[Haskell-cafe] Higher order functor package?

[Rein Henrichs]

I recommend posting this question to StackOverflow and hoping that Conor
McBride notices it.

On Fri, Jul 7, 2017 at 11:46 AM Clinton Mead <clintonmead at gmail.com> wrote:

> Hi Erik and All
>
> I don't think "indexed-core" is what I'm looking for. "indexed-code"
> refers to the following type:
>
> > (a :->
> <http://hackage.haskell.org/package/index-core-1.0.4/docs/Control-Category-Index.html#t::-45--62-> b)
> -> f a :->
> <http://hackage.haskell.org/package/index-core-1.0.4/docs/Control-Category-Index.html#t::-45--62-> f
> b
>
> Where:
>
> > type (:->) a b = forall i. a i -> b i
>
> This effectively makes the result of the functor:
>
> > (forall i1. (a i1 -> b i1)) -> (forall i2. (f a i2 -> f b i2))
>
> But what I want is subtly different:
>
> > (forall i. (a i -> b i)) -> f a -> f b
>
> Indeed, with my code, "f a i" doesn't make much sense as "f a" itself is
> of type *.
>
> What I'd find useful is something like the following:
>
> > class HighFunctor f where
> >   hfmap :: (forall a. t a -> u a) -> f t -> f u
> >
> > class HighFunctor2 f where
> >   hfmap2 :: (forall a. t a -> u a -> v a) -> f t -> f u -> f v
> >
> > class HighFunctorMaybe f where
> >   hfmapMaybe :: (forall a. Maybe (t a) -> u a) -> Maybe (f t) -> f u
> >
> > class HighFunctor2Maybe1 f where
> >   hfmap2maybe1 :: (forall a. Maybe (t a) -> u a -> v a) -> Maybe (f t)
> -> f u -> f v
> >
> > class HighFunctor2Maybe2 f where
> >   hfmap2maybe2 :: (forall a. t a -> Maybe (u a) -> v a) -> f t -> Maybe
> (f u) -> f v
> >
> > class HighFunctor2MaybeBoth f where
> >   hfmap2maybeBoth :: (forall a. Maybe (t a) -> Maybe (u a) -> v a) ->
> Maybe (f t) -> Maybe (f u) -> f v
>
> As you can see. I'm basically hacking up with separate classes what can be
> done easily with applicative, and it's getting a bit messy. I've been
> trying to clean this up, so I don't need so many different functions for
> different combinations of maybes, by defining these helper functions:
>
> > data Transform outerT innerT a = Transform (outerT (innerT a))
> >
> > transformIn :: outerT (f innerT) -> f (Transform outerT innerT)
> >
> > transformOut :: Transform outerT innerT a -> outerT (innerT a)
> > transformOut (Transform x) = x
>
> By applying "transformIn" to an argument on the way in to hfmapN, and
> "transformOut" on the way out, one can pass through maybes to the standard
> top to non-maybe "HighFunctor" instances.
>
> But note that whilst "transformOut" is always trivial to implement, the
> way in, "transformIn" doesn't seem trivial. "transformIn" I think has to be
> implemented for each combination of "outerT" and "f", like so:
>
> > class TransformIn outerT f where
> >   f :: outerT (f innerT) -> f (Transform outerT innerT)
>
> Anyway, the point of all this is that I'd like to be able to just launch
> my base functions (over the "forall i" space) into these higher level
> datatypes that wrap the foralls up in a datatype, in a similar way I can do
> so with functor and applicative.
>
> I think the code in the first post is the best illustration of what I'm
> trying to achieve but with two added things:
>
> 1. The ability to deal with multiple arguments in an applicative style <$>
> <*> way
> 2. The ability to promote "wrapped" types, I think kind of in a way
> "traversable" does.
>
> Sorry if this all is a bit vague, but hopefully the code in the first post
> and this gives the gist of what I'm trying to achieve.
>
> Any help or ideas appreciated.
>
> Thanks,
>
> Clinton
>
> On Fri, Jul 7, 2017 at 4:40 PM, Erik Hesselink <hesselink at gmail.com>
> wrote:
>
>> I think the keyword you're looking for might be 'indexed', although that
>> also seems to be used for something different (two indices for pre and post
>> conditions). Your functor seems to be in 'index-core' [0], and probably
>> other places (it seems there was something in category-extras but it's
>> unclear where it went).
>>
>> Regards,
>>
>> Erik
>>
>> [0]
>> http://hackage.haskell.org/package/index-core-1.0.4/docs/Control-IMonad-Core.html
>>
>> On 7 July 2017 at 06:48, Clinton Mead <clintonmead at gmail.com> wrote:
>>
>>> Consider the illustrative code below:
>>>
>>>
>>> {-# LANGUAGE GADTs #-}
>>> {-# LANGUAGE DataKinds #-}
>>> {-# LANGUAGE KindSignatures #-}
>>> {-# LANGUAGE RankNTypes #-}
>>> {-# LANGUAGE PolyKinds #-}
>>> {-# LANGUAGE StandaloneDeriving #-}
>>> {-# LANGUAGE UndecidableInstances #-}
>>>
>>> data Param = Param1 | Param2
>>>
>>> data T (p :: Param) where
>>>   TInt :: Int -> T Param1
>>>   TInteger :: Integer -> T Param1
>>>   TBool :: Bool -> T Param2
>>>
>>> data U (p :: Param) where
>>>   UDouble :: Double -> U Param1
>>>   UString :: String -> U Param2
>>>
>>> data F (t :: Param -> *) where
>>>   F :: t Param1 -> t Param2 -> F t
>>>
>>> f :: T a -> U a
>>> f (TInt x) = UDouble (fromIntegral x)
>>> f (TInteger x) = UDouble (fromIntegral x)
>>> f (TBool x) = UString (show x)
>>>
>>> class MyFunctor f where
>>>   myFmap :: (forall a. t a -> u a) -> f t -> f u
>>>
>>> instance MyFunctor F where
>>>   myFmap f (F x1 x2) = F (f x1) (f x2)
>>>
>>> deriving instance Show (U a)
>>> deriving instance (Show (t Param1), Show (t Param2)) => Show (F t)
>>>
>>> main = print $ myFmap f (F (TInt 42) (TBool False))
>>>
>>>
>>> Basically this is a sort of "higher order" functor, but I can't seem to
>>> fit it into an ordinary functor.
>>>
>>> But it seems like I'm reinventing the wheel, as my code is suspiciously
>>> like `Functor` but only slightly different.
>>>
>>> Has this sort of class already been created and if so what package is it
>>> in?
>>>
>>>
>>>
>>> _______________________________________________
>>> 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.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.haskell.org/pipermail/haskell-cafe/attachments/20170707/b2a244a0/attachment.html>