Add a createT analogue for arrays

[David Feuer]

Oh, there's actually a much nicer way to write runArraysContextHet,
using runArraysHet:

  newtype S f g t = S {unS :: f t (g t)}

  newtype CS t u a = CS {unCS :: t (S u a)}

  instance (HTraversable t, Traversable' u) => HTraversable (CS t u) where
    htraverse f = fmap CS . htraverse (fmap S . traverse' f . unS) . unCS

  runArraysContextHet
    :: (HTraversable t, Traversable' u)
    => (forall s. ST s (t (S u (MutableArray s))))
    -> t (S u Array)
  runArraysContextHet m = unCS $ runArraysHet (CS <$> m)

So it seems that runArraysHet is powerful enough.

On Fri, Mar 23, 2018 at 12:19 AM, David Feuer <david.feuer at gmail.com> wrote:
> I still think this is a good idea, and probably the furthest it should
> go in the array package proper, but something about it has been
> bothering me: the fact that I can't produce multiple arrays of
> different types. I realized it's actually possible to get that too,
> using something similar to the rtraverse function in vinyl.
>
>   class HTraversable (t :: (k -> Type) -> Type) where
>     htraverse :: Applicative h
>               => (forall x. f x -> h (g x))
>               -> t f -> h (t g)
>
> Vinyl records themselves are a bit backwards for this purpose, but one
> could write
>
>     newtype FlipRec ts f = FlipRec {unFlipRec :: Rec f ts}
>     instance HTraversable (FlipRec ts) where
>       htraverse f (FlipRec xs) = FlipRec <$> rtraverse f xs
>
> Anyway, HTraversable lets us write
>
>     runArraysHet :: HTraversable t
>                  => (forall s. ST s (t (MutableArray s)))
>                  -> t Array
>     runArraysHet m = runST $ m >>= htraverse unsafeFreezeArray
>
> which can produce arrays of multiple types in one go. We can add some
> extra information/context to each array with a little more machinery:
>
>   -- The context will be expressed using Traversable' types
>   class Traversable' (t :: k -> Type -> Type) where
>     traverse' :: Applicative f
>               => (a -> f b) -> t x a -> f (t x b)
>     default traverse' :: (Applicative f, Traversable (t x))
>                       => (a -> f b) -> t x a -> f (t x b)
>     traverse' = traverse
>
>   -- examples
>   instance Traversable' Either
>   instance Traversable' (,)
>
>   newtype S f g t = S {unS :: f t (g t)}
>   newtype Contextify (f :: k -> Type -> Type) (t :: (k -> Type) ->
> Type) (g :: k -> Type) =
>     Contextify {unContextify :: t (S f g)}
>
>   instance (HTraversable t, Traversable' u)
>     => HTraversable (Contextify (u :: k -> Type -> Type) (t :: (k ->
> Type) -> Type)) where
>     htraverse f t = fmap Contextify $ htraverse (fmap S . traverse' f
> . unS) (unContextify t)
>
> and finally
>
>   runArraysContextHet
>     :: (HTraversable t, Traversable' u)
>     => (forall s. ST s (t (S u (MutableArray s))))
>     -> t (S u Array)
>   runArraysContextHet m =
>     runST $ m >>= htraverse (fmap S . traverse' unsafeFreezeArray . unS)
>
> Whew!
>
> On Sun, Mar 11, 2018 at 1:29 AM, David Feuer <david.feuer at gmail.com> wrote:
>> The vector package offers
>>
>> createT :: Traversable t
>>   => (forall s. ST s (t (MVector s a)))
>>   -> t (Vector a)
>>
>> This is a generalization of create, which is very similar to runSTArray in
>> the array package. I suggest we add functions
>>
>> runSTArrays :: Traversable t
>>   => (forall s. ST s (t (STArray s i e)))
>>   -> t (Array i e)
>>
>> runSTUArrays :: Traversable t
>>   => (forall s. ST s (t (STUArray s i e)))
>>   -> t (UArray i e)
>>
>> Why do I think it's worth the trouble? While it's occasionally useful to
>> create multiple arrays of the same type in one go, I think the Maybe and
>> (a,) Traversable instances, and their compositions, are likely more
>> important. I can use (a,) to record some extra information while building an
>> array. I can use Maybe to give up and not produce an array. And the
>> compositions let me do both in different ways.