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MonadCont done right

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The Cont class [[MonadCont]] [http://haskell.org/hawiki/MonadCont] defined in the [[monad template library]] [http://haskell.org/hawiki/MonadTemplateLibrary] could be improved if you are willing to use [[rank two polymorphism]] [http://haskell.org/hawiki/RankTwoPolymorphism].
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The Cont class [[MonadCont]] [http://www.haskell.org/ghc/docs/latest/html/libraries/mtl/Control-Monad-Cont-Class.html] defined in the [[monad template library]] [http://en.wikibooks.org/wiki/Haskell/Monad_transformers#Transformers_are_cousins] could be improved if you are willing to use [[rank two polymorphism]] [http://en.wikibooks.org/wiki/Haskell/Polymorphism#Higher_rank_types].
 
Notice the change in the signature of <hask>callCC</hask>. This allows one to use the passed continuation in different situations inside a <hask>callCC</hask> block. However, you will have to provide an explicit signature for the function you are calling <hask>callCC</hask> with.
 
Notice the change in the signature of <hask>callCC</hask>. This allows one to use the passed continuation in different situations inside a <hask>callCC</hask> block. However, you will have to provide an explicit signature for the function you are calling <hask>callCC</hask> with.
   
== Possible Implementation ==
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== Possible implementation ==
   
 
<haskell>
 
<haskell>
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</haskell>
 
</haskell>
   
== Alternative Implementation ==
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== Alternative implementation ==
 
This implementation has the advantage that it provides a polymorphic version of <hask>callCC</hask> for all instances of MonadCont from <hask>Control.Monad.Cont</hask>. I also added <hask>shift</hask> and <hask>reset</hask> functions for using ComposableContinuations.
 
This implementation has the advantage that it provides a polymorphic version of <hask>callCC</hask> for all instances of MonadCont from <hask>Control.Monad.Cont</hask>. I also added <hask>shift</hask> and <hask>reset</hask> functions for using ComposableContinuations.
   

Latest revision as of 21:27, 6 December 2008

The Cont class MonadCont [1] defined in the monad template library [2] could be improved if you are willing to use rank two polymorphism [3].

Notice the change in the signature of
callCC
. This allows one to use the passed continuation in different situations inside a
callCC
block. However, you will have to provide an explicit signature for the function you are calling
callCC
with.

[edit] 1 Possible implementation

newtype Cont r a = Cont { runCont :: ((a -> r) -> r) } -- r is the final result type of the whole computation
 
class (Monad m) => MonadCont m where
    callCC :: ((a -> (forall b. m b)) -> m a) -> m a
 
instance Monad (Cont r) where
    return a = Cont (\k -> k a)                             -- i.e. return a = \k -> k a
    (Cont c) >>= f = Cont (\k -> c (\a -> runCont (f a) k)) -- i.e. c >>= f = \k -> c (\a -> f a k)
 
instance MonadCont (Cont r) where
    callCC f = Cont (\k -> runCont (f (\a -> Cont (\_ -> k a))) k)

[edit] 2 Alternative implementation

This implementation has the advantage that it provides a polymorphic version of
callCC
for all instances of MonadCont from
Control.Monad.Cont
. I also added
shift
and
reset
functions for using ComposableContinuations.
{-# OPTIONS -fglasgow-exts -fno-warn-unused-binds -cpp #-}
module ContExts (
    callCC',
    shift, reset, shiftT, resetT,
  ) where
 
import Control.Monad.Cont
 
-- Cont' m a is the type of a continuation expecting an a within the 
-- continuation monad Cont m
type Cont' m a = forall r. a -> m r
 
callCC' :: forall a m. MonadCont m => (Cont' m a -> m a) -> m a
#if __GLASGOW_HASKELL__ > 602
callCC' f = callCC f' where
#else
callCC' (f :: ((a -> (forall b. m b)) -> m a) ) = callCC f' where
#endif
  f' :: (a -> m (EmptyMonad m)) -> m a
  f' g = f g' where
    g' :: a -> m b
    g' = (=<<) runEmptyMonad . g
 
-- ghc doesn't allow something like m (forall c. m c)
newtype EmptyMonad m = EmptyMonad { runEmptyMonad :: forall c. m c }
 
-- shift/reset for the Cont monad
shift :: ((a -> Cont s r) -> Cont r r) -> Cont r a
shift e = Cont $ \k -> e (return . k) `runCont` id
 
reset :: Cont a a -> Cont r a 
reset e = return $ e `runCont` id
 
-- shiftT/resetT for the ContT monad transformer
shiftT :: Monad m => ((a -> ContT r m s) -> ContT s m s) -> ContT s m a
shiftT e = ContT $ \k -> e (lift . k) `runContT` return
 
resetT :: Monad m => ContT a m a -> ContT r m a
resetT e = lift $ e `runContT` return

All of this is presumably meant to be under the MIT license, since it wants to be in the library. --SamB 22:44, 30 October 2006 (UTC)