commutative monoid (https://www.youtube.com/watch?v=cMY1KVrJk0w&feature=youtu.be&t=1m51s)

monoidal_sum.hs

import Control.Parallel
import Data.Monoid

data Collection = Collection
  { s       :: Integer
  , average :: Double
  , count   :: Integer
  }
  deriving (Show)

instance Monoid Collection where
  mempty = Collection 0 0 0
  (Collection x1 y1 count1) `mappend` (Collection x2 y2 count2) =
    Collection (x1 + x2) avg newCount
      where
        avg = realToFrac (x1 + x2) / (fromIntegral newCount)
        newCount = count1 + count2
  mconcat = foldr mappend mempty

c1 = Collection 1 1 1
c2 = Collection 10 10 1
c3 = Collection 4 4 1

group1 = replicate 901000 c1
group2 = replicate 991900 c2
group3 = replicate 1391000 c3

mainPar =
  a `par` b `par` c `pseq` mconcat [a,b,c]
    where
      a = mconcat group1
      b = mconcat group2
      c = mconcat group3

mainNormal =
  mconcat group1 <> mconcat group2 <> mconcat group3

main = print mainPar

-- ghc -threaded -rtsopts --make monoidal_sum
-- ./monoidal_sum