[Haskell-cafe] Extracting all pruned sub trees

[Mark Lentczner]

On Jan 20, 2010, at 10:09 AM, Tom Hawkins wrote:
> I'm looking for an elegant way to generate a list of all pruned trees
> where each pruned tree has one of its leaves removed.

This turned out to be a thornier problem than I thought! (pun intended) 

> -- | A simple Tree type. 
> data Tree a = Leaf a | Branches [Tree a]
> 	deriving Show
> 
> -- | Produce a list of all possible Trees that can result from pruning one Leaf
> allPrunings :: Tree a -> [Tree a]
> allPrunings (Leaf _) = []
> allPrunings (Branches ts) = Branches `fmap` pruneInTurn ts
>     where pruneInTurn (a:as) = pruneOneWith a as ++ map (a:) (pruneInTurn as)
>           pruneInTurn _      = []
>           pruneOneWith (Leaf _) as = [ as ]
>           pruneOneWith a        as = map (:as) (allPrunings a)

The difficulty lies in the treatment of Branches vs Leaf: Pruning Branches laves a Tree who's head (well, "root") is of the same form, whereas pruning Leaf leaves nothing (no valid Tree). This gives rise for the need for the pruneOneWith function.

A more complete module with a small parser for a string tree language, and a nice, input and pring all prunings function can be found here:

	http://bitbucket.org/mtnviewmark/haskell-playground/src/tip/cafe/TreePrune.hs

Enjoy!

	- Mark

Mark Lentczner
http://www.ozonehouse.com/mark/
IRC: mtnviewmark