Newest at the top
| 2025-02-24 22:56:44 +0100 | target_i | (~target_i@user/target-i/x-6023099) (Quit: leaving) |
| 2025-02-24 22:56:43 +0100 | <EvanR> | a family of types ? |
| 2025-02-24 22:56:12 +0100 | <EvanR> | I don't know how to comprehend forall a . Maybe a |
| 2025-02-24 22:55:53 +0100 | <tomsmeding> | Int is a set. Maybe Int is a set. Is `forall a. Maybe a` a set? |
| 2025-02-24 22:55:46 +0100 | <EvanR> | and the element is doing quantification somehow |
| 2025-02-24 22:55:45 +0100 | <ncf> | the elements/terms/inhabitants of a universe are types |
| 2025-02-24 22:55:39 +0100 | <EvanR> | So you have some sets, and now we're talking about elements |
| 2025-02-24 22:55:20 +0100 | <EvanR> | "Sets can contain elements that quantify ..." |
| 2025-02-24 22:55:13 +0100 | <tomsmeding> | EvanR: the "quantify" is essential there |
| 2025-02-24 22:55:01 +0100 | <ncf> | Set is just a universe here |
| 2025-02-24 22:54:53 +0100 | <ncf> | huh |
| 2025-02-24 22:54:26 +0100 | <EvanR> | like in set theory? |
| 2025-02-24 22:54:20 +0100 | <EvanR> | the elements of sets are sets? |
| 2025-02-24 22:54:19 +0100 | <ncf> | https://dl.acm.org/doi/pdf/10.1145/3209108.3209130 section 2 has a definition |
| 2025-02-24 22:52:09 +0100 | ash3en | (~Thunderbi@2a03:7846:b6eb:101:93ac:a90a:da67:f207) ash3en |
| 2025-02-24 22:51:15 +0100 | <tomsmeding> | Types of the form "forall A : Set..." are sets. Sets can contain elements that quantify over the universe of sets. |
| 2025-02-24 22:50:26 +0100 | merijn | (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 252 seconds) |
| 2025-02-24 22:50:21 +0100 | Ekho | (~Ekho@user/ekho) (Quit: CORE ERROR, SYSTEM HALTED.) |
| 2025-02-24 22:49:41 +0100 | <EvanR> | ok unnegate it please |
| 2025-02-24 22:48:48 +0100 | wootehfoot | (~wootehfoo@user/wootehfoot) (Read error: Connection reset by peer) |
| 2025-02-24 22:47:36 +0100 | <lyxia> | oh haha |
| 2025-02-24 22:47:22 +0100 | <ncf> | well it means the negation of that |
| 2025-02-24 22:47:03 +0100 | <lyxia> | it means that types of the form "forall A : Set..." are not sets. Sets cannot contain elements that quantify over the universe of sets. |
| 2025-02-24 22:45:53 +0100 | merijn | (~merijn@host-vr.cgnat-g.v4.dfn.nl) merijn |
| 2025-02-24 22:45:16 +0100 | takuan | (~takuan@d8D86B601.access.telenet.be) (Remote host closed the connection) |
| 2025-02-24 22:40:33 +0100 | <EvanR> | what does "Set is impredicative" mean |
| 2025-02-24 22:38:46 +0100 | ljdarj | (~Thunderbi@user/ljdarj) ljdarj |
| 2025-02-24 22:37:59 +0100 | ljdarj | (~Thunderbi@user/ljdarj) (Ping timeout: 244 seconds) |
| 2025-02-24 22:35:02 +0100 | merijn | (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 252 seconds) |
| 2025-02-24 22:34:45 +0100 | ash3en | (~Thunderbi@2a03:7846:b6eb:101:93ac:a90a:da67:f207) (Ping timeout: 265 seconds) |
| 2025-02-24 22:30:07 +0100 | merijn | (~merijn@host-vr.cgnat-g.v4.dfn.nl) merijn |
| 2025-02-24 22:27:45 +0100 | misterfish | (~misterfis@84.53.85.146) (Ping timeout: 248 seconds) |
| 2025-02-24 22:25:41 +0100 | ash3en | (~Thunderbi@2a03:7846:b6eb:101:93ac:a90a:da67:f207) ash3en |
| 2025-02-24 22:23:39 +0100 | alfiee | (~alfiee@user/alfiee) (Ping timeout: 265 seconds) |
| 2025-02-24 22:22:51 +0100 | <ncf> | i know you can make sense of impredicative encodings via abstract nonsense like "if Set is impredicative then the category of sets is large-complete so the limit of the identity functor gives an initial algebra for every functor" but like... that's what i mean by weird |
| 2025-02-24 22:21:55 +0100 | <ncf> | category theory makes normal inductive types make even more sense |
| 2025-02-24 22:21:50 +0100 | Square | (~Square@user/square) (Ping timeout: 252 seconds) |
| 2025-02-24 22:20:22 +0100 | <haskellbridge> | <Bowuigi> Hinze's Generic Programming with Adjunctions illustrates this perspective quite well, with more advanced examples found in the HoTT blog |
| 2025-02-24 22:19:32 +0100 | <haskellbridge> | <Bowuigi> They are, but Category Theory makes them make sense I guess |
| 2025-02-24 22:19:13 +0100 | Square2 | (~Square4@user/square) Square |
| 2025-02-24 22:19:08 +0100 | merijn | (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 245 seconds) |
| 2025-02-24 22:18:51 +0100 | alfiee | (~alfiee@user/alfiee) alfiee |
| 2025-02-24 22:14:44 +0100 | ash3en | (~Thunderbi@2a03:7846:b6eb:101:93ac:a90a:da67:f207) (Ping timeout: 244 seconds) |
| 2025-02-24 22:14:19 +0100 | merijn | (~merijn@host-vr.cgnat-g.v4.dfn.nl) merijn |
| 2025-02-24 22:13:27 +0100 | justsomeguy | (~justsomeg@user/justsomeguy) justsomeguy |
| 2025-02-24 22:07:53 +0100 | merijn | (~merijn@host-vr.cgnat-g.v4.dfn.nl) (Ping timeout: 252 seconds) |
| 2025-02-24 22:05:35 +0100 | j1n37 | (~j1n37@user/j1n37) (Ping timeout: 268 seconds) |
| 2025-02-24 22:04:43 +0100 | j1n37- | (~j1n37@user/j1n37) j1n37 |
| 2025-02-24 22:02:55 +0100 | merijn | (~merijn@host-vr.cgnat-g.v4.dfn.nl) merijn |
| 2025-02-24 21:58:00 +0100 | jespada | (~jespada@r167-61-39-77.dialup.adsl.anteldata.net.uy) (Quit: My Mac has gone to sleep. ZZZzzz…) |