SAFE: a Foldable proposal

[Kris Nuttycombe]

On Thu, Feb 25, 2016 at 4:47 AM, Thomas Tuegel <ttuegel at gmail.com> wrote:

>
> Foldable implies a notion of structural direction through the
> associativity of
> its members. Set is different from the well-behaved Foldables because its
> notion
> of direction or order is not structural, i.e. not preserved by operations
> on
> Set.
>
>
This is the first argument that I've seen in this whole messy thread that
actually rings true for me - the fact that foldability is intricately tied
to the ordering of elements is a very important one given that all that
Monoid gives us is associativity and therefore any operation that we apply
across a data structure that is *not* strictly ordered can have
unpredictable results. Thank you very much for pointing this out.
Converting from a Map or a Set to an ordered data structure before folding
is obviously the principled thing to do - with Map in particular, the fact
that the ordering of the keys is completely unrelated to the ordering of
the values means that any non-commutative operation being applied across
those values with foldMap is essentially a roll of the dice. This is
troubling and something that should be corrected.

This brings me to a question that I've often had but never asked, which is,
where are all the typeclasses for operations which demand commutativity? In
particular, CommutativeApplicative is a typeclass that I've longed for; a
peer to Monad that represents parallelizable rather than sequential
effectful operations.

Kris
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