Questions regarding Bounded

[Simon Jakobi]

Dear Henning,

Thank you for your response! I think I have caused some confusion by not
being quite clear in my email. Sorry!

base _does_ contain Ord instances for both Maybe and Either. So the
question of what the smallest (Maybe Int8) is, is settled: It's Nothing.

My question is, why the corresponding Bounded instances are missing from
base. After all they could simply re-use the bounds implied by the Ord
instances.

Thanks,
Simon



Am Mo., 4. Mai 2020 um 15:30 Uhr schrieb Henning Thielemann <
lemming at henning-thielemann.de>:

>
> On Mon, 4 May 2020, Simon Jakobi via Libraries wrote:
>
> > Possibly relatedly, I was looking for Bounded instances for Maybe and
> > Either. To me the following instances seem sensible:
> >
> > instance Bounded a => Bounded (Maybe a) where
> >    minBound = Nothing
> >    maxBound = Just maxBound
> >
> > instance (Bounded a, Bounded b) => Bounded (Either a b) where
> >   minBound = Left minBound
> >   maxBound = Right maxBound
> >
> > Are these instances omitted for a reason? Interestingly, both types do
> have corresponding Ord instances.
>
> Unfortunately, Ord is dual use:
>
> 1. Comparison for magnitude as suggested by the mathematical symbols (<)
> and (>).
>
> 2. Some arbitrary but total order for use in Set and Map.
>
> E.g. Set (Complex a) makes total sense, but 1:+0 > 0:+1 is unexpected. Ord
> instances on pairs is sensible for Set and Map, but (max (1,0) (0,1) ==
> (1,0)) is strange.
>
> I would not interpret too much into (Bounded a => Maybe a). Nothing may
> mean "smaller than any Just element", but it may also mean "larger than
> any Just element" or "no regular element at all".
>
> Consider a refactoring where a numeric value is extended by Maybe. Do we
> want that comparisons and bounds are silently re-interpreted or would we
> like to be alerted that comparisons and bounds don't make sense anymore?
> I'd prefer the alert. Unfortunately, Ord Maybe is already defined.
>
> For an extra largest or smallest element I would define a custom
> Maybe-like datatype.
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