hello, ergh, its been a while since i looked at that paper, but basically for functors with +ve and -ve recursion, the cata(fold) and ana(unfold) morphisms work together. details can be found in for example "Domains and lambda calculi" by Amadio and Curien, or Andy Pitts' "Relational properties of domains". Here is some Haskell code to illustrate what is going on: -- What 'G' does to objects. type G x y = x -> y -- What 'G' does to arrows. fun :: (a -> x, y -> b) -> (G x y -> G a b) fun (j,i) f = i . f . j -- The "fixpoint" newtype A = A { unA :: A -> A } -- The 'cata' and 'ana' are mutually recursive. univ :: (x -> G y x, G x y -> y) -> (x -> A,A -> y) univ (j,i) = (ana,cata) where cata = i . fun (ana, cata) . unA ana = A . fun (cata, ana) . j hope this helps -Iavor On Tue, 8 Feb 2005 20:06:25 +0100, Johan Glimming <glimming@kth.se> wrote:

Hi

I have a problem with contravariance in the bananas in space setting. If you take catamorphism from a function space such as A=A->A to a type such as BxC, then the negative occurrence of X in the functor GXY=X->Y swaps around BxC into B+C.

This means that maybe in this particular case Meijer-Hutton's original Haskell code for cata/ana does not work, since the type for cata would force BxC and B+C to be the same type.

I might be wrong about this, and I wonder anybody can comment on this.

Med vänliga hälsningar / Yours Sincerely, Johan Glimming _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe