[Haskell-cafe] Foldable for (,)

Wed May 3 14:38:06 UTC 2017

Traversable instances (for "singletons" or not) can be implemented
_uniformly_ using Functor and Foldable instances.
And they are implemented in such way when you derive Traversable. So we
need Foldable constraint for the class.

E.g.
{-# LANGUAGE DeriveFunctor, DeriveFoldable,DeriveTraversable #-}
> data D a = D { f1 :: [a], f2 :: (String, a) } deriving (Show, Eq,
Functor, Foldable, Traversable)
> sum $ D [1..3] ("test",4)
10
> mapM_ print $ sequenceA $ D [[1,2],[3,4]] ("test",[5,6])
D {f1 = [1,3], f2 = ("test",5)}
D {f1 = [1,3], f2 = ("test",6)}
D {f1 = [1,4], f2 = ("test",5)}
D {f1 = [1,4], f2 = ("test",6)}
D {f1 = [2,3], f2 = ("test",5)}
D {f1 = [2,3], f2 = ("test",6)}
D {f1 = [2,4], f2 = ("test",5)}
D {f1 = [2,4], f2 = ("test",6)}

2017-05-03 14:34 GMT+03:00 Jonathon Delgado <voldermort at hotmail.com>:

> Interesting, that's not the one linked to from Dmitry's code.
>
> In any case, is this correct?
>
> 1) Traversable is useful for all containers, including ones which can only
> hold a single value, such as (,) a.
> 2) The traversable definition for containers which can hold multiple
> versions requires Foldable.
> 3) So Traversable has to depend on Foldable.
> 4) So singleton containers also have to implement Foldable, even when it
> doesn't really make sense to do so.
>
> Is there some kind of refactoring which would "fix" this, other than two
> unrelated Traversable classes? I understand that it might be impractical to
> refactor a widely-used standard library, but I would be interested in how
> such a situation could be avoided when starting from scratch.
>
>
>
> From: Haskell-Cafe <haskell-cafe-bounces at haskell.org> on behalf of Tony
> Morris <tonymorris at gmail.com>
> Sent: 03 May 2017 11:21
> To: haskell-cafe at haskell.org
> Subject: Re: [Haskell-cafe] Foldable for (,)
>
> https://i.imgur.com/A2enuhq.png
>
>
> On 03/05/17 21:17, Jonathon Delgado wrote:
> > List.foldr has signature (a -> b -> b) -> b -> [a] -> b, i.e. an actual
> list? How is this effected by the Foldable constraint?
> >
> >
> >
> > From: Dmitry Olshansky <olshanskydr at gmail.com>
> > Sent: 03 May 2017 10:47
> > To: Jonathon Delgado
> > Cc: haskell-cafe at haskell.org
> > Subject: Re: [Haskell-cafe] Foldable for (,)
> >
> >
> >
> > Look how instance for List is defined.
> >
> > instance Traversable [] where     {-# INLINE traverse #-} -- so that
> traverse can fuse     traverse f = List.foldr cons_f (pure [])       where
> cons_f x ys = (:) <$> f x <*> ys It uses List.foldr. Many other instances
> do the same.
> > Functions in all instances of class should have the same signatures. So
> we have to add Foldable constraint to the class.
> > Of cause we can implement 'foldr' internaly in 'traverse' if needed (as
> well as fmap).
> > But this is not so good and more important that in this case we don't
> know how to derive Traversable instances automatically.
> >
> > So the answer - many instances wouldn't compile and DeriveTraversable
> wouldn't work.
> >
> >
> >
> > 2017-05-03 12:56 GMT+03:00 Jonathon Delgado  <voldermort at hotmail.com>:
> >  OK, I understand why Traversable is useful here - thank you Chris and
> Dmitry!
> >
> > The next question is why Traversable requires Foldable. I looked at the
> source, and couldn't see where Foldable is being used, other than as a
> constraint on Traversable. To put the question differently, what would fail
> to compile if this constraint was removed?
> >
> >
> >
> > From: Dmitry Olshansky <olshanskydr at gmail.com>
> > Sent: 03 May 2017 09:53
> > To: Jonathon Delgado
> >
> >
> > Cc: haskell-cafe at haskell.org
> > Subject: Re: [Haskell-cafe] Foldable for (,)
> >
> >
> >
> >
> >
> > With fmap you can only change all values in some "container".
> >
> >  With Foldable you can "fold" it, i.e. calculate some "scalar" result.
> >
> >  With Traversable you can "change order of two containers":
> >> sequenceA [[1,2,3],[4,5]]
> > [[1,4],[1,5],[2,4],[2,5],[3,4],[3,5]]
> >> sequenceA ("test",[2,3,4])
> > [("test",2),("test",3),("test",4)]
> >> sequenceA ("test",([1,2,3],[4,5,6]))
> > ([1,2,3],("test",[4,5,6]))
> >
> >
> >
> >
> >
> > 2017-05-03 12:12 GMT+03:00 Jonathon Delgado  <voldermort at hotmail.com>:
> >  Why do you want to traverse a tuple instead of fmap? i.e. what can you
> do with Foldable/Traversable for (,) that you can't do with Functor?
> >
> > My background, as you can probably guess, is beginner.
> >
> >
> > From: Haskell-Cafe <haskell-cafe-bounces at haskell.org> on behalf of
> Chris Smith <cdsmith at gmail.com>
> > Sent: 03 May 2017 08:51
> > To: Tony Morris
> > Cc: haskell-cafe at haskell.org
> > Subject: Re: [Haskell-cafe] Foldable for (,)
> >
> >
> >
> >
> > Replying to myself, I suppose one good answer is that whether or not you
> care about Foldable instances for tuples, you might care about Traversable
> instances, and those require Foldable as a superclass.
> >
> >
> > For example, one possible specialization of `traverse` is:
> >
> >
> >     traverse :: (a -> IO b) -> (SideValue, a) -> IO (SideValue, b)
> >
> >
> > Jonathon, I don't know how much background you're coming from, so I'd be
> happy to explain that in more detail if you need it.
> >
> >
> > On Wed, May 3, 2017 at 1:44 AM, Chris Smith  <cdsmith at gmail.com> wrote:
> >
> > 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?
> >> _______________________________________________
> >> Haskell-Cafe mailing list
> >> To (un)subscribe, modify options or view archives go to:
> >>     http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
>
>
> Haskell-Cafe Info Page
> mail.haskell.org
> This mailing list is for the discussion of topics related to Haskell. The
> volume may at times be high, as the scope is broader than the main Haskell
> mailing list.
>
> >> Only members subscribed via the mailman list are allowed to post.
> >
> >
> > _______________________________________________
> > Haskell-Cafe mailing list
> > To (un)subscribe, modify options or view archives go to:
> > http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
>
>
> Haskell-Cafe Info Page
> mail.haskell.org
> This mailing list is for the discussion of topics related to Haskell. The
> volume may at times be high, as the scope is broader than the main Haskell
> mailing list.
>
> > Only members subscribed via the mailman list are allowed to post.
> >
> >
> >
> > _______________________________________________
> > Haskell-Cafe mailing list
> > To (un)subscribe, modify options or view archives go to:
> > http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
> > Only members subscribed via the mailman list are allowed to post.
> >
> > _______________________________________________
> > Haskell-Cafe mailing list
> > To (un)subscribe, modify options or view archives go to:
> > http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
> > Only members subscribed via the mailman list are allowed to post.
> >
> > _______________________________________________
> > Haskell-Cafe mailing list
> > To (un)subscribe, modify options or view archives go to:
> > http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
> > Only members subscribed via the mailman list are allowed to post.
>
>
> https://i.imgur.com/A2enuhq.png
>
> _______________________________________________
> Haskell-Cafe mailing list
> To (un)subscribe, modify options or view archives go to:
> http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe
> Only members subscribed via the mailman list are allowed to post.
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.haskell.org/pipermail/haskell-cafe/attachments/20170503/79d05887/attachment.html>