Hello, You might want to look at the scrap your boilerplate papers and/or their implementation in GHC in Data.Generics. -Jeff haskell-cafe-bounces@haskell.org wrote on 03/19/2007 01:11:19 PM:

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 _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

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Edsko de Vries wrote:

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)

I guess you want an applicative functor. See also http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Traversable.html and the accompanying papers. Regards, apfelmus