Proposal: add a foldable law

[Gershom B]

As per: https://wiki.haskell.org/Core_Libraries_Committee emailing
libraries@ should suffice. But in the case it doesn’t, I’m now ccing the
committee alias directly as well.

The law you suggested does not seem to be generally stronger than mine, but
I would be interested in a counterexample if you can produce one[1]. I
agree that “strange GADTy instances” are not ruled out, but I’m not sure if
I’d consider it a limitation of Foldable, but more a characteristic of
GADTs that isn’t per-se wrong, although it sometimes is counterintuitive :-)

Best,
Gershom

[1] If one is to be found, one would think it’d have to do with GADTs. But
I think GADTs are flexible enough that one could still provide an injection
from a GADT without traversable GADT with traversable such that whatever
weird stuff occurs in the former still occurs in the latter.

On May 5, 2018 at 6:23:04 PM, David Feuer (david.feuer at gmail.com) wrote:

You'll have to email the committee if you want them to consider anything.
The law I suggested is rather stronger than yours, but I think it's
probably closer to what you really meant. Neither option prevents strange
GADTy instances, but I suspect that's a fundamental limitation of Foldable.

On Sat, May 5, 2018, 6:13 PM Gershom B <gershomb at gmail.com> wrote:

> Hmm… I think this works, and specifies the same law. Nice. Assuming I’m
> not wrong about that, I’m happy with either version, and will leave it to
> the committee to decide.
>
> Best,
> Gershom
>
> On May 5, 2018 at 5:18:29 PM, David Feuer (david.feuer at gmail.com) wrote:
>
> Let me take that back. Injectivity is necessary. And I meant
>
>     foldMap @t f = foldMapDefault f . toTrav
>
> On Sat, May 5, 2018, 5:11 PM David Feuer <david.feuer at gmail.com> wrote:
>
>> Actually, requiring injectivity shouldn't be necessary.
>>
>> On Sat, May 5, 2018, 5:09 PM David Feuer <david.feuer at gmail.com> wrote:
>>
>>> I have another idea that might be worth considering. I think it's a lot
>>> simpler than yours.
>>>
>>> Law: If t is a Foldable instance, then there must exist:
>>>
>>> 1. A Traversable instance u and
>>> 2. An injective function
>>>        toTrav :: t a -> u a
>>>
>>> Such that
>>>
>>>     foldMap @t = foldMapDefault . toTrav
>>>
>>> I'm pretty sure this gets at the point you're trying to make.
>>>
>>>
>>> On May 3, 2018 11:58 AM, "Gershom B" <gershomb at gmail.com> wrote:
>>>
>>> This came up before (see the prior thread):
>>> https://mail.haskell.org/pipermail/libraries/2015-February/024943.html
>>>
>>> The thread at that time grew rather large, and only at the end did I
>>> come up with what I continue to think is a satisfactory formulation of
>>> the law.
>>>
>>> However, at that point nobody really acted to do anything about it.
>>>
>>> I would like to _formally request that the core libraries committee
>>> review_ the final version of the law as proposed, for addition to
>>> Foldable documentation:
>>>
>>> ==
>>> Given a fresh newtype GenericSet = GenericSet Integer deriving (Eq,
>>> Ord), where GenericSet is otherwise fully abstract:
>>>
>>> forall (g :: forall a. f a -> Maybe a), (x :: f GenericSet).
>>> maybe True (`Foldable.elem` x) (g x) =/= False
>>> ==
>>>
>>> The intuition is: "there is no general way to get an `a` out of `f a`
>>> which cannot be seen by the `Foldable` instance". The use of
>>> `GenericSet` is to handle the case of GADTs, since even parametric
>>> polymorphic functions on them may at given _already known_ types have
>>> specific behaviors.
>>>
>>> This law also works over infinite structures.
>>>
>>> It rules out "obviously wrong" instances and accepts all the instances
>>> we want to that I am aware of.
>>>
>>> My specific motivation for raising this again is that I am rather
>>> tired of people saying "well, Foldable has no laws, and it is in base,
>>> so things without laws are just fine." Foldable does a have a law we
>>> all know to obey. It just has been rather tricky to state. The above
>>> provides a decent way to state it. So we should state it.
>>>
>>> Cheers,
>>> Gershom
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>>>
>>>
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