Traversable instance for ((,) o) ?

[Ben Millwood]

Yeah, I noticed this the other day, and a couple of other instances
which aren't defined, but could be:

http://hpaste.org/56005

I won't pretend I have much use for the Const instance, but it seems
like it should be there anyway, just for completeness (I think it's
possible to define Traversable instances for compositions of functors,
possibly sums and products as well, so Const could be useful in that
context). I think the Either one makes sense, though, as a natural
analogue of the Maybe instance.

On Tue, Jan 3, 2012 at 11:41 PM, Conal Elliott <conal at conal.net> wrote:
> Thanks much for the answers, Conor. They all make sense to me, particularly
> about the typical information discarding in Foldable.
>
> Regards, - Conal
>
>
> On Tue, Jan 3, 2012 at 3:30 PM, Conor McBride <conor at strictlypositive.org>
> wrote:
>>
>>
>> On 3 Jan 2012, at 23:12, Conal Elliott wrote:
>>
>>> I wanted a Traversable instance for pairing, so I defined one:
>>> > instance Traversable ((,) o) where
>>> >   sequenceA (o,fa) = (o,) <$> fa
>>
>>
>> That looks right. Of course, we should really have a BiTraversable
>> class of which (,) is an instance.
>>
>>
>>>
>>> However, Foldable is a superclass of Traversable, so I get an error
>>> message:
>>>
>>>    Could not deduce (Foldable ((,) o)) from the context ()
>>>      arising from the superclasses of an instance declaration
>>>
>>> The best I've thought of is the following:
>>>
>>> > instance Foldable ((,) o) where
>>> >   fold (_,m) = m
>>
>>
>> The best (upto efficiency considerations) is always
>>
>>
>>  instance Foldable ((,) o) where
>>    foldMap = foldMapDefault
>>
>> which amounts to what you chose.
>>
>> SHE makes this a default superclass instance.
>>
>>
>>> However, I don't like how it discards information.
>>
>>
>> But these folds always do discard information, discarding the shape
>> information and accumulating over the contents. For ((,) o), seen as
>> a functor, the first component is shape information and the second is
>> the content.
>>
>>
>>> Some questions:
>>>
>>> * Why is Foldable a superclass of Traversable?
>>
>>
>> Because the constant-monoid Applicative makes every Traversable
>> Foldable in a uniform way.
>>
>>
>>> * Is there a good choice of a Foldable instance of ((,) o)?
>>
>>
>> Yes, the one you chose.
>>
>>
>>> * Are there any other problems with the Traversable instance above
>>> (besides foldability)?
>>
>>
>> Nope. It's the Traversable instance which picks out exactly the
>> contents that correspond to the elements abstracted by the Functor.
>>
>> All the best
>>
>> Conor
>>
>
>
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