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)?
Another encoding of Maybe is through Yoneda Endo
Interesting. I did not yet encounter Yoneda in my own code but will watch out in the future. Sebastian -- Underestimating the novelty of the future is a time-honored tradition. (D.G.)