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2021-05-29 17:35:46 ← ecm parts (~user@103.88.87.15) ()
2021-05-29 17:36:12 × buggy quits (~buggy@user/smorgasbord) (Quit: Lost terminal)
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2021-05-29 18:00:53 <Bartosz> I'm trying to understand the idea of tagless final encoding. They always say that tagless can be done without GADTs. So I assume that using GADTs solves the problem too. The functions they define are just GADT constructors, aren't they?
2021-05-29 18:00:54 <shiraeeshi> ecm: "The book of monads" by Alejandro Serrano Mena
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2021-05-29 18:01:24 <geekosaur> ecm left
2021-05-29 18:01:38 <shiraeeshi> oh, ok
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2021-05-29 18:03:17 <shiraeeshi> Bartosz: "The functions they define are just GADT constructors, aren't they?" - who are "they"?
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2021-05-29 18:03:36 <Bartosz> Kiselyov et al
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2021-05-29 18:06:25 <Bartosz> edwardk : is that right?
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2021-05-29 18:07:19 <siraben> Bartosz: tagless final encoding has better compositional properties
2021-05-29 18:07:37 <siraben> in the paper there's an example of MulSYM and ExpSYM
2021-05-29 18:07:46 <siraben> you can combine them to something like, x = add (lit 3) (mul (lit 3) (lit 5))
2021-05-29 18:08:02 <siraben> then the typeclass constraint on x would be, (ExpSYM a, MulSYM a) => a
2021-05-29 18:08:13 <siraben> notice that this would not typecheck with GADTs
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2021-05-29 18:08:16 <Bartosz> But can you do the same with GADT?
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2021-05-29 18:09:03 <siraben> Let's say you did, data ExpSYM a where Add :: ExpSYM Int → ExpSYM Int → ExpSYM Int
2021-05-29 18:09:08 <Bartosz> Aren't these just smart constructors?
2021-05-29 18:09:14 <siraben> and Lit :: Int → ExpSYM Int
2021-05-29 18:09:34 <siraben> data MulSYM a where Mul :: MulSYM Int → MulSYM Int → MulSYM Int
2021-05-29 18:09:40 <siraben> Add (Lit 3) (Mul (Lit 3) (Lit 5)) would not typecheck
2021-05-29 18:10:27 <siraben> So, while it's basically equivalent with GADTs for a single typeclass, the ability to freely combine things in tagless-final encoding is one of the advantages
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2021-05-29 18:11:56 <Bartosz> I was just reading this blog post, where the guy points out that tagless final has nothing to do with typeclasses. https://www.foxhound.systems/blog/final-tagless/
2021-05-29 18:12:39 <Bartosz> Ben Levy wrote it
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2021-05-29 18:13:20 <siraben> Kiselyov expresses it through typeclasses, I'm only familiar with his presentation of GADTs
2021-05-29 18:13:24 <siraben> Oops I mean, presentation of tagless-final
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2021-05-29 18:13:58 <cdsmith> So basically we're just saying that you're using the type class (or equivalent mechanism) to postpone the choice of model, meaning you can define your x = add (lit 3) (mul (lit 3) (lit 5)) in one place, and maybe instantiate the type with a GADT in one place, or a different model somewhere else?
2021-05-29 18:14:12 <siraben> Bartosz: I only see a single sort going on in that blog post; SqlExpr
2021-05-29 18:15:02 <siraben> In the little example I gave, there's two different kinds of expressions
2021-05-29 18:15:53 <cdsmith> Sure, but eventually, a has to be SOMETHING!
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2021-05-29 18:16:39 <cdsmith> Sorry, I think I was jumping in and confusing things.
2021-05-29 18:16:44 <siraben> Chris Smith: exactly, "choice of model" is a more mathematical way to put it
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2021-05-29 18:18:05 <Bartosz> It seems to me that "tagless" and "final" are specific terms. It so happens that tagless final allows the use of typeclasses to postpone the interpretation.
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2021-05-29 18:18:41 <siraben> it's like in mathematical logic, you can add more and more terms and equations for your logical theory, which possibly constrains the number of models that satisfy that theory
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2021-05-29 18:21:16 <Bartosz> I'm just wondering if the use of GADTs is considered "tagging" the result. My understanding is that GADT tags are only used by the typechecker.
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2021-05-29 18:23:52 <shiraeeshi> siraben: why did you create GADTs like that? How about something like this (it's not even a GADT, just a regular data):
2021-05-29 18:23:55 <shiraeeshi> data Exp where Add {a :: Exp, b :: Exp}; Mult {a :: Exp, b :: Exp}
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2021-05-29 18:24:08 <siraben> the point is that you can extend it post-hoc
2021-05-29 18:24:12 <siraben> without recompiling old code
2021-05-29 18:24:18 <siraben> the tagless-final paper talks about this
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2021-05-29 18:24:46 <siraben> if you added a new case to Exp, then you'd have to go along everywhere you destructed an Exp and handle the new case
2021-05-29 18:25:02 <siraben> with this, the old code that uses values of type (ExpSYM a) => a stay as such
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