[Haskell-cafe] Trouble using State Monad.

[Brent Yorgey]

On Sat, Oct 08, 2011 at 04:28:34PM -0700, Captain Freako wrote:
> Hi all,
> 
> I'm trying to use the State Monad to help implement a digital
> filter:

(a -> EitherT e (State FilterState) a) is definitely not monadic.
There is an 'a' in a negative position (to the left of an odd number
of arrows) so it is not even a Functor.  But I think you want to have
the 'a ->' part separate.

I might do something like

  newtype FilterM e a = F { unFilterM :: EitherT e (State FilterState) a }
    deriving (Functor, Applicative, Monad, MonadState FilterState)

  type Filter e a b = a -> FilterM e b

That is, a Filter is a function from a to b, which can abort with an
error of type e and maintains a FilterState.  Then you can chain
Filters using (>=>): if

  f1 :: Filter e a b
  f2 :: Filter e b c

then

  f1 >=> f2 :: Filter e a c

is a Filter which does first f1 then f2.  Alternatively, if you wanted
to use an Arrow interface you could define

  import Control.Arrow

  type Filter e a b = Kleisli (FilterM e) a b

-Brent