type class Boolean

[David Feuer]

I imagine you'd want (&&) and (||) to live in a Lattice class,
`bottom` and `top` in `BoundedBelow` and `BoundedAbove`, respectively,
and `not` in a `Boolean` one. The relationship between Lattice,
JoinSemilattice, and MeetSemilattice is unfortunately awkward (much
like that between Ring, AbelianGroup, and Monoid), but mumble mumble
something.

On Mon, Dec 21, 2020 at 6:32 PM Tikhon Jelvis <tikhon at jelv.is> wrote:
>
> For me, the most useful kind of instance would be symbolic booleans like SBV's SBool type.
>
> A real bonus would be making if-then-else polymorphic as well—although that doesn't really fit with the lattice abstraction. I know we can do that with RebindableSyntax, but that is a *heavyweight* extension to enable!
>
> Breaking boolean behavior up into a few different classes would work for this application. Boolean algebras for and/not/etc, Conditional for ifThenElse and maybe even Boolish or something for True and False pattern synonyms (or just true and false constants).
>
> I don't think all of this belongs in base, but making booleans and boolean operators more polymorphic would definitely be useful.
>
> On Mon, Dec 21, 2020 at 3:21 PM Ben Franksen <ben.franksen at online.de> wrote:
>>
>> Am 21.12.20 um 19:54 schrieb Tom Ellis:
>> > I think it's worth seeing more instances. As it is I don't understand
>> > in what situations one would use these polymorphically and therefore
>> > why `liftA2 (&&)`, `fmap not`, `pure True` and friends wouldn't
>> > suffice.
>>
>> As with all overloading it's partly a matter of convenience. For
>> instance you can't use 'liftA2 (&&)' as an operator. And your list of
>> alternatives above demonstrates that one has to remember which lifting
>> operator (pure, fmap, liftA2) to use, depending on arity.
>>
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