Is inspectable recursion in Arrows possible?

Dear all,

I am trying to find a way to translate normal recursive notation such
as the |fib| function below to an arrow, retaining as much of the
structure of the recursive notation as possible. In addition I would
like to inspect the arrow. For this I created a datatype containing a
constructor for each Arrow{..} class:

Fib:
> fib 0 = 0
> fib 1 = 1
> fib n = fib (n-2) + fib (n-1)

My R datatype, the instances for this datatype consist of the mapping
to the appropriate constructor:

> data R x y where
>   -- Category
>   Id       :: R a a
>   Comp     :: R b c    -> R a b          -> R a c
>   -- Arrow
>   Arr      :: (a -> b) -> R a b
>   Split    :: R b c    -> R b' c'        -> R (b,b') (c,c')
>   Cache    :: (a -> a -> Bool) -> R a a
>   -- ArrowChoice
>   Choice   :: R b c -> R b' c' -> R (Either b b') (Either c c')
>   -- ArrowLoop
>   Loop     :: R (b, d) (c, d)  -> R b c
>   -- ArrowApply
>   Apply    :: R (R b c, b) c