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 <w...@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<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<http://www.haskell.org/mailman/listinfo/haskell-cafe> >
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