You are right, but I was using "extraction" in a rather non-technical sense. Look at it this way: we have 'x >>= f', let's assume it's the continuation monad. Assuming f has type 'a -> C b' we must have something of type a to be able to call the function be at all. Somehow >>= is able make sure that f is called (modulo non- termination), so I still claim it "extracts" an 'a'. It's not a value that >>= will actually ever get its hands on, it only manages to make sure its passed to f. So somewhere there is an 'a' lurking, or f could not be called. Perhaps you don't want to call that "extraction", and that's fine by me. :) -- Lennart On Sep 3, 2006, at 12:32 , Daniel Fischer wrote:
Am Sonntag, 3. September 2006 15:39 schrieb Lennart Augustsson:
Well, bind is extracting an 'a'. I clearly see a '\ a -> ...'; it getting an 'a' so it can give that to g. Granted, the extraction is very convoluted, but it's there.
-- Lennart
But
instance Monad (Cont r) where return = flip id (>>=) = (. flip) . (.) -- or would you prefer (>>=) = (.) (flip (.) flip) (.) ?
if we write it points-free. No '\a -> ...' around. And, being more serious, I don't think, bind is extracting an 'a' from m. How could it? m does not produce a value of type a, like a (State f) does (if provided with an initial state), nor does it contain values of type a, like [] or Maybe maybe do. And to my eyes it looks rather as though the '\a -> ...' tells us that we do _not_ get an 'a' out of m, it specifies to which function we will eventually apply m, namely 'flip g k'. But I've never really understood the Continuation Monad, so if I'm dead wrong, would you kindly correct me?
And if anybody knows a nontrivial but not too advanced example which could help understanding CPS, I'd be glad to hear of it.
Cheers, Daniel
On Sep 2, 2006, at 19:44 , Udo Stenzel wrote:
Benjamin Franksen wrote:
Sure. Your definition of bind (>>=): ... applies f to something that it has extracted from m, via deconstructor unpack, namely a. Thus, your bind implementation must know how to produce an a from its first argument m.
I still have no idea what you're driving at, but could you explain how the CPS monad 'extracts' a value from something that's missing something that's missing a value (if that makes sense at all)?
For reference (newtype constructor elided for clarity):
type Cont r a = (a -> r) -> r
instance Monad (Cont r) where return a = \k -> k a m >>= g = \k -> m (\a -> g a k)
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