[Haskell-cafe] Sum and Product do not respect the Monoid laws

[Noon Silk]

> for equational laws to be sensible requires a sensible notion of
equality,
> the Eq for Floating point numbers is

could it not be then that for floating points to be a monoid you must
specify a satisfying notion of equality? (well, i guess nothing is stopping
anyone from doing that themselves; and your point is that simply not having
floats as a monoid is somehow "bad"?)



On Sat, Sep 27, 2014 at 5:41 AM, Carter Schonwald <
carter.schonwald at gmail.com> wrote:

> for equational laws to be sensible requires a sensible notion of equality,
> the Eq for Floating point numbers is
> meant for handling corner cases (eg: am i about to divide by zero), not
> "semantic/denotational equivalence"
>
> Exact equality is fundamentally incorrect for finite precision
> mathematical computation.
> You typically want to have something like
>
> nearlyEq  tolerance a b = if distance a b <= tolerance then True else False
>
> Floating point is geometry, not exact things
> https://hackage.haskell.org/package/ieee754-0.7.3/docs/Data-AEq.html
> is a package that provides an approx equality notion.
>
> Basically, floating points work the way they do because its a compromise
> that works decently for those who really need it.
> If you dont need to use floating point, dont! :)
>
>
>
> On Fri, Sep 26, 2014 at 9:28 AM, Jason Choy <jjwchoy at gmail.com> wrote:
>
>> subject to certain caveats.  It's not unfair to say that
>>> floating point multiplication is (nearly) associative
>>> "within a few ulp".
>>>
>>
>> I'm not disputing this.
>>
>> However, you can't deny that this monoid law is broken for the floating
>> point operations:
>>
>> mappend x (mappend y z) = mappend (mappend x y) z
>>
>> Perhaps I'm being pedantic, but this law should hold for all x, y, z, and
>> it clearly doesn't.
>>
>
>
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-- 
Noon Silk, ن

https://sites.google.com/site/noonsilk/

"Every morning when I wake up, I experience an exquisite joy — the joy
of being this signature."
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