Container type classes

Andrey Mokhov andrey.mokhov at
Thu May 30 21:36:50 UTC 2019

Hi Brandon,

Could you show the code?

I have no idea how indexed monads could possibly be related here. All I want is to have a type class that unifies these two methods:

singleton :: a -> Set a
map :: Ord b => (a -> b) -> Set a -> Set b

singleton :: Int -> IntSet
map :: (Int -> Int) -> IntSet -> IntSet


From: Brandon Allbery [mailto:allbery.b at]
Sent: 30 May 2019 22:32
To: Andrey Mokhov <andrey.mokhov at>
Cc: Artem Pelenitsyn <a.pelenitsyn at>; Andreas Klebinger <klebinger.andreas at>; ghc-devs at
Subject: Re: Container type classes

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<mailto:andrey.mokhov at>> 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*


From: Artem Pelenitsyn [mailto:a.pelenitsyn at<mailto:a.pelenitsyn at>]
Sent: 30 May 2019 20:56
To: Andrey Mokhov <andrey.mokhov at<mailto:andrey.mokhov at>>
Cc: ghc-devs at<mailto:ghc-devs at>; Andreas Klebinger <klebinger.andreas at<mailto:klebinger.andreas at>>
Subject: Re: Container type classes

Hi Andrey,

FWIW, 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,

On Thu, 30 May 2019 at 20:11, Andrey Mokhov <andrey.mokhov at<mailto:andrey.mokhov at>> 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 =

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.


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