bob zhang wrote:
I thought the right type for ContT should be newtype ContT m a = ContT {runContT :: forall r. (a-> m r) -> m r} and other control operators shift :: Monad m => (forall r . (a-> ContT m r) -> ContT m r) -> ContT m a reset :: Monad m => ContT m a -> ContT m a callCC :: ((a-> (forall r . ContT m r)) -> ContT m a) -> ContT m a unfortunately, I can not make callCC type check, and don't know how to do it.
Precisely that problem was discussed in http://okmij.org/ftp/continuations/undelimited.html#proper-contM Your ContT is CPS1 in the above article. The article shows why you cannot write callCC with the above type of ContT. The article talks about other types. BTW, if you faithfully defined the monad for undelimited control than shift/reset cannot be expressed. Undelimited continuations are strictly less expressible than delimited ones. The above page gives the pointers to the papers with the proof.