Good stuff! You might also want to consider including code from Uustalu et al, "Recursion Schemes from Comonads", 2001 http://citeseer.ist.psu.edu/uustalu01recursion.html Chapter 7 has code formatted as Literate Haskell that generalizes cata, ana, hylo (iteration), and para (primitive recursion) to define a generalized catamorphism (distributive comonad), thence zygomorphisms (semi-mutual iteration), and histomorphisms (course-of-value iteration), and then gives one-liner definitions of add, mult, fact, and fibo functions, without which I'd never have figured out how to use any of the above. They also list numerous cancellation, reflection, and fusion laws which presumably might be translated into GHC rewrite rules. Although the paper uses the "older" scheme of newtype Mu f = In (f (Mu f)) unIn :: Mu f -> f (Mu f) unIn (In x) = x cata :: Functor f => (f c -> c) -> Mu f -> c cata phi = phi . fmap (cata phi) . unIn the types map cleanly to the ADT approach and, heck, the code is already written! I think in any case the source code of the examples add, mult, fact, and fibo would be very helpful in the documentation. Dan Roman Leshchinskiy wrote:

I'm pleased to announce fixpoint 0.1, a (for now) small generic programming library which allows data types to be manipulated as fixpoints of their underlying functors. The library is mostly based on "Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire" by Erik Meijer, Maarten Fokkinga and Ross Paterson.

The basic idea is to use associated data types, a recent GHC extension, to associate recursive types with their underlying functors. The core of the library is just one typeclass:

class Functor (Pre t) => Fixpoint t where data Pre t :: * -> *

-- | Projection from the data type to its underlying functor. project :: t -> Pre t t

-- | Injection from the underlying functor into the data type. inject :: Pre t t -> t

Here, Pre t is a functor such that its fixpoint is t. For instance, for lists we have:

instance Fixpoint [a] where data Pre [a] s = Nil | Cons a s

project [] = Nil project (x:xs) = Cons x xs

inject Nil = [] inject (Cons x xs) = x : xs

With this, we can easily define things like catamorphisms:

cata :: Fixpoint t => (Pre t s -> s) -> t -> s cata f = f . fmap (cata f) . project

which can then be used for generic programming:

size :: (Fixpoint t, Foldable (Pre t)) => t -> Int size = cata (F.foldr (+) 1)

At the moment, the package doesn't contain much more than the above but this will change soon(ish).

To enjoy the minimalistic interface of fixpoint-0.1, grab it from Hackage or from my site:

http://hackage.haskell.org/cgi-bin/hackage-scripts/package/fixpoint-0.1 http://www.cse.unsw.edu.au/~rl/code/fixpoint.html

Comments and suggestion are always welcome.

Roman

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