[Haskell-cafe] Nested monadic monoids via Traversable?

Hans Höglund hans
Thu Oct 10 16:25:30 UTC 2013

I have been experimenting with compositions of monads carrying associated monoids (i.e. Writer-style) and discovered the following pattern:

{-# LANGUAGE     
    GeneralizedNewtypeDeriving #-}

import Control.Monad
import Control.Monad.Writer hiding ((<>))
import Data.Semigroup
import Data.Foldable (Foldable)
import Data.Traversable (Traversable)
import qualified Data.Traversable as Traversable

newtype Foo m a = Foo (Writer m a)
    deriving (Monad, MonadWriter m, Functor, Foldable, Traversable)

newtype Bar m a = Bar { getBar :: [Foo m a] }
    deriving (Semigroup, Functor, Foldable, Traversable)
instance Monoid m => Monad (Bar m) where
    return = Bar . return . return
    Bar ns >>= f = Bar $ ns >>= joinedSeq . fmap (getBar . f)
            joinedSeq = fmap join . Traversable.sequence

runFoo (Foo x) = runWriter x
runBar (Bar xs) = fmap runFoo xs

That is, given a type that is Monadic and Traversable, we can define a list of the same type as a monad, whose binding action "glues together" the nested Monoid values. A trivial example:

-- annotate all elements in bar
tells :: String -> Bar String a -> Bar String a
tells a (Bar xs) = Bar $ fmap (tell a >>) xs

-- a bar with no annotations
x :: Bar String Int
x = return 0

-- annotations compose with >>=
y :: Bar String Int
y = x <> tells "a" x >>= (tells "b" . return)

-- and with join
z :: Bar String Int
z = join $ tells "d" $ return (tells "c" (return 0) <> return 1)

-- runBar y ==> [(0,"b"),(0,"ab")]
-- runBar z ==> [(0,"dc"),(1,"d")]

However, I am concerned about the (Monad Bar) instance which seems ad-hoc to me, especially the use of sequence. Is there a more general pattern which uses a class other than Traversable? Any pointers would be much appreciated.


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