Logs: liberachat/#haskell
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| 2021-08-10 05:19:56 | <koz> | dibblego: https://twitter.com/PLT_Borat/status/228009057670291456 |
| 2021-08-10 05:20:01 | <koz> | I have found this gem once again. |
| 2021-08-10 05:20:45 | <dibblego> | heh |
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| 2021-08-10 05:57:02 | <euouae> | Hello I want to ask about ((->) a) |
| 2021-08-10 05:57:07 | <euouae> | Is this a Yoneda embedding? |
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| 2021-08-10 05:57:59 | <euouae> | Or rather, sorry, is it just the hom functor in the second argument? |
| 2021-08-10 06:01:30 | <dibblego> | @type id :: e -> e |
| 2021-08-10 06:01:31 | <lambdabot> | e -> e |
| 2021-08-10 06:01:34 | <dibblego> | @type id :: (->) e e |
| 2021-08-10 06:01:35 | <lambdabot> | e -> e |
| 2021-08-10 06:01:40 | <dibblego> | @type id :: ((->) e) e |
| 2021-08-10 06:01:41 | <lambdabot> | e -> e |
| 2021-08-10 06:02:22 | <euouae> | Right but I'm asking about ((->) a) being a functor |
| 2021-08-10 06:02:36 | <dibblego> | @type fmap |
| 2021-08-10 06:02:37 | <lambdabot> | Functor f => (a -> b) -> f a -> f b |
| 2021-08-10 06:02:40 | <dibblego> | @type fmap :: (a -> b) -> [a] -> [b] |
| 2021-08-10 06:02:41 | <lambdabot> | (a -> b) -> [a] -> [b] |
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| 2021-08-10 06:02:50 | <dibblego> | @type fmap :: (a -> b) -> ((-> e) a) -> ((->) e b) |
| 2021-08-10 06:02:51 | <lambdabot> | error: parse error on input ‘e’ |
| 2021-08-10 06:02:57 | <dibblego> | @type fmap :: (a -> b) -> ((->) e a) -> ((->) e b) |
| 2021-08-10 06:02:58 | <lambdabot> | (a -> b) -> (e -> a) -> e -> b |
| 2021-08-10 06:04:06 | <euouae> | Hm.. I can't quite put into words what I'm thinking. I just realized that ((->) a) being a functor had to do with the Yoneda lemma |
| 2021-08-10 06:04:19 | <euouae> | Or rather, the statement of the Yoneda lemma uses that functor |
| 2021-08-10 06:06:39 | <Gurkenglas> | euouae, the yoneda embedding takes the b in (a -> b) as its first argument |
| 2021-08-10 06:06:49 | <Gurkenglas> | it's flip (->), basically. |
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| 2021-08-10 06:07:20 | <euouae> | Gurkenglas: You can have it both ways right? |
| 2021-08-10 06:07:20 | <dsal> | :t ((->) a) |
| 2021-08-10 06:07:21 | <lambdabot> | error: parse error on input ‘->’ |
| 2021-08-10 06:07:35 | <Axman6> | it's be :kind |
| 2021-08-10 06:07:39 | <Axman6> | it'd* |
| 2021-08-10 06:08:26 | <dsal> | I was going type would be useful. But yeah, they kind is illustrative. |
| 2021-08-10 06:08:27 | <euouae> | :kind ((->) *) |
| 2021-08-10 06:08:37 | <euouae> | Hmm it works in ghci |
| 2021-08-10 06:08:53 | <dibblego> | @kind ((->) *) |
| 2021-08-10 06:08:54 | <lambdabot> | * -> * |
| 2021-08-10 06:09:05 | <dsal> | If you can imagine ((->) a) bring a mapping of a to b, then youb can imagine seeing how a function of b->c can be fmapped |
| 2021-08-10 06:09:24 | <Gurkenglas> | euouae, if you want to understand the yoneda lemma you need to pay attention to the difference; the difference between the a and the b is that the result is "covariant" in the b and "contravariant" in the a. This means that given some b->b' you can turn each a->b into some a->b', but given some a->a' you get *get* some a->b *from* each a'->b |
| 2021-08-10 06:09:36 | <dsal> | 'a' was confusing there... I should be asleep |
| 2021-08-10 06:09:53 | <euouae> | Gurkenglas: But Yoneda lemma has both versions |
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| 2021-08-10 06:10:28 | <euouae> | I'm not saying they're not different, but in an inessential way. You are right the classical one is flip (->) |
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| 2021-08-10 06:10:51 | <euouae> | I was just curious if there's some insight of Haskell types with regards to that functor and the Yoneda lemma |
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