[Haskell-cafe] Functor in terms of Arrow

[Peter Gammie]

Tom,

On 19/02/2012, at 3:21 AM, Tom Schouten wrote:

> Does AFunctor below have a standard name?  It's a generalization of
> the Functor class in terms of Arrow instead of (->):
> 
>      fmap  :: Functor f           => (i -> o) -> f i  ->  f o
>      afmap :: Arrow a, AFunctor f => a i o    -> a (f i) (f o)
> 
> It pops up in less general form (AFunctor = []) in iterated functions
> (difference equations / state space models), where the arrow is the
> update function parameterized by state type:
> 
>  data Iter s i o = Iter ((s,i) -> (s,o))
>  instance Arrow (Iter s)

I think you can work with Arrow transformers instead. See:

http://hackage.haskell.org/packages/archive/arrows/latest/doc/html/Control-Arrow-Transformer-Stream.html#t:StreamArrow

It may be that you can generalise to arbitrary functors, but satisfying the Arrow laws may require some care.

cheers
peter

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