Container type classes

[Brandon Allbery]

They can, with more work. You want indexed monads, so you can describe
types that have e.g. an ordering constraint as well as the Monad constraint.

On Thu, May 30, 2019 at 5:26 PM Andrey Mokhov <andrey.mokhov at newcastle.ac.uk>
wrote:

> Hi Artem,
>
>
>
> Thanks for the pointer, but this doesn’t seem to be a solution to my
> challenge: they simply give up on overloading `map` for both Set and
> IntSet. As a result, we can’t write polymorphic functions over Set and
> IntSet if they involve any mapping.
>
>
>
> I looked at the prototype by Andreas Klebinger, and it doesn’t include the
> method `setMap` either.
>
>
>
> Perhaps, Haskell’s type classes just can’t cope with this problem.
>
>
>
> *ducks for cover*
>
>
>
> Cheers,
>
> Andrey
>
>
>
> *From:* Artem Pelenitsyn [mailto:a.pelenitsyn at gmail.com]
> *Sent:* 30 May 2019 20:56
> *To:* Andrey Mokhov <andrey.mokhov at newcastle.ac.uk>
> *Cc:* ghc-devs at haskell.org; Andreas Klebinger <klebinger.andreas at gmx.at>
> *Subject:* Re: Container type classes
>
>
>
> Hi Andrey,
>
>
>
> FWIW, mono-traversable (
> http://hackage.haskell.org/package/mono-traversable) suggests decoupling
> IsSet and Funtor-like.
>
>
>
> In a nutshell, they define the IsSet class (in Data.Containers) with
> typical set operations like member and singleton, union and intersection.
> And then they tackle a (seemingly) independent problem of mapping
> monomorphic containers (like IntSet, ByteString, etc.) with a separate
> class MonoFunctor (in Data.MonoTraversable):
>
>
>
> class MonoFunctor mono where
>     omap :: (Element mono -> Element mono) -> mono -> mono
>
>
>
> And gazillion of instances for both polymorphic containers with a fixed
> type parameter and monomorphic ones.
>
>
>
> --
>
> Best wishes,
>
> Artem
>
>
>
> On Thu, 30 May 2019 at 20:11, Andrey Mokhov <andrey.mokhov at newcastle.ac.uk>
> wrote:
>
> Hi all,
>
> I tried to use type classes for unifying APIs of several similar data
> structures and it didn't work well. (In my case I was working with graphs,
> instead of sets or maps.)
>
> First, you rarely want to be polymorphic over the set representation,
> because you care about performance. You really want to use that
> Very.Special.Set.insert because it has the right performance
> characteristics for your task at hand. I found only *one* use-case for
> writing polymorphic functions operating on something like IsSet: the
> testsuite. Of course, it is very nice to write a single property test like
>
> memberInsertProperty x set = (member x (insert x set) == True)
>
> and then use it for testing all set data structures that implement
> `member` and `insert`. Here you don't care about performance, only about
> correctness!
>
> However, this approach leads to problems with type inference, confusing
> error messages, and complexity. I found that it is much nicer to use
> explicit dictionary passing and write something like this instead:
>
> memberInsertProperty SetAPI{..} x set = (member x (insert x set) == True)
>
> where `member` and `insert` come from the SetAPI record via
> RecordWildCards.
>
> Finally, I'm not even sure how to create a type class covering Set and
> IntSet with the following two methods:
>
> singleton :: a -> Set a
> map :: Ord b => (a -> b) -> Set a -> Set b
>
> singleton :: Int -> IntSet
> map :: (Int -> Int) -> IntSet -> IntSet
>
> Could anyone please enlighten me about the right way to abstract over this
> using type classes?
>
> I tried a few approaches, for example:
>
> class IsSet s where
>     type Elem s
>     singleton :: Elem s -> s
>     map :: Ord (Elem t) => (Elem s -> Elem t) -> s -> t
>
> Looks nice, but I can't define the IntSet instance:
>
> instance IsSet IntSet where
>     type Elem IntSet = Int
>     singleton = IntSet.singleton
>     map = IntSet.map
>
> This fails with: Couldn't match type `t' with `IntSet' -- and indeed, how
> do I tell the compiler that in the IntSet case s ~ t in the map signature?
> Shall I add more associated types, or "associated constraints" using
> ConstraintKinds? I tried and failed, at various stages, repeatedly.
>
> ...And then you discover that there is Set.cartesianProduct :: Set a ->
> Set b -> Set (a, b), but no equivalent in IntSet and things get even more
> grim.
>
> Cheers,
> Andrey
>
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-- 
brandon s allbery kf8nh
allbery.b at gmail.com
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