[Haskell-cafe] Existential question
Tom Schouten
tom at zwizwa.be
Sun Aug 21 12:22:03 CEST 2011
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
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