[Haskell-beginners] pattern for tree traversel with a state

[Andreas-Christoph Bernstein]

Hi,

Is there a pattern for tree traversal with a state ?

I am developing a small scenegraph represented by a tree. To draw a 
scenegraph one traverses over the graph starting with a global state. 
Inner Nodes can overwrite the inherited state for their subtree (e.g. 
Transformations are accumulated). The accumulated state is then either 
used immediately to draw the geometry in the leaf nodes, or a secondary 
data structure is build. This secondary data structure (a list or a 
tree) can then be sorted for optimal drawing performance.

So i want to do the second and create a list of all leaves with the 
accumulated global state. To illustrate my problem i appended some code. 
The idea similar applies to a scenegraph.

So my Question is: Is there allready a pattern for traversal with a state ?

 > module Main
 > where

produces: Fork (0,"a") (Fork (1,"a") (Leaf (2,"a")) (Leaf (1,"a"))) 
(Leaf (0,"a"))

 > newTree :: BTree State
 > newTree = traverse modState globalState sampleTree

produces: [(0,"a"),(1,"a"),(2,"a"),(1,"a"),(0,"a")]

 > stateList = flattenTree newTree

 > flattenTree (Leaf x) = [x]
 > flattenTree (Fork x l r) = [x] ++ flattenTree l ++ flattenTree r

 > type State = (Int, String)
 >
 > globalState :: State
 > globalState = (0, "a")

State modifiers

 > data StateMod
 >   = ModInt
 >   | ModString
 >   | ModNop
 >   deriving Show

 > modState :: StateMod -> State -> State
 > modState ModInt (x,w) = (x+1,w)
 > modState ModNop s = s
 > modState ModString (x,w) = (x,'b':w)

 > data BTree a = Fork a (BTree a) (BTree a)
 >               | Leaf a
 >               deriving Show

traverses the tree and executes a function which modifies the current 
state depending on the statemodifier

 > traverse :: (a -> b -> b) -> b -> BTree a -> BTree b
 > traverse f state (Leaf x) = Leaf (f x state)
 > traverse f state (Fork x l r) =
 >   Fork (f x state) newLeft newRight
 >   where newLeft   = traverse f (f x state) l
 >         newRight  = traverse f (f x state) r

an example tree

 > sampleTree :: BTree StateMod
 > sampleTree = Fork ModNop
 >               (Fork ModInt (Leaf ModInt) (Leaf ModNop))
 >                (Leaf ModNop)

creates a list from a tree

 > flattenTree (Leaf x) = [x]
 > flattenTree (Fork x l r) = [x] ++ flattenTree l ++ flattenTree r

Thanks for any help and ideas

Andreas