# [Haskell-cafe] catamorphisms and attribute grammars

Sun Jan 27 08:20:07 CET 2013

```Hi Petr,

Congratulations -- you've just implemented a Moore machine! [1]

I posted something very much like this just last year [2]. It's a very
common pattern in Haskell, forming the basis of coroutines and
iteratees and many other things.

Edward Kmett includes it in his machines package [3]. His variation,
like mine, hides the state inside a closure, removing the need for
existentials. pipes 2.0 contains one implemented as a free monad [4].

[1] http://en.wikipedia.org/wiki/Moore_machine

Chris

On Sun, Jan 27, 2013 at 11:03 AM, Petr P <petr.mvd at gmail.com> wrote:
>
> I read some stuff about attribute grammars recently [1] and how UUAGC [2]
> can be used for code generation. I felt like this should be possible inside
> Haskell too so I did some experiments and I realized that indeed
> catamorphisms can be represented in such a way that they can be combined
> together and all run in a single pass over a data structure. In fact, they
> form an applicative functor.
>
> [2] Utrecht University Attribute Grammar Compiler
>
> To give an example, let's say we want to compute the average value of a
> binary tree. If we compute a sum first and then count the elements, the
> whole tree is retained in memory (and moreover, deforestation won't happen).
> So it's desirable to compute both values at once during a single pass:
>
> -- Count nodes in a tree.
> count' :: (Num i) => CataBase (BinTree a) i
> count' = ...
>
> -- Sums all nodes in a tree.
> sum' :: (Num n) => CataBase (BinTree n) n
> sum' = ...
>
> -- Computes the average value of a tree.
> avg' :: (Fractional b) => CataBase (BinTree b) b
> avg' = (/) <\$> sum' <*> count'
>
> Then we can compute the average in a single pass like
>
>     runHylo avg' treeAnamorphism seed
>
> My experiments together with the example are available at
> https://github.com/ppetr/recursion-attributes
>
> I wonder, is there an existing library that expresses this idea?
>
>   Best regards,
>   Petr Pudlak
>
>
> _______________________________________________