[Haskell-cafe] Extracting all pruned sub trees

[Tom Hawkins]

On Thu, Jan 21, 2010 at 4:07 PM, Mark Lentczner <markl at glyphic.com> wrote:
> 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!

Very nice.  Thanks!

-Tom