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| 2026-01-15 22:17:26 +0100 | <jreicher> | Yes partial functions will definitely happen. But maybe we can accept those. The bigger problem is that if there are many y for a given x for which S(x,y) then a sub relation that is a function will not really resemble S in any meaningful way |
| 2026-01-15 22:16:32 +0100 | <dolio> | Otherwise you could only hope to get a partial function in general. |
| 2026-01-15 22:16:18 +0100 | <dolio> | I guess, you should be able to restrict the domain, too. |
| 2026-01-15 22:15:28 +0100 | Lears | Leary |
| 2026-01-15 22:15:09 +0100 | <dolio> | No, R is a sub-relation of S if R(x,y) implies S(x,y) forall x and y. |
| 2026-01-15 22:14:35 +0100 | Leary | (~Leary@user/Leary/x-0910699) (Ping timeout: 240 seconds) |
| 2026-01-15 22:14:14 +0100 | <jreicher> | dolio: And what do you mean by sub-relation? Does it also mean restricting the domain to a subset? |
| 2026-01-15 22:13:40 +0100 | <dolio> | It means there's a sub-relation that is a function. |
| 2026-01-15 22:13:26 +0100 | <jreicher> | int-e: I suspect you underestimate the significance of "most convenient". Mathematical definitions are language design in much the same way that programming languages are designed. So if a mathematician says something is "convenient", it means it's a good design. And mathematicians have been working on this much longer than computer scientists. |
| 2026-01-15 22:13:19 +0100 | Lears | (~Leary@user/Leary/x-0910699) Leary |
| 2026-01-15 22:12:55 +0100 | merijn | (~merijn@host-cl.cgnat-g.v4.dfn.nl) (Ping timeout: 246 seconds) |
| 2026-01-15 22:12:07 +0100 | <jreicher> | dolio: I'm not sure what you mean by "contain", but I'm fairly sure the answer will be "no", regardless of what meaning you choose. |
| 2026-01-15 22:09:49 +0100 | <dolio> | Not that every relation from A to B is a function from A to B. |
| 2026-01-15 22:09:22 +0100 | <dolio> | jreicher: Also, relations are functions in that they are maps into a collection of truth values. |
| 2026-01-15 22:08:39 +0100 | merijn | (~merijn@host-cl.cgnat-g.v4.dfn.nl) merijn |
| 2026-01-15 22:07:38 +0100 | <EvanR> | you can get a relation for any function also lets you avoid subtyping |
| 2026-01-15 22:06:56 +0100 | <dolio> | jreicher: But does every relation contain a function? |
| 2026-01-15 22:04:49 +0100 | <EvanR> | sometimes taking the place of |
| 2026-01-15 22:04:33 +0100 | <EvanR> | how concepts interrelate is more interesting than "what they are really" |
| 2026-01-15 22:03:49 +0100 | <EvanR> | :D |
| 2026-01-15 22:03:35 +0100 | <EvanR> | math entities are a pure construction of the mind |
| 2026-01-15 22:02:54 +0100 | <int-e> | First-order logic has many-sorted variants. There are algebras with more than one carrier set and operators that aren't homogenous either, like vector spaces. |
| 2026-01-15 22:01:55 +0100 | <int-e> | "in mathematics" - there is no such thing really; mathematicians will take whatever view is most convenient in a context. In classical logic, predicates can and will be used as functions. Logicians who want to allow logics without the law of excluded middle will disagree. |
| 2026-01-15 22:01:25 +0100 | <EvanR> | you can get a relation for any function, then functions don't need to be implemented as literal relations if you don't want them to be! |
| 2026-01-15 21:55:46 +0100 | trickard_ | (~trickard@cpe-84-98-47-163.wireline.com.au) |
| 2026-01-15 21:55:31 +0100 | merijn | (~merijn@host-cl.cgnat-g.v4.dfn.nl) (Ping timeout: 264 seconds) |
| 2026-01-15 21:54:35 +0100 | <jreicher> | monochrom: a function is a relation, but the converse is not true |
| 2026-01-15 21:53:04 +0100 | trickard_ | (~trickard@cpe-84-98-47-163.wireline.com.au) (Read error: Connection reset by peer) |
| 2026-01-15 21:53:03 +0100 | <c_wraith> | it's closed! |
| 2026-01-15 21:52:59 +0100 | <lambdabot> | LT |
| 2026-01-15 21:52:58 +0100 | <c_wraith> | > LT `compare` GT |
| 2026-01-15 21:51:08 +0100 | <jreicher> | thenightmail: I'm fairly sure in mathematics the comparison "operators" are not operators at all. In algebra an operator on a set produces another element from the same set. Comparison, on the other hand, is a predicate. |
| 2026-01-15 21:50:21 +0100 | merijn | (~merijn@host-cl.cgnat-g.v4.dfn.nl) merijn |
| 2026-01-15 21:49:50 +0100 | peterbecich | (~Thunderbi@71.84.33.135) (Ping timeout: 256 seconds) |
| 2026-01-15 21:46:48 +0100 | Enrico63 | (~Enrico63@2001:b07:646b:5fed:9efc:e8ff:fe24:3213) (Client Quit) |
| 2026-01-15 21:46:01 +0100 | <[exa]> | -XLexicalKinds |
| 2026-01-15 21:43:37 +0100 | Enrico63 | (~Enrico63@2001:b07:646b:5fed:9efc:e8ff:fe24:3213) Enrico63 |
| 2026-01-15 21:43:37 +0100 | merijn | (~merijn@host-cl.cgnat-g.v4.dfn.nl) (Ping timeout: 256 seconds) |
| 2026-01-15 21:43:35 +0100 | jreicher | (~joelr@user/jreicher) jreicher |
| 2026-01-15 21:42:59 +0100 | <monochrom> | TypeDirectedLexicalResolution? >:) |
| 2026-01-15 21:42:52 +0100 | divlamir | (~divlamir@user/divlamir) divlamir |
| 2026-01-15 21:42:25 +0100 | <humasect> | yeah |
| 2026-01-15 21:42:23 +0100 | <dolio> | That's innovation. |
| 2026-01-15 21:42:11 +0100 | <dolio> | Anyhow, as I said, Haskell can take it to the next level by making lexing undecidable. |
| 2026-01-15 21:41:03 +0100 | humasect | (~humasect@dyn-192-249-132-90.nexicom.net) humasect |
| 2026-01-15 21:40:35 +0100 | divlamir | (~divlamir@user/divlamir) (Ping timeout: 240 seconds) |
| 2026-01-15 21:38:47 +0100 | merijn | (~merijn@host-cl.cgnat-g.v4.dfn.nl) merijn |
| 2026-01-15 21:37:42 +0100 | <davean> | dolio: https://blog.reverberate.org/2013/08/parsing-c-is-literally-undecidable.html "C++ grammar: the type name vs object name issue" and others |
| 2026-01-15 21:36:21 +0100 | <dolio> | I guess perl has to actually evaluate code. |
| 2026-01-15 21:36:01 +0100 | <dolio> | davean: Does C++ do that, too? I thought that was perl's distinction. |