MINIMAL XOR (Was: Proposal: Make Eq type class single method)

[David Feuer]

NULL is not like NaN. It's perfectly sensible to stick `NULL` in a `Set` or
something.

On Wed, Oct 27, 2021, 8:09 PM Keith <keith.wygant at gmail.com> wrote:

> For what it's worth, Haskell says that NaN is `GT` NaN. So maybe it would
> also claim than NULL is `GT` NULL.
>
> (NaN is not `==` to NaN, and is not `<=` to NaN, so it must be GT.)
> —
> Sent from my phone with K-9 Mail.
>
>
> On 27 October 2021 15:32:40 UTC, Viktor Dukhovni <ietf-dane at dukhovni.org>
> wrote:
>>
>> On Wed, Oct 27, 2021 at 11:14:45AM -0400, Carter Schonwald wrote:
>>
>>> not necessarily ... there could be  contradictory sets of methods! :)
>>>
>>> like the minimal sets for Field type class,  the xor would be for defining
>>> '/' in terms of reciprocal and times or vice versa (/ vs recip) and
>>> likewise (negate vs minus) etc etc
>>>
>>
>> Logically redundant definitions aren't always redundant in practice if
>> one considers performance, floating point accuracy or even sometimes
>> divergence.
>>
>>       For example, foldl on infinite snoc lists is not definable in
>>       terms of foldr which diverges, though admittedly I rather think
>>       that infinite snoc lists violate all reasonable expectations of
>>       a Foldable instance.
>>
>> So in many cases redundancy warnings would not be viable.  The Eq
>> situation is likely more the exception that the rule.
>>
>> The SQL NULL instances that are False for both "==" and "/=" look
>> like they could be a mistake to me, but presumably they work out
>> OK in practice, and I would expect that e.g. the relevant `Ord`
>> instances do return `EQ` for `compare Null Null`...  Less clear
>> is whether the non-lawful Eq defintion is in some predicably useful
>> way essential.
>>
>> --
>>     Viktor.
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