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2021-06-18 00:37:27 <spider_> .
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2021-06-18 00:52:55 <Nak42> I have some co-inductive list type: ```data Colist a = forall s. Colist (s -> Maybe (a,s)) s```, and I'm bashing my head against the wall trying to figure out if it's possible to define cons and nil over it - any ideas?
2021-06-18 00:53:43 <shachaf> Yes, it's possible.
2021-06-18 00:54:13 <Axman6> is nil = Colist (\_ -> Nothing) undefined?
2021-06-18 00:54:24 <Axman6> I mean, it could be anything I guess
2021-06-18 00:54:26 <shachaf> Well, yes, but I wouldn't use undefined there.
2021-06-18 00:54:34 <Axman6> () also works
2021-06-18 00:55:10 <Nak42> Axman6 Yeah, I've got that one so far
2021-06-18 00:55:12 <shachaf> If you want to understand this style of definition, you might have an easier type with data Conat = forall s. Conat (s -> Maybe s) s
2021-06-18 00:55:18 <shachaf> Uh, an easier time.
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2021-06-18 00:55:20 <shachaf> Both, I suppose.
2021-06-18 00:55:27 <Axman6> this feels a lot like how stream fusion is defined, but I don't remember how you do cons there either
2021-06-18 00:56:09 <shachaf> You should think of either of these as a sort of state machine. There's some internal state, and you can put the state into the function to tick it one step.
2021-06-18 00:56:13 <Nak42> Haha yeah, I saw the type signature in some guys blog post on stream fusion and I got curious
2021-06-18 00:56:23 <shachaf> And then maybe it yields a new state, or maybe it halts.
2021-06-18 00:56:37 <Nak42> Thanks shachaf, that's a really good idea
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2021-06-18 00:57:22 <Axman6> cons a (Colist f s) = Colist (\(b,s') -> if b then Just (a, (False, s')) else ((False,) <$> f s') (True, s)?
2021-06-18 00:57:38 <shachaf> That looks too complicated.
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2021-06-18 01:01:42 <shachaf> Hmm, cons is kind of annoying, actually.
2021-06-18 01:01:43 <Axman6> Well, it works I believe :)
2021-06-18 01:01:46 <Axman6> yes
2021-06-18 01:01:58 <shachaf> I guess it works, then!
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2021-06-18 01:02:20 <Axman6> IIRC this is pretty close to for it works in stream fusion. ideally you could return a new step function and have a different type for the state
2021-06-18 01:02:23 <shachaf> The issue is that (Bool,s) has twice as many states as s, when really you just want one more.
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2021-06-18 01:03:19 <Axman6> There's probably a version with s as Maybe initially set to Nothing
2021-06-18 01:03:37 <shachaf> Right.
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2021-06-18 01:03:59 <shachaf> I guess using lists rather than numbers shows an interesting wrinkle there, because you have to cons onto the beginning, not the en.
2021-06-18 01:04:57 <Axman6> cons a (Colist f s) = Colist (\ms -> (ms >>= f) <|> Just (a,Just s)) Nothing
2021-06-18 01:05:25 <Axman6> cons a (Colist f s) = Colist (\ms -> (ms >>= fmap Just . f) <|> Just (a,Just s)) Nothing
2021-06-18 01:05:29 <Axman6> or something...
2021-06-18 01:06:31 <Axman6> probably missing another fmap actually
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