Logs on 2023-06-13 (liberachat/#haskell)

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08:43:57	<Athas>	Does anyone here have experience with using Liquid Haskell?
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10:35:30	<arrowhead>	I need to put a reference-like thing in two lists, then change the value of that reference-like thing, then check the two lists and see that they changed as well. I tried IORefs but they're not acting like OCaml refs.
10:36:45	<Rembane>	arrowhead: Have you looked into STRefs?
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10:37:28	<arrowhead>	Rembane: more or less. Aren't they just the same but in ST instead of in IO ?
10:37:48	<arrowhead>	I thought in IO would be the "freest" behavior and for sure would change in the two lists, but nope
10:39:05	<arrowhead>	e.g. (a >>= (\x -> writeIORef x 2)) >> (((b !! 0) >>= (\x -> readIORef x)) >>= putStrLn . show) >> (((c !! 0) >>= (\x -> readIORef x)) >>= putStrLn . show) is printing 1 1 but I expected 2 2
10:39:10	<arrowhead>	b and c are both [a]
10:39:14	<arrowhead>	and a is a newIORef 1
10:40:59	<Rembane>	arrowhead: That's interesting. Let me play around a bit with it.
10:41:24	<arrowhead>	@Rembane please
10:41:24	<lambdabot>	Unknown command, try @list
10:42:35	<[Leary]>	arrowhead: `newIORef 1` is an IO action that produces a new IORef. If you run it three times, you will produce three unrelated IORefs.
10:43:03	<arrowhead>	[Leary]: I understand that part. I'm coming from OCaml looking for something like their ref
10:43:14	<arrowhead>	I only ran newIORef once and put it into two lists
10:43:24	<arrowhead>	but the things in the lists never change after I change the IO thing
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10:44:56	<arrowhead>	I want to see code that 1. does newIORef once, 2. puts the result in two lists, 3. updates that IORef from outside the lists 4. peers into the lists and sees the changes there
10:45:15	<ncf>	% do a <- newIORef 1; let b = [a]; c = [a] in do writeIORef a 2; traverse readIORef b >>= print; traverse readIORef c >>= print
10:45:15	<yahb2>	[2] ; [2]
10:45:16	<arrowhead>	my attempt above fails for a reason I cannot understand
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10:45:50	<ncf>	your attempt above is missing code
10:46:32	<arrowhead>	ncf: I don't think I can afford to use let... in, that is a very narrow scenario where you can code within the same scope
10:46:40	<ncf>	what
10:46:43	<arrowhead>	not really the behavior of OCaml's ref
10:46:58	<ncf>	haskell is not ocaml. haskell does not have ocaml-style references
10:47:15	<arrowhead>	at all? not even outside IORef? something else with another name?
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10:48:00	<geekosaur>	haskell is pure outside of IO. OCaml refs are not pure
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10:49:10	<Rembane>	Meh. I had an example there. Oh well. For the rest of you: https://gist.github.com/Rembane/faa60107d2c7add230ff5dfd36a9c4c1
10:49:24	<Rembane>	It took me way too long to realize that 0 * 2 never will be interesting.
10:49:40	<geekosaur>	heh
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10:50:40	ncf	wonders what makes someone think they can't use let...in
10:51:09	<Axman6>	that was a bizarre conversation
10:51:34	<geekosaur>	^
10:51:54	<ncf>	i guess it was more like "let...in does not accurately describe the code i'm already working with but i won't tell you what it is"
10:52:03	<ncf>	anyway
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10:55:48	<Axman6>	not sure why they insistedin writing the code in such a difficult to read manner either. particularly it left out thecrucial definition of what 'a' is
10:56:30	<Rembane>	Some list of something I think they eventually wrote
10:56:36	<Rembane>	Eh... not very clear
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11:53:53	<Unicorn_Princess>	i'm using emacs and lsp-haskell, and i'm trying to disable lsp automatically inserting import statements when I tab-complete something that's not yet imported. i've got lsp-haskell-plugin-ghcide-completions-config-auto-extend-on set to nil, but that only half fixed it, because when i tab-complete a constructor that's not in scope, it adds an "import Module.Name (TheType(TheCtor))" on top of my file anyway
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12:04:11	<ncf>	did you restart hls?
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12:05:20	<Unicorn_Princess>	i'll try restarting the whole lot (tho i've had that setting set to nil for a while, not a recent change)
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12:06:57	<Unicorn_Princess>	didn't help. in fact i tried just a generic tab-complete a function that's not imported, and it auto-imported the module all the same
12:07:26	<Unicorn_Princess>	so doesn't seem limited to constructors. i could have sworn i'd managed to turn it off..
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12:08:15	<Unicorn_Princess>	has anyone manage to disable auto-inserting-imports in any other editor, and how?
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12:16:34	<lortabac>	ncf: "what makes someone think they can't use let...in" -> they thought IORef behaved like mutable variables
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12:17:08	<lortabac>	consider this example in Scheme:
12:17:38	<lortabac>	(let ([x 1]) (set! x 2) (write x)) ;;; prints 2
12:18:49	<lortabac>	now try modifying the variable outside of the scope:
12:19:10	<lortabac>	(define (modify-arg x) (set! x 2)) (let ([x 1]) (modify-arg x) (write x)) ;;; prints 1
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12:22:15	<lortabac>	that's why they asked for an example where the mutation happens in a different scope
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13:54:30	<kuribas>	I really don't get how people think exploratory programming is much easier without types.
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13:55:33	<kuribas>	I am currently writing python with types, and still making small changes to my logic and types. The ability to directly see how a change impacts the code is just invaluable.
13:55:44	<kuribas>	I just don't see how not having types makes it easier.
13:56:15	<kuribas>	I know there was some company that went from haskell to untyped ruby for that reason.
13:58:16	<lortabac>	kuribas: when you are exploring you just want to try out things and see what happens
13:58:40	<lortabac>	you don't want to think about plenty of tiny details which are irrelevant to your exploration
13:59:02	<lortabac>	but static type checking forces you to get everything right upfront
13:59:11	<kuribas>	how do you see what happens without details?
13:59:18	<kuribas>	lortabac: also, I disagree.
13:59:31	<kuribas>	I can very easily leave holes, in types, in implementations...
13:59:49	<lortabac>	maybe we are not thinking of the same scenario
14:00:14	<__monty__>	kuribas: Whenever structural subtyping would be required it does tend to get annoying.
14:01:36	<lortabac>	lack of static typing makes your first "hello world" easier when you try a new library or API
14:01:52	<lortabac>	but the advantage more or less ends there
14:02:29	<kuribas>	I am much faster with a haskell library than clojure/python, because it is more precise.
14:02:50	<kuribas>	I often find my self going through walls of text in python/clojure in order to find some functionality.
14:03:02	<kuribas>	While in haskell I just search through the types.
14:03:09	<kuribas>	Which usually tell me quickly if it is possible or not.
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14:04:02	<lortabac>	I don't know, personally I like to use dynamically-typed languages for very simple projects
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14:04:28	<kuribas>	sure, so do I, like a bash script.
14:04:35	<kuribas>	Or a small calculation in Python.
14:04:37	<lortabac>	it's not just the types, it's the entire thing that is built around the idea of no boilerplate
14:04:45	<kuribas>	anything that isn't > 100 lines.
14:05:05	<lortabac>	in Haskell I need to set up a cabal project, declare the modules, import a bunch of stuff...
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14:05:29	<lortabac>	I don't do it unless it's worth
14:05:50	<kuribas>	yeah, that's a pain. But has nothing to do with types.
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14:06:19	<lortabac>	I know, but it's one "symptom" of a different culture
14:06:54	<glguy>	I do the same thing in python projects
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14:13:14	<merijn>	lortabac: You can put the cabal stuff inside a single file
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14:13:48	<merijn>	admittedly, I think that's not super well documented/discoverable
14:14:41	<lortabac>	merijn: do you mean I can have a single file with both the cabal configuration and the code?
14:14:54	<merijn>	lortabac: Yes
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14:15:16	<merijn>	lortabac: See the cabal run documentation: https://cabal.readthedocs.io/en/stable/cabal-commands.html#cabal-run
14:15:51	<lortabac>	merijn: thanks, that's very useful
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14:16:58	<merijn>	iirc this has been available for, well, approaching a decade now, but it hasn't been well documented for a long time (the new cabal-run docs seem pretty decent, though)
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14:23:01	<dolio>	kuribas: I don't understand it either, for what it's worth.
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14:27:51	<dolio>	(Probably not worth much.)
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15:40:00	<albet70>	lortabac , I like scheme too
15:41:02	<albet70>	I think scheme and haskell are two wonderful languages, and in some way they are very similar except on type
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15:44:12	<tokie>	i wrote a scheme compiler for the web (WASM)! https://www.marwood.io/
15:44:19	<tokie>	scheme was super fun to implement :)
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15:45:32	<Rembane>	\o/
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15:47:28	<Hecate>	tokie: nice!
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15:53:36	<talismanick>	How can I eval inline code like `-- >>> 1 + 1` inside Emacs via lsp-mode? Apparently this is supported by HLS: https://hackage.haskell.org/package/hls-eval-plugin
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15:57:04	<glguy>	talismanick: when I tried it I see this: https://ibb.co/5TXFWkP
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15:57:13	<glguy>	and when I clicked on evaluate..., it did
15:57:17	<albet70>	what's that callCC definition by function?
15:59:50	<EvanR>	is that emacs? it looks like something off of hollywood OS
16:00:04	<glguy>	EvanR: it's emacs configured with spacemacs
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16:01:23	<EvanR>	wow spacemacs has lifestyle brand merchandise and everything
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16:04:09	<ncf>	albet70: rephrase?
16:04:16	<EvanR>	I noticed on tomsmeding paste on chrome on OSX if I type -> a prompt appears to let me auto replace with →. Snazzy. It doesn't work in firefox on linux. Not snazzy :'(
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16:13:01	<talismanick>	glguy: you're right, it works with a mouse click... too bad I can't seem to figure out which function it is so I can bind it
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16:33:43	<glguy>	talismanick: I don't know enough emacs to know how to do it without the click
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16:49:22	<ijqq_>	Hello
16:49:42	<geekosaur>	hello
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16:50:18	<[exa]>	o/
16:50:36	<ijqq_>	How's it going?
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16:52:40	<ijqq_>	I recently watched a video by tsoding on "creating a json parser from scratch in 110 lines of code" and I want to write something similar for a toy language that my friend created. It looks a bit like C.
16:52:40	<ijqq_>	I also read a bit about parsing online and they say you can first tokenise the input and then convert the input into a syntax tree. My question is, does it make sense to tokenise before parsing when creating a parser for his language, as it isn't whitespace sensitive? So I could make a function to strip whitespace at the start or just make the parser functions ignore whitespace?
16:53:08	<ijqq_>	I'm a noob in regards to both parsing and haskell, so I'm a bit confused.
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17:07:09	<__monty__>	ijqq_: Parsing in Haskell is usually done with parser combinators (I recommend Megaparsec). Usually there's no separate lexing/tokenizing step with that approach. Your separate parsers would just eat trailing whitespace or whatever.
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17:08:41	<__monty__>	I'm not sure how closely you want to follow Tsoding's example though, they may have used Alex/Happy, which is the lexing and parsing combination you're probably finding on the web.
17:09:50	<ijqq_>	They did it from scratch, I think the approach was parser combinators though. They defined a parser for chars, used that to parse words, etc. . And made the parser applicative and combined them together
17:10:11	<ijqq_>	The terminology I used might be wrong, I'm quite new, but I think that's what it was
17:10:46	<[exa]>	that sounds like a parser combinator yeah.
17:11:09	<ijqq_>	Okay, so I shouldn't bother with a separate tokenisation step then?
17:11:29	<[exa]>	depends on a language you parse but it's generally not required
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17:13:02	<[exa]>	sometimes it really helps for disambiguating stuff around whitespace separators (some languages consider `a (` and `a(` to be different code), and in certain cases it limits unnecessary backtracking over all characters to a reasonable minimum
17:14:24	<ijqq_>	alright nice, thank you
17:14:43	<EvanR>	I got a lot of traction during advent of code by tokenizing first :sunglasses:
17:14:45	<__monty__>	Either way it wouldn't be all that separate a step, it's still binding parsers together.
17:14:57	<EvanR>	but I didn't use megaparsec which makes dropping space easy
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17:15:53	<__monty__>	I think ijqq_ wants to do it without Megaparsec though, maybe they should take a look at your AoC repo. Unless you used Parsec or ReadP?
17:16:07	<EvanR>	I used raw haskell pattern matching xD
17:16:22	<EvanR>	and the simplifying assumption that the input was well formed
17:16:29	<EvanR>	so maybe not a great example
17:17:29	<[exa]>	ijqq_: one extra concern is error reporting; tokenization usually produces comprehensible errors and the subsequent parsing cannot hallucinate on "hey it might parse if we changed this character in the most weird way possible"
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17:25:21	<ijqq_>	do you have any good resources to learn about this kind of stuff?
17:25:26	<ijqq_>	like how to write a programming language?
17:28:45	<geekosaur>	write yourself a scheme?
17:29:57	<geekosaur>	@where WYaS
17:29:57	<lambdabot>	I know nothing about wyas.
17:30:00	<geekosaur>	sad
17:30:38	<geekosaur>	https://en.wikibooks.org/wiki/Write_Yourself_a_Scheme_in_48_Hours
17:31:12	<yushyin>	the dragon book would be a classic
17:32:58	<geekosaur>	@where+ WYaS https://en.wikibooks.org/wiki/Write_Yourself_a_Scheme_in_48_Hours
17:32:58	<lambdabot>	Done.
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17:36:55	<yushyin>	(but the dragon book is more about compiler/interpreter implementation and less about language design. nevertheless a good read)
17:37:02	<pyrex>	fwiw, I think tokenizing first is a good idea just because the humans reading your code very likely think of it as being written in words and sentences
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17:37:33	<pyrex>	you are likely to produce confusing errors if your parser's definition of "a word" depends on the parser's state, because it is different from what humans assume
17:37:52	<pyrex>	i think this is similar to what [exa] is pointing out, I'm just giving a specific example of how not tokenizing can go weirdly
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17:40:00	<pyrex>	i also think that for certain languages, it is really hard to show "this can be parsed without backtracking" if the code that recognizes an identifier looks like it can backtrack indefinitely
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17:40:23	<pyrex>	when a language claims "don't worry, I'm in LL(1)" they almost always mean "... with a tokenizer!"
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17:42:10	<pyrex>	(if you have not seen the term LL(1), it just means "if you write a naive 'backtrack and try again' parser, it only needs to backtrack one token" -- and that has the advantage that you can often write a parser for it the same way you would write a non-backtracking parser -- you just have an extra peek() operation that looks a single token ahead)
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17:46:40	<ijqq_>	ah okay
17:46:51	<ijqq_>	thank you for the information and the recommendations :)
17:47:00	<pyrex>	i hope it helps!!! this kind of project is usually pretty fun
17:47:06	<ijqq_>	i have lots to learn
17:47:28	<ijqq_>	yes i hope so
17:47:39	<pyrex>	if you find the parser to be tricky, remember that many real parsers are just trying every rule, then giving up and trying the next rule if the previous one doesn't work
17:48:13	<pyrex>	also, arithmetic expressions are always a butt and it's ok to special case them!!!!!
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17:58:36	<segfaultfizzbuzz>	what? "It's also possible to abstract Lists and Trees into polynomials, as every polynomial looks like a sum of terms." - https://functionalcs.github.io/curriculum/
17:59:00	<segfaultfizzbuzz>	oh because sum and product type?
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17:59:29	<dolio>	List A = Σ_i A^i
17:59:37	<dolio>	Unless you're in Haskell.
17:59:44	<segfaultfizzbuzz>	A^i is what?
18:00:09	<ddellacosta>	is it a bad idea to use the websockets library along with http-client? It's not clear to me how to write websocket code with http-client, if it's even possible
18:00:09	<dolio>	The i-fold product of A.
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18:00:19	<dolio>	Or functions from a finite set of size i to A.
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18:01:54	<segfaultfizzbuzz>	does that translate to this? " the type of List A is [A] or [A, A], or [A, A, A], or [A, A, A, A], or etc..."
18:02:10	<dolio>	Yeah, although you missed the 0 case.
18:02:27	<segfaultfizzbuzz>	...sounds like a java null disaster?
18:03:12	<segfaultfizzbuzz>	actually i have never considered whether it would make sense to forbid empty lists and whether to annotate that possibility in the type signature...
18:03:28	<jade[m]>	NonEmpty
18:04:14	<ncf>	x(1 + x + x² + x³ + ...) = x + x² + x³ + ...
18:05:09	<dolio>	Sometimes you want empty lists.
18:05:11	<segfaultfizzbuzz>	so why would i want to model things this way, is there a type galois theory or somtehing?
18:07:04	<ncf>	as a cute application of this, the type of one-hole contexts of a type constructor is its derivative
18:07:16	<ncf>	https://en.wikibooks.org/wiki/Haskell/Zippers#Zippers_via_Differentiation
18:07:44	<ncf>	er, #Differentiation_of_data_types
18:10:11	<segfaultfizzbuzz>	oh wow this seems like a great website thanks for the link
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18:13:35	<ijqq_>	wow i found this website online, crafting interpreters
18:13:42	<ijqq_>	looks great
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18:24:27	<tomsmeding>	EvanR: Does that not happen in other textboxes in chrome?
18:24:31	<tomsmeding>	the -> replacement
18:25:06	<tomsmeding>	it's just a <textbox> :p
18:25:12	<tomsmeding>	er, <textarea>
18:26:48	<EvanR>	you would be a terrible president. Refusing to take credit for stuff you're not responsible for in any way!
18:28:13	<geekosaur>	it's not happening for me, fwiw (chrome, linux)
18:28:24	<geekosaur>	I would wonder if it's a locally installed extension
18:28:57	<ijqq_>	Hi guys, a big noob question here. http://sprunge.us/dPeQmx at the end of runPrompt I get an error that i'm trying to do run line runPrompt but I want to do run line, and then runPrompt. How can I do that?
18:29:22	<dolio>	segfaultfizzbuzz: Polynomial types are a common class of types of interest in type theory. They are a more semantic characterization of the class of types that can be defined via strictly positive Haskell-alike data declarations.
18:30:12	<dolio>	And they can be shown to exist in a lot of scenaraios. Like, sets can encode polynomial types.
18:30:18	<segfaultfizzbuzz>	are type declarations in haskell "terminating"? no, right?
18:30:42	<dolio>	I don't know what you mean by that.
18:30:51	<segfaultfizzbuzz>	that is to say, when haskell looks at my type declaration, does it need to chase the types all the way down so that they are known at compile time
18:31:23	<ncf>	as opposed to what?
18:32:15	<geekosaur>	ijqq_, `else do`
18:32:24	<xerox>	segfaultfizzbuzz: there exists this https://downloads.haskell.org/ghc/latest/docs/users_guide/exts/defer_type_errors.html
18:32:42	<segfaultfizzbuzz>	i suppose at runtime you could define a type...?
18:32:48	<ijqq_>	thank you :)
18:33:36	<geekosaur>	otherwise it's just a continnued expression
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18:34:38	<segfaultfizzbuzz>	another way of asking this is: if we define some essential atomic types such as Int, Char, String, List A, etc then all types constructed in haskell must reduce to the atomic types (e.g. be a polynomial of the atoms)?
18:36:01	<dolio>	Haskell allows definitions of types that don't correspond to polynomials (at least, excepting possibly cases where in a particular model the semantics coincide).
18:36:13	<geekosaur>	I have a feeling the answer is "there is more in heaven and earth, Horation, than is dreamt of in your philosophy"
18:36:19	<geekosaur>	*Horatio
18:36:47	<dolio>	Like: data Hyper a = H ((Hyper a -> a) -> a)
18:37:12	<__monty__>	Define a type at run-time?
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18:38:15	<segfaultfizzbuzz>	what haha? a generic type which takes a generic function returning the genera and maps that function onto a genera? not sure what H does there
18:38:17	<dolio>	And yeah, conceptually, everything to do with types happens (or can happen) in a phase prior to runtime.
18:38:44	<segfaultfizzbuzz>	so typechecking is "strict" and "must terminate"
18:38:55	<segfaultfizzbuzz>	i mean unless you want to wait infinitely long for your program to compile lol
18:39:33	<dolio>	There are extensions that can allow type checking to diverge (undecidable instances). But it's normally supposed to complete.
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18:47:46	<segfaultfizzbuzz>	so a type is a polynomial, but... what would be the significance of a "polynomial coefficient"--it seems like there cannot be one...?
18:48:05	<segfaultfizzbuzz>	like what would 2*Int^3 be, as compared to Int^3 ?
18:48:41	<ncf>	a polynomial data type is a polynomial
18:49:12	<ncf>	we're talking about type constructors here, data types with an argument
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18:49:25	<ncf>	the argument plays the role of the indeterminate X in the polynomial
18:49:47	<mauke>	2*Int^3 = (Bool, Ordering -> Int) -- if I remember my algebra
18:49:57	<ncf>	it doesn't make sense to call 2*Int^3 a polynomial, just like it doesn't make sense to call 42 a polynomial (unless you're considering it as the constant polynomial X ↦ 42)
18:50:36	<segfaultfizzbuzz>	then let my polynomial P = (-1)(Int^2) + (5)(Int^3)
18:50:54	<ncf>	but in types 2* would translate as (Bool,)
18:51:07	<mauke>	that still looks like a constant to me
18:51:16	<segfaultfizzbuzz>	...so 2 refers to the cardinality of the type?
18:51:24	<segfaultfizzbuzz>	so types with equal cardinality are equivalent or something...?
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18:51:34	<mauke>	you can isomorph them
18:52:32	<segfaultfizzbuzz>	wow this is blowing my mind
18:53:13	<segfaultfizzbuzz>	so (2*) is Bool, but it also is like CheckersPlayer and ComputerPowerStatus, and so on?
18:53:53	<segfaultfizzbuzz>	"infinite" types like Int make this a bit difficult to think about,... especially sine then Int^2 would equal Int due to equal cardinality...?
18:54:01	<segfaultfizzbuzz>	*especially since'
18:54:26	<geekosaur>	exponentiation is a function
18:54:35	<ncf>	gotta be careful with equality, but they would at least be isomorphic
18:54:36	<geekosaur>	note what mauke said earlier
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18:55:06	<ncf>	(but the isomorphism isn't quite as nice as the isomorphisms we usually want to think about)
18:55:24	<mauke>	> maxBound :: Int
18:55:25	<lambdabot>	9223372036854775807
18:55:36	<ncf>	oh yeah, i'm thinking of Integer
18:55:47	<ncf>	Int is a finite type :p
18:57:07	<segfaultfizzbuzz>	oops that was my mistake, yeah i mean the lazy/infinite Integer type there
18:57:09	<dolio>	Yeah, Int^2 is not isomorphic to Int. You need Integer for that.
18:57:16	<segfaultfizzbuzz>	so Integer^2 = Integer
18:57:44	<geekosaur>	isn't it Bool -> Integer?
18:57:49	<mauke>	don't think Integer is lazy
18:58:16	<ncf>	geekosaur: yes, for example
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18:58:55	<ncf>	we're using pseudocode here
18:59:28	<segfaultfizzbuzz>	Integer^2 = Bool -> Integer ?
18:59:50	<dolio>	Yeah.
19:00:04	<mauke>	(Integer, Integer) = Bool -> Integer
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19:00:28	<segfaultfizzbuzz>	...but then you aren't just using cardinality, since Bool -> Integer is countable, and so is Integer
19:00:46	<segfaultfizzbuzz>	so this is using something other than that to define equality/equivalence
19:00:57	<ncf>	we're defining it as isomorphism
19:01:13	<ncf>	A and B are isomorphic if there are functions to :: A → B, from :: B → A such that to . from = id and from . to = id
19:01:33	<segfaultfizzbuzz>	hmm unfortunately that applies here
19:01:47	<segfaultfizzbuzz>	there is an isomorphism from (Integer, Integer) to Integer
19:01:55	<ncf>	yes, which is why they are isomorphic
19:02:06	<ncf>	why is this unfortunate?
19:02:38	<segfaultfizzbuzz>	which seems like any time you touch an infinite type it is an Integer
19:02:51	<geekosaur>	it is isomorphic to
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19:03:03	<ncf>	Integer → Integer is larger than Integer
19:03:06	<geekosaur>	meaning you could assign an Integer value to any value in the type
19:03:12	<segfaultfizzbuzz>	unfortunate because it feels like a loss of information or pathology, like divide by zero
19:03:12	<geekosaur>	not that they're identical
19:03:48	<jade[m]>	any countable set is isomorphic to the set of integers right
19:03:52	<mauke>	everything in RAM is represented as a sequence of bits. a sequence of bits is an integer
19:03:53	<chromoblob>	ncf: computable stuff, though, isn't
19:04:07	<jade[m]>	more or less by definition
19:05:15	<ncf>	this is irrelevant to the matter at hand, which is that you couldn't define an isomorphism between Integer and Integer → Integer in haskell (without cheating and looking at the RAM, i guess)
19:06:17	<segfaultfizzbuzz>	but you could define one on paper mathematically...?
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19:06:33	<mauke>	no, only in practice
19:06:35	<dolio>	Being represented by an integer isn't sufficient for such an isomorphism to exist.
19:06:37	<ncf>	in the effective topos, maybe
19:06:53	<mauke>	if you do it rigorously, it doesn't work
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19:07:31	<segfaultfizzbuzz>	oh wow really?
19:07:38	<dolio>	For instance, equal functions can be represented by distinct integers, so if you just try to extract the bits of a particular function, it will fail to actually be a well defined function.
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19:08:05	<pyrex>	i agree that regarding integer as finite is kind of cheaty
19:09:04	<dolio>	So, e.g. in the effective topos, Church's principle holds "for all functions, there is a number referring to a computation of that function." But that does not extend to a _function_ from functions to numbers.
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19:09:55	<ncf>	right
19:11:31	<ncf>	can someone remind me why cantor's diagonal argument fails in the effective topos
19:11:45	<segfaultfizzbuzz>	so... do you move up in cardinality every time you add an Integer...? you are saying that Integer -> Integer -> Integer is higher cradinality than Integer -> Integer, which is higher than Integer...?
19:11:46	<ncf>	well, does it?
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19:11:57	<dolio>	It works.
19:11:59	<ncf>	oh ok
19:12:19	<dolio>	It proves, "2^ℕ is computably uncountable."
19:12:55	<ncf>	segfaultfizzbuzz: no, because Integer → Integer → Integer is the same as (Integer, Integer) → Integer, and you can apply the isomorphism to the domain
19:13:01	<dolio>	Where 2^ℕ is the type of computable functions from ℕ to 2.
19:13:06	<ncf>	on the other hand, (Integer → Integer) → Integer is larger than Integer → Integer
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19:13:44	<dolio>	Well, that last one is dubious.
19:14:06	<ncf>	is it?
19:14:13	<dolio>	Yeah.
19:14:23	<chromoblob>	why at all care about uncomputable stuff
19:14:29	<ncf>	doesn't cantor's theorem apply?
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19:14:58	<chromoblob>	well, i care about true randomness
19:15:01	<chromoblob>	but other than that
19:15:09	<EvanR>	that the uncountable has an analog within the realm of "everything is computable" is interesting
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19:15:21	<dolio>	No, because Cantor's theorem is about maps A -> B^A.
19:15:43	<ncf>	A := Integer → Integer, B := Integer
19:16:09	<jade[m]>	if you had foo x y \| x == y = x; otherwise = 1 and foo' f = product . map f $ [1..] wouldn't that work
19:16:24	<jade[m]>	i mean not in haskell because infinite and shit
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19:17:20	<ncf>	jade[m]: work?
19:17:48	<jade[m]>	i mean create a bijection between `Integer` and `Integer -> Integer`
19:17:49	<ncf>	which types are you trying to prove isomorphic?
19:17:54	<jade[m]>	might just be stupid
19:17:59	<dolio>	ncf: Cantor's theorem is, "maps A -> B^A are not surjections." But you're talking about ℤ^ℤ -> ℤ.
19:18:27	<pyrex>	i think you cannot create a bijection between Integer and (Integer -> Integer) and the diagonal argument shows it
19:18:52	<pyrex>	if you attempt to do so, i can generate a new Integer -> Integer that differs from every element in your map in at least one position
19:18:54	<jade[m]>	pyrex: the diagonal argument doesn't apply here
19:19:05	<dolio>	If you used your instantiation, it'd be about Z^Z -> Z^(Z^Z).
19:19:06	<ncf>	dolio: no, i'm saying that "maps ℤ^ℤ → ℤ^(ℤ^ℤ) are not surjections", in other words ℤ^(ℤ^ℤ) is larger than ℤ^ℤ
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19:19:10	<jade[m]>	or wait
19:19:17	<pyrex>	jade[m]: you sure? I may have missed something about the context
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19:19:42	<probie>	pyrex: like in general, or in Haskell land? There's definitely a bijection between values of type `Integer` and function in Haskell of type `Integer -> Integer`
19:19:50	<jade[m]>	isn't `(Integer -> Integer)` isomorphic to `(Integer, Integer)`?
19:19:55	<ncf>	jade[m]: how do you take the product of an infinite list of integers?
19:19:57	<pyrex>	my function looks like this: `f position = (yourMap !! position) + 1`
19:20:00	<ncf>	jade[m]: no
19:20:13	<jade[m]>	ncf: yeah it doesn't work in haskell
19:20:19	<ncf>	when does it work?
19:20:23	<pyrex>	probie: i think i have to be clear on how "in Haskell-land" we are
19:20:40	<pyrex>	like, there's numerous reasons we can't represent this on an actual computer
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19:20:44	<dolio>	ncf: Oh, well, in that case, the problem is that, "there is no surjection," cannot reasonably be interpreted as "is smaller than."
19:21:03	<pyrex>	i would say that if you examine the function i just wrote and conclude that my function is unwritable in your world, then my argument doesn't apply
19:21:08	<jade[m]>	I was using haskell syntax but I meant to show a general pattern
19:21:35	<ncf>	dolio: classically, sure it can
19:21:45	<dolio>	We're not in a classical setting.
19:21:51	<ncf>	okay, fair
19:21:59	<dolio>	Also I'm not sure it's even reasonable there. :þ
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19:22:05	<pyrex>	er, wait, my function is slightly garbled. i meant `f position = (yourMap !! position) position + 1`
19:22:15	<ncf>	i still think saying 2^A is larger than A makes sense in constructiveland
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19:22:37	<ncf>	you can define that as "there's no surjection" if you like
19:22:41	<jade[m]>	<jade[m]> "if you had foo x y \| x == y = x..." <- but like, would this be an isomorphism if we had a notion of taking an infinite peoduct?
19:22:50	<dolio>	I think 2^2^ℕ ≅ ℕ in the effective topos.
19:23:01	<ncf>	?????
19:23:08	<ncf>	ok i take it all back lol
19:23:09	<dolio>	If not there, then there are constructive settings where it works out.
19:23:42	<dolio>	Another setting is topological spaces. Because the maps involved are continuous.
19:23:54	<dolio>	(Which is also the case for computable maps.)
19:23:55	<ncf>	jade[m]: i'm struggling to assign meaning to this question
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19:25:10	<jade[m]>	yeah i don't really know either
19:25:17	<jade[m]>	forget it lmao
19:25:24	<ncf>	i guess you're thinking of some sort of "free"/"syntactic" product which keeps all of the integers you give it around? but it seems like in order to make this formal you'd have to define something that looks very much like Integer → Integer
19:25:28	<probie>	pyrex: I just meant that `Integer -> Integer` in Haskell doesn't represent `ℤ → ℤ` in maths, because all functions in Haskell must have a finite representation in the language, and the number of possible programs is simply ℕ
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19:26:31	<dolio>	probie: All functions in the effective topos have finite presentations (in terms of whatever computation system you start with).
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19:30:59	<dolio>	ncf: If you use the actual power set, you don't get into situations like that, BTW.
19:31:19	<kritty>	fun times in theory land
19:31:21	<ncf>	so Ω^ℤ ?
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19:31:41	<dolio>	There's a slightly more involved proof that the double power set can't up being equivalent to what you started with.
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19:32:38	<dolio>	Yeah.
19:33:46	<ncf>	i am still not over the fact that "no surjections from A to T(A)" does not mean "no surjections from A to T(T(A))"
19:33:50	<dolio>	I think Ω being closed under things like quantifiers over your original set enters into it importantly.
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19:35:13	<xerox>	ncf: what is T in this context?
19:35:25	<ncf>	a type operator, in this case 2^
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19:35:45	<ncf>	(a functor, i guess)
19:38:14	<ncf>	dolio: wait, are you saying that "no surjections from A to 2^A" is also false in the effective topos, until you replace 2 with Ω?
19:38:17	<ncf>	or at least unprovable
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19:38:35	<tomsmeding>	EvanR: there are more things I would be terrible at :p
19:38:38	<dolio>	Well, in this specific case, it can also be read, "there is no surjection 2^ℕ -> ℕ." Which isn't necessarily surprising unless the only reason you believe a surjection can fail to exist is some kind of "bigness."
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19:39:20	<dolio>	ncf: No, that one works with 2, too.
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19:40:01	<ncf>	i should sit down and work through the details...
19:40:34	<delYsid>	Is there a package for processing JSON Schema other then aeson-schema{s} and json-schema? From skimming the docs, it looks like both are not sufficient for the OpenAI function_call API...
19:40:39	<dolio>	I'm not 100% sure the 2^2^ℕ ≅ ℕ thing holds in the effective topos. But there are constructively consistent axioms that do imply it.
19:40:57	<ncf>	which axioms are you thinking of?
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19:41:32	<dolio>	The reason is that, in some sense, continuity of maps 2^ℕ -> ℕ is a strong limitation.
19:41:39	<dolio>	Er, 2^ℕ -> 2.
19:42:27	<ncf>	right
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19:43:57	<dolio>	I forget which axiom. I guess probably a function continuity one.
19:47:15	<dolio>	https://math.andrej.com/2009/10/12/constructive-gem-double-exponentials/
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19:49:40	<dolio>	"All functions 2^ℕ -> 2 are uniformly continuous."
19:50:12	<dolio>	I imagine it works in the effective topos, because he's using computer programs as an example.
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19:50:44	<dolio>	But for instance, "the Cantor space is compact," isn't valid, I think.
19:51:05	<dolio>	So you can't derive it from the two other principles there, if it is true.
19:52:48	<dolio>	(But Brouwerian intuitionism would be another example setting, I guess.)
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23:36:44	<ijqq_>	I am looking at this tutorial and they have a Token class with various fields, and one of them is value which they have of type Object
23:36:56	<ijqq_>	How can I do something like this in Haskell?
23:37:29	<Axman6>	I don't understand the question, can you share the tutorial?
23:37:33	<ijqq_>	Like is it possible to have something like data Token = SimpleToken {kind :: TokenKind, line :: Int} \| LiteralToken a {kind :: TokenKind, line :: Int, value :: a}?
23:37:35	<ijqq_>	Sure
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23:38:01	<ijqq_>	https://craftinginterpreters.com/scanning.html#lexemes-and-tokens
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23:38:19	<chromoblob>	ijqq_: at which moment the "a" is determined?
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23:38:38	<Axman6>	data Token a = SimpleToken TokenKind Int \| LiteralToken TokenKind Int a -- that would work
23:38:41	<ncf>	move the a from after LiteralToken to after Token and you have valid haskell
23:38:58	<Axman6>	constructors don't have type parameters, their types do
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23:40:29	<ijqq_>	Ahh, thank you
23:41:26	<ijqq_>	data Token a = SimpleToken {kind :: TokenKind, line :: Int} \| LiteralToken {kind :: TokenKind, line :: Int, value :: a} deriving (Show)
23:41:33	<ijqq_>	This works too
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23:41:51	<ijqq_>	so what is the a in data Token a?
23:42:02	<ijqq_>	value :: a this means that the type is a
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23:42:05	<Axman6>	it's a type parameter
23:42:19	<Axman6>	it's like data Token<A> in other languages
23:42:40	<ncf>	same as the x in f x = x + 1
23:42:56	<ijqq_>	But you don't have to use it? So simlpetoken is fine
23:43:05	<Axman6>	data Either a b = Left a \| Right b -- means you can have Left "Hello" :: Either String Int, Right 7 :: Either String Int
23:43:38	<Axman6>	no, you can have type parameters that don't appear in some, or even any, of the constructors (the latter usually called phantom types)
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23:45:25	<ijqq_>	okay cool
23:45:49	<chromoblob>	ijqq_: you may run into problems if you attempt to use "a" as dynamic type
23:46:49	<ijqq_>	and is this a good way to represent the tokens? as in, for the java version the author can just use object and then have some fields potentially blank (empty strings). so i thought in haskell i should try to make different tokens types?
23:47:20	<chromoblob>	whenever "value" is set in a LiteralToken, the "a" in its type is set rigidly and cannot be interchanged with tokens which have different "a"
23:47:24	<ijqq_>	actually i think i only need StringLiteral and NumericLiteral here so I perhaps can just add those as separate token types and I don't need to make it dynamic
23:47:33	<ijqq_>	that would be better to do right?
23:47:38	<ncf>	you could perhaps merge the constructors and have value :: Maybe a
23:48:17	<ijqq_>	So a token such as LEFT_PARENT will jsut have value as Nothing, and a string can have value as Just "foo"?
23:48:33	<chromoblob>	ijqq_: what is TokenKind?
23:48:39	<ijqq_>	PAREN sorry*
23:49:10	<ijqq_>	http://sprunge.us/8Con2F here is my file
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23:49:24	<ijqq_>	i am trying to follow that tutorial but write it in haskell
23:49:37	<ijqq_>	as you can see i am struggling a bit
23:50:15	<chromoblob>	so, i think you should refactor your types
23:50:36	<chromoblob>	note that every token has a line number, and then a kind and other data depending on kind
23:50:55	<chromoblob>	so you should create a type Token: data Token = Token { line :: Int, content :: TokenContent }
23:51:18	<chromoblob>	then data type TokenContent has exactly one constructor for each token kind
23:51:38	<chromoblob>	its String constructor should have field of type String
23:51:50	<chromoblob>	its Number constructor should have field of type Float
23:52:05	<geekosaur>	Double, surely?
23:52:05	<chromoblob>	for Identifier, probably field of type String
23:52:15	<chromoblob>	and other constructors should have no fields
23:52:43	<Axman6>	This is one of the places where understanding the algebraic part of ADT can be useful, you can evaluate several equivalent implementations and decide which makes more sense for how you want to use it
23:54:32	<Axman6>	like understanding that Either a a is equivalent to (Bool,a) - which one makes more sense depends on your project
23:55:43	<chromoblob>	languages for other languages may not work well for Haskell in some cases
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23:55:50	<chromoblob>	tutorials for other languages *
23:57:42	<ijqq_>	sorry chromo, I am a little confused. If I have something like data Token = Token { line :: Int, content :: TokenContent } and the data TokenContent a = StringContent { value :: a } it is asking for another argument to TokenContent
23:57:52	<ijqq_>	maybe I have misunderstood ?
23:58:06	<geekosaur>	you have misunderstood
23:58:41	<geekosaur>	you no longer want or need the a
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23:59:01	<chromoblob>	data TokenContent = LEFT_PAREN \| ... \| IDENTIFIER String \| STRING String \| NUMBER Float \| AND \| ...
23:59:35	<ijqq_>	Ohh I see what you are saying
23:59:36	<ijqq_>	I get it
23:59:44	<ijqq_>	thank you guys, you are very helpful
23:59:51	<chromoblob>	you may also want to group the constructors

All times are in UTC on 2023-06-13.