-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Nino,
I am also interested in knowing what zygomorphisms and paramorphisms are? and how can u build a gcata?? (a cata for all datatypes).
Regarding paramorphisms: Consider the catamorphism on the type of Peano naturals, data Nat = Zero | Succ Nat cataNat :: a -> (a -> a) -> Nat -> a cataNat e f = cata where cata Zero = e cata (Succ k) = f (cata k) Have a look at the case for Succ. Note that cata only operates on the immediate child n; it leaves the Succ node itself untouched. This makes it quite hard to define structural-recursive functions that also need access to the complete node. For instance, a clumsy way to define the factorial on Peano naturals is fac' :: Nat -> Nat fac' = snd . cataNat e f where e = (Zero, Succ Zero) f (n, k) = (Succ n, Succ n `times` k) Paramorphisms are like catamorphisms but provide access to the nodes themselves too: paraNat :: a -> (Nat -> a -> a) -> Nat -> a paraNat e g = para where para Zero = e para n@(Succ k) = g n (para k) The factorial can now be written as fac :: Nat -> Nat fac = paraNat (Succ Zero) times Another example is the paramorphism on lists: paraList :: b -> (a -> [a] -> b -> b) -> [a] -> b paraList e g = para where para [] = e para (x : xs) = g x xs (para xs) Regarding generic catamorphisms: check out (datatype) generic programming or polytypic programming. HTH, Stefan -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.1 (Darwin) iD8DBQFD38lLX0lh0JDNIpwRAthxAJ9iSndWFz/FHDiGPqAwMUXFIfbAAgCcCwnd 17Ahn/T8DNx4V8oRsFCFvCM= =V7lp -----END PGP SIGNATURE-----