Recently I was looking for an A-star search algorithm. I've found a package but I couldn't understand the code. Then I saw some blogposts but they were difficult to understand too. I thought about some easier solution that relies on laziness. And I've come to this: Heuristic search is like depth-first search but solutions in sub-trees are concatenated with mergeBy function, that concatenates two list by specific order: module Search where import Control.Applicative import Data.Function(on) import Control.Arrow(second) import Data.Tree -- | Heuristic search. Nodes are visited from smaller to greater. searchBy :: (a -> a -> Ordering) -> Tree a -> [a] searchBy heur (Node v ts) = v : foldr (mergeBy heur) [] (searchBy heur <$> ts) -- | Merge two lists. Elements concatenated in specified order. mergeBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a] mergeBy _ a [] = a mergeBy _ [] b = b mergeBy p (a:as) (b:bs) | a `p` b == LT = a : mergeBy p as (b:bs) | otherwise = b : mergeBy p bs (a:as) Now we can define specific heuristic search in terms of searchBy: -- | Heuristic is distance to goal. bestFirst :: Ord h => (a -> h) -> (a -> [a]) -> a -> [a] bestFirst dist alts = searchBy (compare `on` dist) . unfoldTree (\a -> (a, alts a)) -- | A-star search. -- Heuristic is estimated length of whole path. astar :: (Ord h, Num h) => (a -> h) -> (a -> [(a, h)]) -> a -> [a] astar dist alts s0 = fmap fst $ searchBy (compare `on` astarDist) $ unfoldTree gen (s0, 0) where astarDist (a, d) = dist a + d gen (a, d) = d `seq` ((a, d), second (+d) <$> alts a) I'm wondering is it effective enough? Anton