+
+-- | Build a tree from a seed value
+unfoldTree :: (b -> (a, [b])) -> b -> Tree a
+unfoldTree f b = let (a, bs) = f b in Node a (unfoldForest f bs)
+
+-- | Build a forest from a list of seed values
+unfoldForest :: (b -> (a, [b])) -> [b] -> Forest a
+unfoldForest f = map (unfoldTree f)
+
+-- | Monadic tree builder, in depth-first order
+unfoldTreeM :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
+unfoldTreeM f b = do
+ (a, bs) <- f b
+ ts <- unfoldForestM f bs
+ return (Node a ts)
+
+-- | Monadic forest builder, in depth-first order
+unfoldForestM :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
+unfoldForestM f = mapM (unfoldTreeM f)
+
+-- | Monadic tree builder, in breadth-first order,
+-- using an algorithm adapted from
+-- /BreadthÂFirst Numbering: Lessons from a Small Exercise in Algorithm Design/,
+-- by Chris Okasaki, /ICFP'00/.
+unfoldTreeM_BF :: Monad m => (b -> m (a, [b])) -> b -> m (Tree a)
+unfoldTreeM_BF f b = liftM (fst . fromJust . deQueue) $
+ unfoldForestQ f (listToQueue [b])
+
+-- | Monadic forest builder, in breadth-first order,
+-- using an algorithm adapted from
+-- /BreadthÂFirst Numbering: Lessons from a Small Exercise in Algorithm Design/,
+-- by Chris Okasaki, /ICFP'00/.
+unfoldForestM_BF :: Monad m => (b -> m (a, [b])) -> [b] -> m (Forest a)
+unfoldForestM_BF f = liftM (reverseOnto []) . unfoldForestQ f . listToQueue
+ where reverseOnto :: [a] -> Queue a -> [a]
+ reverseOnto as q = case deQueue q of
+ Nothing -> as
+ Just (a, q') -> reverseOnto (a:as) q'
+
+-- takes a queue of seeds
+-- produces a queue of trees of the same length, but in the reverse order
+unfoldForestQ :: Monad m => (b -> m (a, [b])) -> Queue b -> m (Queue (Tree a))
+unfoldForestQ f aQ = case deQueue aQ of
+ Nothing -> return emptyQueue
+ Just (a, aQ) -> do
+ (b, as) <- f a
+ tQ <- unfoldForestQ f (foldl addToQueue aQ as)
+ let (ts, tQ') = splitOnto [] as tQ
+ return (addToQueue tQ' (Node b ts))
+ where splitOnto :: [a] -> [b] -> Queue a -> ([a], Queue a)
+ splitOnto as [] q = (as, q)
+ splitOnto as (_:bs) q = case fromJust (deQueue q) of
+ (a, q') -> splitOnto (a:as) bs q'