[Haskell-cafe] Higher order functor package?

[Ivan Lazar Miljenovic]

On 7 July 2017 at 14:48, 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?

The type signature of myFmap looks a bit like that for hoist:
http://hackage.haskell.org/package/mmorph-1.1.0/docs/Control-Monad-Morph.html#v:hoist

-- 
Ivan Lazar Miljenovic
Ivan.Miljenovic at gmail.com
http://IvanMiljenovic.wordpress.com