[Haskell-cafe] Re: Different choice operations in a continuation monad

[Sebastian Fischer]

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.)