Logs: liberachat/#haskell
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| 2025-12-26 13:11:18 | <ncf> | Map k isn't a Monad, but it is a Bind (a monad without unit, or "semigroupad"). it is also equipped with a morphism Map k (Either a (Map k a)) → Map k a, which means that Either a (Map k a) is in a sense the "free monad" on this semigroupad (equivalently, Map k is the T₀ part of an ideal monad https://hackage.haskell.org/package/monad-ideals) |
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| 2025-12-26 13:24:01 | <yin> | Morj: I used to have haskell-language-server-wrapper. I still do, but I used to too. |
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| 2025-12-26 13:49:55 | <[exa]> | meh, is there any intuition/good examples for explaining why Monad Complex is written as it is? `a :+ b >>= f = realPart (f a) :+ imagPart (f b)` |
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| 2025-12-26 13:51:46 | <Franciman> | seems like monad for (a, a) |
| 2025-12-26 13:52:17 | <Franciman> | ah no |
| 2025-12-26 13:55:06 | <Franciman> | f :: x -> Complex x, but you only extract real part |
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| 2025-12-26 13:56:08 | <Franciman> | what example has type x -> Complex x ? |
| 2025-12-26 13:56:36 | <Franciman> | given a real, you want to build a complex |
| 2025-12-26 13:57:46 | <Franciman> | ok one example is given theta, build e^{i*theta} = sin(theta) + i cos(theta) |
| 2025-12-26 14:00:01 | <Franciman> | [exa]: https://vitez.me/complex-monad |
| 2025-12-26 14:00:16 | <Franciman> | here they say they don't like it, and it seems it's more for general pairing than actual complex structure |
| 2025-12-26 14:00:41 | <Franciman> | this is more interesting |
| 2025-12-26 14:00:43 | <Franciman> | https://stackoverflow.com/questions/47181078/meaning-and-usage-of-complex-number-functor-and-monad |
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| 2025-12-26 14:05:02 | <ncf> | [exa]: it's the Pair monad, aka Reader Bool |
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| 2025-12-26 14:05:37 | <ncf> | (i don't know why Complex needs a Monad instance, but here you go) |
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| 2025-12-26 15:18:20 | <[exa]> | Franciman ncf oh so it's mainly to force the instance into existence while aligning with how the applicative works |
| 2025-12-26 15:18:24 | <[exa]> | ok fair enough |
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