[Haskell-cafe] Thoughts about redesigning "Num" type class

[Carter Schonwald]

I have this deep worry that any changes to num hierarchy that aren't first
demonstrated in userland.  This is perhaps me being a little bit of a
curmudgeon.  I just feel like it's a complicated topic that needs lots of
concrete example experiments to really pin down what's what.

Additionally, most of the proposals over time  seem to a) have some latent
form of abstraction blindness with respect to some notion of
parametrization that we can't even name / describe with Haskell
(Which is actually something I'm starting to think about, though often
passing around records of functions is good enough, ignoring the question
of performance implications)

B) there's usually a whole bunch of different computable realizations of
how to Manipulate a given mathematical object, which when exposed as apis
hsve wildly different performance characteristics and ease of use

An example of (a) is we can't really talk about a family of type classes
which are parametrized over the names of their methods. (We spend so much
time jumping through that hoop when relating ring and group structures!

An example of the latter (b) would be any model of integration / measurable
functions. We as humans are still learning on that front. Witness the huge
amount of work (still nascent) in probabilistic programming, which is
essentially about "what is an efficient and usable way to talk about
integrating over interesting things"

On Saturday, September 12, 2015, Jerzy Karczmarczuk <
jerzy.karczmarczuk at unicaen.fr> wrote:

>
> Le 12/09/2015 14:39, Olaf Klinke a écrit :
>
>> semirings might be a useful typeclass to have. Another example:
>> Non-negative reals with infinity, the values that a measure can take.
>>
> Could you mention, please, a system whose measures are for sure positive
> reals, infinity included?
> Perhaps your definition of "measure"should be precised...
> Thanks.
>
> Jerzy Karczmarczuk
>
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