[Haskell-cafe] Monad laws

[Brandon Allbery]

On Sun, Jun 29, 2014 at 12:15 AM, Mike Meyer <mwm at mired.org> wrote:

> On Sat, Jun 28, 2014 at 10:52 PM, Brandon Allbery <allbery.b at gmail.com>
> wrote:
>
>> I imagine that, like Ord, a decision was made to implement the proper
>> mathematical abstraction and not merely a convenient one. This seems to be
>> the "Haskell way". (I'm not sure how it explains Double, though the numeric
>> hierarchy has a lot of compromises in the name of convenience or expected
>> behavior. Possibly Monad was in some sense a reaction to this, even: "we
>> got that one wrong, let's do this one correctly".)
>>
>
> Double, like Int, is a computer construct, not a mathematical one.  They
> both map to hardware types that act like mathematical ones until you look
> closely, but have better performance than the software constructs that have
> better behavior.
>

Sure, but that doesn't change the fact that IEEE754 NaN in particular means
there is no total ordering.

-- 
brandon s allbery kf8nh                               sine nomine associates
allbery.b at gmail.com                                  ballbery at sinenomine.net
unix, openafs, kerberos, infrastructure, xmonad        http://sinenomine.net
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