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

Sure; you just let any computation either finish with a result, or suspend itself, giving an action to be used on resume, along with the state at the time:

data Pause s a = Pause { runPause :: s -> (PauseResult s a, s) }

data PauseResult s a
    = Done a
    | Suspend (Pause s a)

instance Monad (Pause s) where
    return a = Pause (\s -> (Done a, s))
    m >>= k = Pause $ \s ->
        case runPause m s of
            (Done a, s') -> runPause (k a) s'
            (Suspend m', s') -> (Suspend (m' >>= k), s')

get :: Pause s s
get = Pause (\s -> (Done s, s))

put :: s -> Pause s ()
put s = Pause (\_ -> (Done (), s))

yield :: Pause s ()
yield = Pause (\s -> (Suspend (return ()), s))

step :: Pause s () -> s -> (Maybe (Pause s ()), s)
step m s =
    case runPause m s of
        (Done _, s') -> (Nothing, s')
        (Suspend m', s') -> (Just m', s')

The Monad instance just sequences things in the normal way, passing the final result to the k continuation, or adding the rest of the computation to be done on suspension.