[Haskell-cafe] Partially-applied type synonyms?

[Lyle Kopnicky]

Chung-chieh,

Well, I tried what you suggested, and it seems to work.  Unfortunately, 
it's not very useful.  The point of creating MonadPCont, was, like 
MonadCont or MonadState, to automatically provide features to a monad 
built from a transformer, without having to redefine them.  Since ContT 
is the monad transformer, I want any monad created from it to 
automatically support the MonadPCont operations.  But they can't, 
because I can't make ContT an instance of MonadPCont.

I can make FlipContT an instance of MonadPCont, but I can't make 
FlipContT a monad transformer.  So what you have to do is create your 
layered monadwith ContT on top, and then apply the FlipCont constructor 
to get a monad with the methods of MonadPCont.  Now since FlipContT 
isn't a monad transformer, you can't lift things into it.  You can lift 
them into ContT and then write a wrapper around that.

My point is that, unfortunately,  I don't think it's very practical to 
create this type class.  I think the problem is that, although MonadCont 
attempts to describe a monad as having certain operations, MonadPCont 
attempts to describe a group of related monads as having certain 
operations.  They are related by being formed from the same type 
constructor.

Here's the modified code:

module MonadPCont where

import Control.Monad
import Control.Monad.Cont
import Control.Monad.Trans
import Control.Monad.Reader
import Control.Monad.Writer
import Control.Monad.State
import Control.Monad.RWS 

class (Monad (mc a), Monad (mc r)) => MonadPCont mc a r where
    shift :: ((forall b. Monad (mc b) => a -> mc b r) -> mc r r) -> mc r a
    reset :: mc a a -> mc r a

instance MonadPCont Cont a r where
    shift f = Cont (\c -> runCont (f (\x -> Cont (\c' -> c' (c x)))) id)
    reset m = Cont (\c -> c (runCont m id))

data FlipContT m r a = FlipContT { unFlipContT :: (ContT r m a)}

instance Monad m => Monad (FlipContT m r) where
    return x = FlipContT $ return x
    (FlipContT m') >>= f = FlipContT $ m' >>= (unFlipContT . f)

runFlipContT :: FlipContT m r a -> (a -> m r) -> m r
runFlipContT (FlipContT m) = runContT m
                      
instance Monad m => MonadPCont (FlipContT m) a r where
    shift f = FlipContT $ ContT $ \c ->
                runFlipContT (f (\x -> FlipContT $ ContT $ \c' -> c x 
 >>= c'))
                             return
    reset m = FlipContT $ ContT $ \c -> runFlipContT m return >>= c

- Lyle

Chung-chieh Shan wrote:

>On 2004-08-31T09:55:10-0700, Lyle Kopnicky wrote:
>  
>
>>Sorry, I don't think I made myself clear.  I'm not defining PI, it's the 
>>standard type binding operator, like lambda is the variable binding 
>>operator.  Maybe I could write it as 'II' so it looks more like a 
>>capital pi.  It's not a feature of Haskell, but part of type theory 
>>(dependent types).  I was mixing and matching and making it look like 
>>Haskell.  So instead of 'PI r -> ContT r m', I could write 'flip ContT', 
>>except that 'flip' needs to work on a type level instead of a value 
>>level.  Or I could write '(`ContT` m)', or 'ContT _ m', where the '_' is 
>>a hole.  Does this make sense now?
>>    
>>
>
>Yes, it makes sense now.  You need to define
>
>    newtype FlipContT m r a = FlipContT (ContT r m a)
>
>or more generally,
>
>    newtype Flip c (m :: * -> *) r a = Flip (c r m a)
>
>The rationale for disallowing matching partially-applied type synonyms
>is that higher-order unification is undecidable.
>
>See also:
>
>Neubauer, Matthias, and Peter Thiemann. 2002.  Type classes with
>more higher-order polymorphism.  In ICFP '02: Proceedings of the ACM
>international conference on functional programming. New York: ACM Press.
>http://www.informatik.uni-freiburg.de/~neubauer/papers/icfp02.pdf
>http://www.informatik.uni-freiburg.de/~neubauer/papers/icfp02.ps.gz
>
>  
>