[Haskell-cafe] Foldable for (,)

[Chris Smith]

I'm also interested in Jonathon's question, so let me try to bring things
back to the question.  Everyone agrees that there's only one reasonable way
to define this instance if it exists.  But the question is: why is it
defined at all?

That's an easy question to answer for Functor, Applicative, and Monad.  But
I am having trouble giving a simple or accessible answer for Foldable.  Do
you know one?

On Wed, May 3, 2017 at 1:32 AM, Tony Morris <tonymorris at gmail.com> wrote:

> It's Foldable for ((,) a).
>
> It is not Foldable for any of these things:
>
> * (,)
> * tuples
> * pairs
>
> In fact, to talk about a Foldable for (,) or "tuples" is itself a kind
> error. There is no good English name for the type constructor ((,) a)
> which I suspect, along with being unfamiliar with utilising the
> practical purpose of types (and types of types) is the root cause of all
> the confusion in this discussion.
>
> Ask yourself what the length of this value is:
>
> [[1,2,3], [4,5,6]]
>
> Is it 6? What about this one:
>
> [(1, 'a'), (undefined, 77)]
>
> Is it 4? No, obviously not, which we can determine by:
>
> :kind Foldable :: (* -> *) -> Constraint
> :kind [] :: * -> *
>
> Therefore, there is no possible way that the Foldable instance for []
> can inspect the elements (and determine that they are pairs in this
> case). By this method, we conclude that the length of the value is 2. It
> cannot be anything else, some assumptions about length itself put aside.
>
> By this ubiquitous and very practical method of reasoning, the length of
> any ((,) a) is not only one, but very obviously so.
>
> On 03/05/17 17:21, Jonathon Delgado wrote:
> > I sent the following post to the Beginners list a couple of weeks ago
> (which failed to furnish an actual concrete example that answered the
> question). Upon request I'm reposting it to Café:
> >
> > I've seen many threads, including the one going on now, about why we
> need to have:
> >
> > length (2,3) = 1
> > product (2,3) = 3
> > sum (2,3) = 3
> > or (True,False) = False
> >
> > but the justifications all go over my head. Is there a beginner-friendly
> explanation for why such seemingly unintuitive operations should be allowed
> by default?
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