |
| 03:21:18 | <EvanR> | ok you can't draw a circle |
| 03:21:20 | <haskellbridge> | <thirdofmay18081814goya> so if the list is "[(0,0), (1,1), (2,2)]", we have two lines |
| 03:21:47 | <haskellbridge> | <thirdofmay18081814goya> EvanR: you can't draw a circle, but you can approximate a circle with abritrary precision (including to an extent indistinguishable to the human eye) |
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| 03:22:53 | <geekosaur> | are (visualizations of) Mandelbröt sets geometric diagrams? |
| 03:22:57 | <haskellbridge> | <thirdofmay18081814goya> with this idea, you can specify a circle as a function "approximate :: Nat -> CircleApproximation", where "approximate n" approximates the circle more closely than "approximate (n + 1)" |
| 03:22:57 | <geekosaur> | 😈 |
| 03:22:58 | <EvanR> | this is gratuitously low quality xD |
| 03:23:28 | <haskellbridge> | <thirdofmay18081814goya> uh, the contrary, "approximate (n + 1)" has lower error than "approximate n" |
| 03:23:31 | <EvanR> | Mandelbrot "set" is actually a Locus so yes |
| 03:23:51 | <haskellbridge> | <thirdofmay18081814goya> then "circle = approximate" :D |
| 03:24:05 | <EvanR> | a theory of approximations wasn't called for |
| 03:24:35 | <EvanR> | actual circles have been accepted as "geometric" since forever |
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| 03:26:47 | <haskellbridge> | <thirdofmay18081814goya> i secretely will use "approximate (100!^100!)" and will tell you it's a circle and you won't be able to tell it's secretly a polygon, so you'll agree with me 😈 |
| 03:26:48 | <EvanR> | that's a good one, the mandlebrot set seems to need an infinite number of steps, to keep adding lobes |
| 03:27:14 | <EvanR> | (and then it would probably miss a lot in the end) |
| 03:28:24 | <haskellbridge> | <thirdofmay18081814goya> actually, there is an "n :: Natural" such that "approximate" cannot designate a circle that is physically closer to any other approximation (due to the size of atoms, or alternatively your screen resolution) |
| 03:28:31 | <haskellbridge> | <Bowuigi> Fractals in general do that AFAIK |
| 03:28:41 | <EvanR> | ultrafinitist confirmed |
| 03:29:28 | <EvanR> | straight line segments are really bad at approximating curves btw, at least use parabolic segments |
| 03:31:04 | <haskellbridge> | <thirdofmay18081814goya> right, well the point where mathematical and cs-theoretical perfection coincides is to consider "approximate" itself as the circle, instead of "approximate n" for a given n |
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| 03:31:18 | <haskellbridge> | <thirdofmay18081814goya> then you can do stuff by function composition |
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| 03:31:52 | <EvanR> | it would be better if you do the approximation at the end of the program than at the beginning |
| 03:32:08 | <haskellbridge> | <thirdofmay18081814goya> yeah |
| 03:32:51 | <EvanR> | (if necessary) |
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| 03:37:18 | <EvanR> | instead of "human eye" test I wonder if you could instead specify the limit of precision by saying lines and shapes have a minimum "pen size" so if you keep trying to draw the mandlebrot set you'll just start getting the same blob over again |
| 03:37:29 | <EvanR> | at which point you stop |
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| 03:47:13 | <haskellbridge> | <thirdofmay18081814goya> speaking of which |
| 03:47:22 | <haskellbridge> | <thirdofmay18081814goya> is there a standard wrt rendering 2D in haskell? |
| 03:47:48 | <haskellbridge> | <thirdofmay18081814goya> or, how do people usually do 2D rendering in haskell |
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| 03:50:57 | <geekosaur> | gloss and relativrd |
| 03:51:02 | <geekosaur> | *relatives |
| 03:52:40 | <EvanR> | there's the diagrams library |
| 03:53:02 | <EvanR> | there are bindings to SDL, glfw |
| 03:53:09 | <EvanR> | ... and gtk ... |
| 03:54:07 | <EvanR> | three penny gui was an early web-based thing |
| 03:54:28 | <EvanR> | now there's ghcjs so you can use whatever is in the browser |
| 03:54:43 | <haskellbridge> | <thirdofmay18081814goya> neat thanks for all the references! |
| 03:55:08 | <haskellbridge> | <dmjio> thirdofmay18081814goya check out diagrams |
| 03:55:41 | <haskellbridge> | <thirdofmay18081814goya> will do ty! |
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| 03:56:24 | <EvanR> | diagrams is great |
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| 04:07:30 | <haskellbridge> | <dmjio> Anything Brent Yorgey is great, especially the typeclassopdia |
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| 06:17:46 | <haskellbridge> | <thirdofmay18081814goya> what's a case where "Either" wasn't enough for your error handling needs? |
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| 09:48:21 | <Rembane> | There's an opposite to Either that's very useful for validating e.g. forms. When there can be loads of errors in different places and execution should never stop. Just seeing the definition makes me surprisingly happy: https://hackage.haskell.org/package/validation-1.1.3/docs/Data-Validation.html#t:Validation |
| 09:48:29 | <Rembane> | ...for some values of opposite. :D |
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| 10:44:53 | <[exa]> | Rembane: so many opposites. Why don't we have a Up Down type? |
| 10:45:44 | <Rembane> | [exa]: I think we have some of those. They're usually Monoid/Semigroup newtypes. |
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| 10:47:11 | <Rembane> | [exa]: Bah, they don't actually exist. The closest I can get to them is Dual. What would Up and Down do? |
| 10:47:40 | <[exa]> | absolutely not sure, just wanted to point out that the "opposite" is a very free definition :D |
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| 10:48:35 | <Rembane> | [exa]: Yeah, it's usually better for inspiration than a clear definition. :D |
| 10:48:47 | <[exa]> | what's annoying on validation and either that neither of these provides the "just shortcircuit with errory error" behavior unless you write the MonadFail yourself |
| 10:49:09 | <Rembane> | I thought Either did that, what does it do instead? |
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| 10:53:42 | <int-e> | Either doesn't have a MonadFail instance |
| 10:54:10 | <Rembane> | Got it. |
| 10:54:30 | <int-e> | ExceptT e Foo a uses the MonadFail instance of Foo. ErrorT e Foo a was removed because it was deprecated in favor of ExceptT despite having a different MonadFail instance. |
| 10:56:39 | <Rembane> | That sounds potentially controversial. I never used ErrorT because of the deprecated message on top of the documentation of the module. |
| 10:56:47 | <Rembane> | Was it a good MonadFail instance? |
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| 10:58:05 | <int-e> | Rembane: Well I used it before it was deprecated because it offered the behavior that Either had before the MonadFail proposal. |
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| 10:59:19 | <Rembane> | int-e: Ah, this has some history. |
| 10:59:26 | <int-e> | yes |
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| 11:00:31 | <haskellbridge> | <thirdofmay18081814goya> @Rembane neat! didn't know about it, ty |
| 11:00:33 | <int-e> | `fail` used to be in `Monad` and the Monad instance for Either used to be instance Error e => Monad (Either e) where `Error` had a function to convert String into an e, which was used to implement `fail`. |
| 11:01:16 | <int-e> | And Control.Monad.Error mimicked that after the MonadFail class was introduced. |
| 11:01:24 | <Rembane> | thirdofmay18081814goya: No worries! :) |
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| 11:18:43 | <haskellbridge> | <thirdofmay18081814goya> hm what's the optic that will remove the elements of a list located at an even index? some combination using the enumeration "Iso' [a] [(Int, a)]" and something involving "traversed . filtered even", right? |
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| 18:59:43 | <haskellbridge> | <thirdofmay18081814goya> or in general, is there a pattern consisting of propagating the changes to an "Iso" to the original datatype? |
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| 19:48:32 | <haskellbridge> | <Bowuigi> Just apply the Iso backwards |
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| 21:22:00 | <halloy8765> | hello |
| 21:23:01 | <geekosaur> | hello |
| 21:23:08 | <halloy8765> | is this discord |
| 21:23:33 | × | berberman quits (~berberman@user/berberman) (Quit: ZNC 1.8.2 - https://znc.in) |
| 21:25:30 | <geekosaur> | no |
| 21:25:38 | <halloy8765> | how do I install discord |
| 21:25:43 | <geekosaur> | it's IRC, and it's bridged to a Matrix room |
| 21:25:51 | <halloy8765> | wait so am I neo |
| 21:26:40 | <geekosaur> | https://discord.com/ |
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| 21:26:49 | <EvanR> | follow the recursive knights of lambda calculus logo and see how deep it goes |
| 21:26:51 | <halloy8765> | im not clicking that |
| 21:26:54 | <halloy8765> | I think thats a vius |
| 21:27:11 | <geekosaur> | you're not going to get very far with Discord, then |
| 21:27:22 | <EvanR> | better to stick with IRC anyway |
| 21:27:26 | <halloy8765> | whats irc |
| 21:27:38 | <halloy8765> | I want to use discord to get an egirlfriend tho |
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| 21:35:13 | <haskellbridge> | <thirdofmay18081814goya> people please we need to focus, how is this done |
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| 21:36:04 | <haskellbridge> | <thirdofmay18081814goya> i recently discovered the possibility that "Iso" might not even be the appropriate optic here and using an indexed optic might be the thing |
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| 21:37:23 | <haskellbridge> | <thirdofmay18081814goya> "^@.. itraversed" annotates a list with an ordering |
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| 21:52:56 | <haskellbridge> | <thirdofmay18081814goya> "['a'..'z'] ^.. itraversed . indices even" bingo |
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| 21:55:28 | <haskellbridge> | <thirdofmay18081814goya> still interested whether there's an "Iso" form, if anyone knows |
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| 23:36:35 | <monochrom> | Is "we need to focus" a pun, given the context of lens? >:) |
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| 23:41:11 | <haskellbridge> | <thirdofmay18081814goya> "under (from enumerateIso) (filter (even . fst)) ['a'..'z']" 😎😎😎😎😎😎😎😎😎 |
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| 23:42:39 | <haskellbridge> | <thirdofmay18081814goya> probably a more idiomatic way to do this, but it's a start |
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