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| 2024-12-29 04:18:33 +0100 | <haskellbridge> | <thirdofmay18081814goya> Bowuigi: the extent of the work that can be done by an indexing type is that of specifying another type, so it has type "IndexType -> Type", where "IndexType : Type" |
| 2024-12-29 04:18:13 +0100 | <Leary> | I don't see what an ordering on the index kind has to do with anything. |
| 2024-12-29 04:17:05 +0100 | <haskellbridge> | <Bowuigi> Wait how? |
| 2024-12-29 04:16:00 +0100 | ljdarj | (~Thunderbi@user/ljdarj) (Ping timeout: 265 seconds) |
| 2024-12-29 04:14:23 +0100 | <haskellbridge> | <thirdofmay18081814goya> pattern matching, that is |
| 2024-12-29 04:13:37 +0100 | <haskellbridge> | <thirdofmay18081814goya> simply because the work of an indexing type is delimited simply by how many ways you can pattern match on it. i.e. this completely specifies the extent of the work an indexing type can do |
| 2024-12-29 04:11:00 +0100 | <haskellbridge> | <thirdofmay18081814goya> i.e. any work that can done by a type, as an indexing type, will be the same as can be done by either "Finite n" or the type of natural numbers |
| 2024-12-29 04:10:30 +0100 | prasad | (~Thunderbi@c-73-75-25-251.hsd1.in.comcast.net) (Ping timeout: 260 seconds) |
| 2024-12-29 04:08:43 +0100 | <haskellbridge> | <thirdofmay18081814goya> there is no type that can carry more information as an indexing type*** |
| 2024-12-29 04:08:25 +0100 | <haskellbridge> | <thirdofmay18081814goya> there is no type that can carry more information that either "Finite n" or "Nat", so I think it is a good starting point |
| 2024-12-29 04:07:49 +0100 | <haskellbridge> | <thirdofmay18081814goya> well |
| 2024-12-29 04:07:23 +0100 | <haskellbridge> | <thirdofmay18081814goya> thinking about specifically the case where the indexes are given by "Finite n" |
| 2024-12-29 04:07:18 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) (Ping timeout: 265 seconds) |
| 2024-12-29 04:05:34 +0100 | op_4 | (~tslil@user/op-4/x-9116473) op_4 |
| 2024-12-29 04:05:03 +0100 | op_4 | (~tslil@user/op-4/x-9116473) (Remote host closed the connection) |
| 2024-12-29 04:02:45 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) merijn |
| 2024-12-29 04:00:27 +0100 | notzmv | (~umar@user/notzmv) notzmv |
| 2024-12-29 04:00:07 +0100 | <haskellbridge> | <thirdofmay18081814goya> we want there to be a strict ordering in the indexing type/sort right? |
| 2024-12-29 03:59:50 +0100 | <haskellbridge> | <thirdofmay18081814goya> hm |
| 2024-12-29 03:52:52 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) (Ping timeout: 252 seconds) |
| 2024-12-29 03:45:04 +0100 | notzmv | (~umar@user/notzmv) (Ping timeout: 265 seconds) |
| 2024-12-29 03:44:53 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) merijn |
| 2024-12-29 03:32:16 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) (Ping timeout: 252 seconds) |
| 2024-12-29 03:27:53 +0100 | <Leary> | This is clearer when looking at a corresponding indexed applicative: `unit :: f i i (); fuse :: f i j a -> f j k b -> f i k (a, b)` |
| 2024-12-29 03:27:51 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) merijn |
| 2024-12-29 03:24:00 +0100 | <Leary> | thirdofmay: The Atkey indexed monad has two indices for the same reason `Category` arrows do; its bind performs a kind of composition. Simple examples include the indexed writer monad, which writes category arrows rather than monoids, and the indexed state monad which has distinct types for the initial and final state. |
| 2024-12-29 03:16:33 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) (Ping timeout: 246 seconds) |
| 2024-12-29 03:12:10 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) merijn |
| 2024-12-29 03:11:41 +0100 | <lambdabot> | Consider it noted. |
| 2024-12-29 03:11:40 +0100 | <Leary> | @tell prsteele https://play.haskell.org/saved/J7bdQ5zn |
| 2024-12-29 03:06:24 +0100 | peterbecich | (~Thunderbi@syn-047-229-123-186.res.spectrum.com) (Ping timeout: 265 seconds) |
| 2024-12-29 03:04:56 +0100 | thatonelutenist | (8216c46202@2a03:6000:1812:100::fb3) thatonelutenist |
| 2024-12-29 03:03:11 +0100 | euleritian | (~euleritia@dynamic-176-006-135-074.176.6.pool.telefonica.de) |
| 2024-12-29 03:00:21 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) (Ping timeout: 276 seconds) |
| 2024-12-29 02:55:47 +0100 | comonad | (~comonad@p200300d027182d00bcfd40be9d94d2dc.dip0.t-ipconnect.de) |
| 2024-12-29 02:54:07 +0100 | Square | (~Square@user/square) (Ping timeout: 264 seconds) |
| 2024-12-29 02:54:03 +0100 | comonad | (~comonad@p200300d0270bcb00d2bd35ff80c069c9.dip0.t-ipconnect.de) (Ping timeout: 244 seconds) |
| 2024-12-29 02:53:02 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) merijn |
| 2024-12-29 02:52:22 +0100 | euleritian | (~euleritia@dynamic-176-006-135-074.176.6.pool.telefonica.de) (Ping timeout: 252 seconds) |
| 2024-12-29 02:47:33 +0100 | machinedgod | (~machinedg@d108-173-18-100.abhsia.telus.net) (Ping timeout: 248 seconds) |
| 2024-12-29 02:44:58 +0100 | peterbecich | (~Thunderbi@syn-047-229-123-186.res.spectrum.com) peterbecich |
| 2024-12-29 02:39:49 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) (Ping timeout: 265 seconds) |
| 2024-12-29 02:37:53 +0100 | acidjnk_new3 | (~acidjnk@p200300d6e7283f42bc4ebb891d7561a4.dip0.t-ipconnect.de) (Ping timeout: 248 seconds) |
| 2024-12-29 02:36:55 +0100 | <hololeap> | ok I think I see what you mean |
| 2024-12-29 02:35:06 +0100 | merijn | (~merijn@128-137-045-062.dynamic.caiway.nl) merijn |
| 2024-12-29 02:32:11 +0100 | <ncf> | i.e. applicative functors are monoids in the category of endofunctors *with Day convolution as the monoidal product* |
| 2024-12-29 02:31:34 +0100 | <ncf> | well that doesn't tell you which monoidal structure you put on it |
| 2024-12-29 02:31:29 +0100 | <hololeap> | (I barely understand this stuff so don't take me too seriously) |
| 2024-12-29 02:30:10 +0100 | <hololeap> | isn't that usually just referred to as "the category of endofunctors" |
| 2024-12-29 02:28:29 +0100 | <ncf> | i.e. the endomorphism monoidal category on Set in the bicategory of categories |