Patrick Bahr does something very similar in Modular Tree Automata [1], also noting the relation to attribute grammars. It's implemented in the compdata package [2]. [1] Patrick Bahr, Modular Tree Automata (MPC 2012), http://dx.doi.org/10.1007/978-3-642-31113-0_14 [2] http://hackage.haskell.org/package/compdata / Emil 2013-01-26 23:03, Petr P skrev:
Dear Haskellers,
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.
[1] http://www.haskell.org/haskellwiki/Attribute_grammar [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
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