On Fri, Jun 18, 2010 at 12:44 PM, Heinrich Apfelmus
Sebastian Fischer wrote:
Edward Kmett wrote:
Sebastian Fischer wrote:
Heinrich Apfelmus wrote: newtype CMaybe a = CMaybe (forall r. (a -> Maybe r) -> Maybe r) Yes, with this type `orElse` has the same type as `mplus`, which is very nice.
This type is the same as "Codensity Maybe" using category-extras which is a 'bit bigger than Maybe'. (To see why, figure out how Codensity Reader is isomorphic to State!) This is the wiggle room you're using to get the distributive operator.
I encounter the Codensity type constructor every now and then. I used it to Reinvent Haskell Backtracking, learned about implementing a state monad with a reader monad wrapped in Codensity when implementing Lazy Nondeterministic Programming and Janis Voigtländer also used it to improve the asymptotics of free monads.
I wonder whether for every monad `m` and `a :: Codensity m a`
getCodensity a f = getCodensity a return >>= f
Is this true? Why (not)?
It's not true.
a = Codensity $ \x -> Just 42 f = return . (+1)
getCodensity a f = Just 42 ≠ getCodensity a return >>= f = Just 42 >>= f = Just 43
What definition are you using for Codensity? Under the definition I'm
familiar with, that definition of a is invalid.
newtype Codensity m a = Codensity { runCodensity :: forall b. (a -> m
b) -> m b }
Which is not to say that you can't come up with improper values of
Codensity. E.g.,
Codensity (\k -> k () >> k ())
\m -> Codensity (\k -> k () >>= \b -> m >> return b)
--
Dave Menendez