Arrow Classes

27 Jun 2003

      In article <200306271927.36405.wolfgang@jeltsch.net>,
 Wolfgang Jeltsch  wrote:
...
This brings me to another point. One year ago we had a discussion on The 
Haskell Mailing List concerning arrows. (The subject of the mails was just 
"arrows".) The point was that it seemed strange to me that first and second 
are included in the basic arrow class Arrow while left and right have their 
extra class ArrowChoice. Not only that it seemed strange to me but it made it 
impossible to make Parser baseMonad an instance of Arrow. Parser baseMonad 
has nice implementations of pure and (>>>) but none of first or second.
I agree. My own Arrow module hierarchy looks more or less like this:

  class Compositor comp where
    identity :: comp a a
    compose :: comp b c -> comp a b -> comp a c

  class (Compositor arrow) => Arrow arrow where
    arrFunction :: (p -> q) -> arrow p q

  -- | corresponds to Hughes\' \'Arrow\'
  class (Arrow arrow) => ProductArrow arrow where
    arrApply :: arrow p (q -> r) -> arrow p q -> arrow p r
    arrProduct :: arrow p q -> arrow p r -> arrow p (q,r)
    arrProduct = liftA2 (,)

  class (Arrow arrow) => CoproductArrow arrow where
    arrCoproduct :: arrow p r -> arrow q r -> arrow (Either p q) r

  -- | corresponds to Hughes\' \'ArrowChoice\'
  class (ProductArrow arrow,CoproductArrow arrow) => FullArrow arrow
  instance (ProductArrow arrow,CoproductArrow arrow) => FullArrow arrow

  class (Arrow arrow) => ArrowFix arrow where
    arrFix :: arrow (p,q) q -> arrow p q

  class (FullArrow arrow) => ApplyArrow arrow where
    arrApplyArrow :: arrow (arrow p q,p) q

Note the symmetry between ProductArrow and CoproductArrow.

See 
<http://cvs.sourceforge.net/cgi-bin/viewcvs.cgi/*checkout*/hbase/Source/H
Base/Category/Arrow.hs?rev=HEAD&content-type=text/plain> for all the 
details.

-- 
Ashley Yakeley, Seattle WA