This is not just about map, but it also a problem for the Monoid instance. You
are basically adding an extra identity element, 0, to the max monoid, which
works but is weird. You'll have to call norm everywhere to make it work, f.e.
you would expect this to work:
empty' = insert () $ delete () empty
but:
empty' <> delete () empty == empty'
while:
empty <> delete () empty == delete () empty
(I couldn't test it as I don't have base 4.5, so I hope I didn't make a mistake
here.)
greetings,
Sjoerd
On Apr 23, 2012, at 2:07 PM, Stefan Holdermans wrote:
> Sjoerd,
>
>>>>> For a specific example, I haven't the faintest intuition about
>>>>> what 'map' should do. Suppose we have
>>>>> {(k1)x1, (k2)x2}
>>>>> and f x1 == f x2 = y. Should the value of map f {...} be
>>>>> {(k1+k2)y} or {(k1`max`k2)y} or what?
>
>> I don't think max would be a good choice, as that would mean that the
>> default multiplicity would have to be negative infinity (the identity
>> element of max) instead of 0, and then using Int as the type for
>> multiplicity would not cut it.
>
> Why would one need such an identity element for map?
>
> Note that the monoidal structure isn't defined over the "maximum of
> multiplicites" but over the "maximum of *nonzero* multiplicites". (For
> ordinary sets and ordinary multisets these operations happen to coincide.)
>
> Cheers,
>
> Stefan
>
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