The Pause monad

Question

Monads can do many amazing, crazy things. They can create variables which hold a superposition of values. They can allow you to access data from the future before you comput

Answer 1

Doesn't match your type signatures exactly, but certainly simple:

{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances #-}
import Control.Monad.State

newtype ContinuableT m a = Continuable { runContinuable :: m (Either a (ContinuableT m a)) }
instance Monad m => Monad (ContinuableT m) where
    return = Continuable . return . Left
    Continuable m >>= f = Continuable $ do
        v <- m
        case v of
            Left  a -> runContinuable (f a)
            Right b -> return (Right (b >>= f))

instance MonadTrans ContinuableT where
    lift m = Continuable (liftM Left m)

instance MonadState s m => MonadState s (ContinuableT m) where
    get = lift get
    put = lift . put

yield :: Monad m => ContinuableT m a -> ContinuableT m a
yield = Continuable . return . Right

step :: ContinuableT (State s) a -> s -> (Either a (ContinuableT (State s) a), s)
step = runState . runContinuable

-- mutate unnecessary, just use modify