[Haskell] ANNOUNCE: fixpoint 0.1
Dan Weston
westondan at imageworks.com
Tue Nov 20 14:57:57 EST 2007
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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