Hey, I have a structure containing Xs in various places, like so data X data Structure = Structure .. [X] .. [X] .. And I defined mapStructure mapStructure :: (X -> X) -> (Structure -> Structure) I then wanted to use mapStructure to define queries as well as transformations on structures. I generalized mapStructure to mapStructureM: mapStructure :: Monad m => (X -> m X) -> (Structure -> m Structure) and then defined the following search monad:
data Search f a b = Found (f a) b
class Monad (m a) => SearchMonad m a where found :: a -> m a a
fromSearch :: Search f a b -> f a fromSearch (Found a _) = a
search :: (SearchMonad m a) => (a -> Bool) -> a -> m a a search f a | f a = found a | otherwise = return a
Instances of the monad for finding one and for finding all elements:
instance SearchMonad (Search Maybe) a where found a = Found (Just a) a
instance SearchMonad (Search []) a where found a = Found [a] a
instance Monad (Search Maybe a) where return b = Found Nothing b Found (Just a) a' >>= f = case f a' of Found _ b -> Found (Just a) b Found Nothing a' >>= f = f a'
instance Monad (Search [] a) where return b = Found [] b Found as a' >>= f = case f a' of Found as' b -> Found (as ++ as') b
Here is a simple sample session with ghci *Util> fromSearch $ mapM (search even) [1,3,5] :: Maybe Int Nothing *Util> fromSearch $ mapM (search even) [1,2,3,4,5] :: Maybe Int Just 2 *Util> fromSearch $ mapM (search even) [1,2,3,4,5] :: [Int] [2,4] What I'm wondering about is if this monad is an instance of a more general monad(if so, which one?), and generally if people have any comments about these definitions. Thanks! Edsko