martin
Let's forget about this particular monad for a while and focus on intuition in general.
I managed to dissect the continuation monad and write the bind operator correctly. But it took me hours and the train of thought is very elusive. I wouldn't call this "understanding".
When I truly understand things I can come up with analogies, counter examples and the like. I can draw diagrams to visualize the thing. I can embed the new thing into a world of old things.
But I cannot do any of these things with the Continuation Monad. Right now I am trying to get there by staring at it, asking myself questions, trying to write bind in different ways - hoping that one day it will click.
So I wonder what you guys do to develop intuition about tricky haskell things, such as the Continuation monad.
Bind can often be a bit tricky. I usually find it easier to define bind as:
x >>= f = join (fmap f x)
Then ignore it and focus on fmap and join instead. This is a 'divide and conquer' approach.
fmap :: (Functor f) => (a -> b) -> f a -> f b
This is the usual Functor method. We can ignore all the monadic stuff when defining it, which makes our life easier. With fmap defined, we can turn "f :: a -> m b" and "x :: m a" into "fmap f x :: m (m b)"
join :: (Monad m) => m (m a) -> m a
This needs to turn two nested monadic "wrappers" into one, using some logic specific to our monad. I find this easier to think about than bind since we're now only dealing with one argument. Cheers, Chris