Questions regarding Bounded

[Simon Jakobi]

Thanks David,

I agree that having separate type classes for lower and upper bounds
would be the better design.

I really like your names, BoundedBelow and BoundedAbove, too!

Am Mi., 6. Mai 2020 um 21:13 Uhr schrieb David Feuer <david.feuer at gmail.com>:
>
> The Bounded class is broken because it combines two distinct concepts:
> BoundedAbove and BoundedBelow. If Maybe is to have instances similar
> to what it has now, they should surely look like
>
> instance BoundedBelow (Maybe a) where
>   minBound = Nothing
> instance BoundedAbove a => BoundedAbove (Maybe a) where
>   maxBound = Just maxBound
>
> On Wed, May 6, 2020 at 1:52 PM Simon Jakobi via Libraries
> <libraries at haskell.org> wrote:
> >
> > Dear Henning,
> >
> > I've re-read your email now and thought about it a bit more.
> >
> > > 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.
> >
> > Personally, I find nothing strange about (max (1,0) (0,1) == (1,0)),
> > but I started wondering how other languages handle these examples. I
> > tried Python:
> >
> > $ python3
> > Python 3.5.2 (default, Apr 16 2020, 17:47:17)
> > [GCC 5.4.0 20160609] on linux
> > Type "help", "copyright", "credits" or "license" for more information.
> > >>> max((1,0),(0,1))
> > (1, 0)
> > >>> complex(1,0) > complex(0,1)
> > Traceback (most recent call last):
> >   File "<stdin>", line 1, in <module>
> > TypeError: unorderable types: complex() > complex()
> >
> > I also find the Ord Maybe instance quite intuitive: "Nothing is less
> > than something (Just)"
> >
> > It is also consistent with the interpretation of Maybe as a list of at
> > most one element:
> >
> > $ ghci
> > > [] < [()]
> > True
> >
> > So in my view the Bounded Maybe instance still seems like a good idea.
> >
> > Cheers,
> > Simon
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