[Haskell-cafe] Re: Re: A free monad theorem?
lennart at augustsson.net
Mon Sep 4 01:44:28 EDT 2006
You are right, but I was using "extraction" in a rather non-technical
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
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
> 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
> '\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.
>> 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
>>>> unpack, namely a. Thus, your bind implementation must know how to
>>>> 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
>>> 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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