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

[Edward Kmett]

On Wed, Jun 16, 2010 at 9:11 AM, Sebastian Fischer <
sebf at informatik.uni-kiel.de> wrote:

>
> Heinrich Apfelmus wrote:
>
>  Sebastian Fischer wrote:
>>
>>> I still don't understand why it is impossible to provide `orElse` with
>>> the original type. I will think more about the reason you gave.
>>>
>>
>> The reason is that you have chosen the "wrong" type for your
>> continuation monad; it should be
>>
>>  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.

Another encoding of Maybe is through Yoneda Endo

newtype YEMaybe a = YEMaybe (forall r. (a -> r) -> r -> r)

and it is isomorphic to the original Maybe type, with its same limitations.
A definition that is equivalent to this is in my monad-ran package, along
with definitions CPS/right-kan-extension-based definitions for other common
monads, including the MTL, IO, ST s, and STM.

-Edward Kmett
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