Thanks Wren. That was my guess too, but it seems not necessary: http://stackoverflow.com/questions/12103309/when-is-a-composition-of-catamorphisms-a-catamorphism

On Sat, Aug 25, 2012 at 10:33 PM, wren ng thornton <wren@freegeek.org> wrote:
On 8/24/12 3:44 AM, Sebastien Zany wrote:
More specifically (assuming I understood the statement correctly):

Suppose I have two base functors F1 and F2 and folds for each: fold1 :: (F1
a -> a) -> (μF1 -> a) and fold2 :: (F2 a -> a) -> (μF2 -> a).

Now suppose I have two algebras f :: F1 μF2 -> μF2 and g :: F2 A -> A.

When is the composition (fold2 g) . (fold1 f) :: μF1 -> A a catamorphism?

>From <http://comonad.com/haskell/catamorphisms.html> we have the law:

    Given
        F, a functor
        G, a functor
        e, a natural transformation from F to G
            (i.e., e :: forall a. F a -> G a)
        g, a G-algebra
            (i.e., f :: G X -> X, for some fixed X)

    it follows that

        cata g . cata (In . e) = cata (g . e)

The proof of which is easy. So it's sufficient to be a catamorphism if your f = In . e for some e. I don't recall off-hand whether that's necessary, though it seems likely

--
Live well,
~wren

_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe