New subject: Container type classes

30 May 2019

      Thanks again Iavor,

Despite the type inference issue, and the fact that this requires a separate type class, this is the best solution I've seen so far.

Cheers,
Andrey

-----Original Message-----
From: Iavor Diatchki [mailto:iavor.diatchki@gmail.com] 
Sent: 30 May 2019 23:16
To: Andrey Mokhov 
Cc: Brandon Allbery ; Andreas Klebinger ; ghc-devs@haskell.org
Subject: Re: Container type classes

Yeah, there is really no relation between the two parameters of `Fun`,
so you'd have to specify the intermediate type manually. For example:

add3 :: forall s. (Fun s s, Elem s ~ Int) => s -> s
add3 = colMap @s (+1) . colMap (+2)

I wouldn't say that it's a particularly convenient interface to work
with, unless you are working in a setting where most of the containers
have known types.

On Thu, May 30, 2019 at 2:58 PM Andrey Mokhov
 wrote:
...
Many thanks Iavor,
This looks very promising! I played with your encoding a little, but quickly came across type inference issues. The following doesn't compile:
add3 :: (Fun s s, Elem s ~ Int) => s -> s
add3 = colMap (+1) . colMap (+2)
I'm getting:
* Could not deduce: Elem a0 ~ Int
      from the context: (Fun s s, Elem s ~ Int)
        bound by the type signature for:
                   add3 :: forall s. (Fun s s, Elem s ~ Int) => s -> s
      Expected type: Elem a0 -> Elem s
        Actual type: Int -> Int
      The type variable `a0' is ambiguous
Fun s s is supposed to say that the intermediate type is `s` too, but I guess this is not how type class resolution works.
Cheers,
Andrey
-----Original Message-----
From: Iavor Diatchki [mailto:iavor.diatchki@gmail.com]
Sent: 30 May 2019 22:38
To: Brandon Allbery 
Cc: Andrey Mokhov ; Andreas Klebinger ; ghc-devs@haskell.org
Subject: Re: Container type classes
This is how you could define `map`.  This is just for fun, and to
discuss Haskell idioms---I am not suggesting we should do it.  Of
course, it might be a bit more general than what you'd like---for
example it allows defining instances like `Fun IntSet (Set Int)` that,
perhaps?, you'd like to disallow:
{-# LANGUAGE MultiParamTypeClasses, TypeFamilies #-}
import Data.Set (Set)
import qualified Data.Set as Set
import Data.IntSet (IntSet)
import qualified Data.IntSet as ISet
class Col t where
  type Elem t
  -- ... As in Andreas's example
class (Col a, Col b) => Fun a b where
  colMap :: (Elem a -> Elem b) -> a -> b
instance Col (Set a) where
  type Elem (Set a) = a
instance Col IntSet where
  type Elem IntSet = Int
instance Fun IntSet IntSet where
  colMap = ISet.map
instance Ord b => Fun (Set a) (Set b) where
  colMap = Set.map
On Thu, May 30, 2019 at 2:32 PM Brandon Allbery  wrote:
...
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  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@gmail.com]
Sent: 30 May 2019 20:56
To: Andrey Mokhov 
Cc: ghc-devs@haskell.org; Andreas Klebinger 
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  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@gmail.com
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RE: Container type classes

Andrey Mokhov

Clinton Mead

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