Logs: liberachat/#haskell
| 2026-02-24 07:21:58 | <lambdabot> | In the expression: minBound |
| 2026-02-24 07:22:24 | <Leary> | Ah, Forgot to derive `Bounded`. Well, you get the idea. |
| 2026-02-24 07:23:04 | <Leary> | > [minBound .. maxBound] :: [FooBarEnum] |
| 2026-02-24 07:23:05 | <lambdabot> | [Foo,Bar] |
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| 2026-02-24 07:27:01 | <gentauro> | Leary: now that was nifty <3 |
| 2026-02-24 07:27:32 | <gentauro> | many thx |
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| 2026-02-24 09:31:27 | <dminuoso> | % :t minBound |
| 2026-02-24 09:31:27 | <yahb2> | minBound :: Bounded a => a |
| 2026-02-24 09:31:58 | <dminuoso> | Curious, why is Ord not a superclass of Bounded? |
| 2026-02-24 09:32:19 | <dminuoso> | What does `minimum/maximum` even mean in the absence of an ordering? |
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| 2026-02-24 09:33:40 | <tomsmeding> | perhaps it makes sense that an Enum has a first and a last value for enumeration, but while it has an ordering compatible with that Enum instance, that ordering makes no semantical sense and is hence not defined? |
| 2026-02-24 09:33:53 | <tomsmeding> | but then you could argue that you should give that Ord instance anyway |
| 2026-02-24 09:34:47 | <humasect> | it says right in the first sentence https://hackage-content.haskell.org/package/base-4.22.0.0/docs/Data-Bounded.html |
| 2026-02-24 09:35:05 | <tomsmeding> | lol, dminuoso ^ |
| 2026-02-24 09:35:24 | tomsmeding | should have thought of that |
| 2026-02-24 09:35:32 | <dminuoso> | humasect: Yes, and its not much of an explanation. |
| 2026-02-24 09:35:43 | <dminuoso> | It reads nonsensical to me. |
| 2026-02-24 09:35:48 | <humasect> | perhaps look into its meaning, disassemble it to understanding |
| 2026-02-24 09:35:50 | <tomsmeding> | dminuoso: not every ordering is total |
| 2026-02-24 09:35:54 | <dminuoso> | Oh. |
| 2026-02-24 09:35:54 | <tomsmeding> | partial orders are a thing |
| 2026-02-24 09:35:55 | <humasect> | how to learn ? |
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| 2026-02-24 09:36:22 | <dminuoso> | tomsmeding: Is there a notion of `minimum` in a partially ordered set, then? |
| 2026-02-24 09:36:30 | <dminuoso> | Im not even sure what that would mean. |
| 2026-02-24 09:36:32 | <__monty__> | tomsmeding: But Bounded doesn't deal with just any partial order. |
| 2026-02-24 09:36:43 | <tomsmeding> | dminuoso: yes, a lower bound :) https://en.wikipedia.org/wiki/Lattice_(order) |
| 2026-02-24 09:36:44 | <__monty__> | It's restricted to partial orders that have a single lower and upper bound. |
| 2026-02-24 09:37:15 | <tomsmeding> | sure, but even those need not have a total ordering |
| 2026-02-24 09:37:27 | <tomsmeding> | perhaps "lower bound" is not the technically correct term here |
| 2026-02-24 09:37:38 | <tomsmeding> | (but then, it's probably "minimum", which would not have helped dminuoso) |
| 2026-02-24 09:38:17 | <tomsmeding> | dminuoso: all subset of a given set S are partially ordered by inclusion, and they have a unique minimum ({}) and maximum (S), but they are not totally ordered |
| 2026-02-24 09:38:47 | <dminuoso> | tomsmeding: Okay so what you're saying is that Bounded is just synonmous for Lattice? |
| 2026-02-24 09:38:55 | <tomsmeding> | perhaps? |
| 2026-02-24 09:39:16 | <tomsmeding> | well, a bounded lattice |
| 2026-02-24 09:39:46 | <dminuoso> | tomsmeding: Aren't all lattices bounded by their suprema? |
| 2026-02-24 09:40:04 | <dminuoso> | Ohh wait. |
| 2026-02-24 09:40:06 | <dminuoso> | I see. |
| 2026-02-24 09:40:07 | <tomsmeding> | according to the wikipedia definition that I'm currently reading, a plain "lattice" requires joins and meets of _two_ elements |
| 2026-02-24 09:40:10 | <tomsmeding> | and thus finite sets |
| 2026-02-24 09:40:27 | <tomsmeding> | a _complete lattice_ additionally requires suprema and infima of larger sets |
| 2026-02-24 09:40:38 | <tomsmeding> | thus all complete lattices are bounded, but not all bounded lattices are complete? Perhaps? |
| 2026-02-24 09:40:55 | dminuoso | wonders why lattices are called lattices |
| 2026-02-24 09:41:19 | <tomsmeding> | because of this picture I always assumed https://commons.wikimedia.org/wiki/File:Pow3nonlattice.svg |
| 2026-02-24 09:41:39 | <jreicher> | dminuoso: hasse diagrams |
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| 2026-02-24 09:42:06 | <jreicher> | https://en.wikipedia.org/wiki/Hasse_diagram |
| 2026-02-24 09:42:21 | <tomsmeding> | which that picture is an example of |
| 2026-02-24 09:42:40 | <Leary> | It's a bounded partial order with minimal and maximal elements---that doesn't imply unique suprema or infima. |
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| 2026-02-24 09:43:09 | <tomsmeding> | fair! Even pairs need not have unique joins or meets |
| 2026-02-24 09:43:48 | <dminuoso> | Leary: Are you saying that Bounded does not have uniqueness requirements? |
| 2026-02-24 09:44:16 | <tomsmeding> | dminuoso: even if there is a maximal element of the entire set, that does not necessarily mean there is a _unique_ smallest upper bound of any subset of the set |
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