[Haskell-cafe] Existential question

[Tom Schouten]

On 08/21/2011 05:33 AM, Felipe Almeida Lessa wrote:
> On Sat, Aug 20, 2011 at 6:26 PM, Tom Schouten<tom at zwizwa.be>  wrote:
>> data Kl i o = forall s. Kl s (i ->    s ->    (s, o))
>>
>> This is an Arrow.  At first I wondered if there was also an associated
>> Monad, hence the iso function.
> Given
>
>    data Kl i o = forall s. Kl s (i ->    s ->    (s, o))
>
>    instance ArrrowApply KI where
>      ...
>
> then 'ArrowMonad KI' [1] is a monad isomorphic to
>
>    data KIM o = forall s. KIM s (s ->  (s, o))
>
> Is this what you are looking for?
>
Yes, but I run into the same problem.


data Kl i o = forall s. Kl (i -> s -> (s, o))

-- OK
instance Category Kl where
   id = Kl $ \ i () -> ((), i)
   (.) (Kl u2) (Kl u1) = (Kl u12) where
     u12 a (s1, s2) = ((s1',s2'), c) where
       (s1', b) = u1 a s1
       (s2', c) = u2 b s2

-- OK
instance Arrow Kl where
   arr f = Kl $ \i () -> ((), f i)
   first (Kl u) = (Kl u') where
     u' (i, x) s = (s', (o, x)) where
       (s', o) = u i s

-- Can't make this work.  The problem seems to be the same as before:
-- there's no way to require that the hidden types of both Kl
-- constructors are the same.
instance ArrowApply Kl where
   app = Kl $ \((Kl f), a) -> f a