Benjamin Franksen
martin wrote:
I am trying to understand the ideas of Koen Klaessen, published in Functional Pearls: "A poor man's concurrency" (1993).
[...]
m >>= k = \f -> m (\x -> k x f)
If you re-add the newtype wrapping and unwrapping, this is exactly the same as your definition above.
This is one answer to the question of how one can arrive at a suitable definition of >>= for the continuation monad. But it does not tell us anything about how to arrive at an intuition about what this implementation really does. Maybe someone else can explain this...
Values of `Cont a` are functions in continuation-passing style. That is, they are functions that hand their results to a continuation passing function, instead of returning. I think the trickiness of this stuff has more to do with continuation-passing style in general and less to do with any inherent abstruseness of monadic bind. With some CPS familiarity, you can see that `m` is just a function that accepts a continuation, and `k` is a function that accepts the intermediate result and the next continuation. We know that our new CPS function is going to accept a continuation argument. We also know -- by the semantics of CPS -- that this continuation will be handed to `k`. So this CPS function \f -> m (\x -> k x f) says: given a continuation `f`, invoke `m` with a continuation that hands the intermediate result to `k` with the continuation `f`. You can see how a chain like (given the actual Monad instance) do x <- m1 y <- m2 x m3 y will expand into a CPS function that passes along the continuation such that `m3` is finally invoked with the continuation of the entire block. And then, the presence of the Monad constraint just makes it obvious that this can be used as a monad transformer. -- Mikael Brockman mikael@silk.co