Arrow Notation - Command combinators don't work with higher rank types? (GHC 7.4)

[Ross Paterson]

On Sun, Jan 15, 2012 at 11:42:28AM +0000, Ben Moseley wrote:
> The real application is trying to process a structure containing GADTs - something more like this:
> 
> {-# LANGUAGE GADTs,Arrows,Rank2Types #-}
> import Control.Arrow
> 
> data G a where
>     G1 :: Int -> G Char
>     G2 :: Int -> G Bool
> 
> -- mapcomb :: Arrow a => (a (env,G x) (G x)) -> a (env,(G b,G c)) (G b,G c)
> -- mapcomb _aegg = proc (_env,bc) -> returnA -< bc
> 
> process :: Int -> G x -> G x
> process i (G1 n) = G1 $ succ n
> process i (G2 n) = G2 $ succ n
> 
> processA :: Arrow a => a (Int,G x) (G x)
> processA = proc (i,gx) -> returnA -< process i gx
> 
> mapcomb :: Arrow a => (forall x . a (env,G x) (G x)) -> a (env,(G b,G c)) (G b,G c)
> mapcomb aegg = proc (env,(g1,g2)) -> do
>                  g1' <- aegg -< (env,g1)
>                  g2' <- aegg -< (env,g2)
>                  returnA -< (g1',g2')
> 
> myarr :: Arrow a => a Int Bool
> myarr = proc i -> do
>           (|mapcomb (\g -> processA -< (i,g)) |) (G1 3,G2 3)
>           -- (| (mapcomb (processA <<^ (\(_,g)->(7,g)) )) |) (G1 3,G2 3)
>           returnA -< False
> 
> I guess to do this it'll be necessary to plumb 'i' through manually (changing the type of 'mapcomb') ?

In this particular case you could give mapcomb two arguments:

mapcomb :: Arrow a => a (env,G b) (G b) -> a (env,G c) (G c) -> a (env,(G b,G c)) (G b,G c)

and pass processA twice, but that wouldn't work in general (with an
unlimited number of variants).