ch15_15.14_20.hs

import Data.Monoid (Monoid, (<>))

-- writer monad.  is a way to put a monad structure on tuples
-- see https://wiki.haskell.org/Monoid#On_the_Writer_monad
{-
  (w,x) >>= f =
  case f x of
    (v, y) -> (w <> v, y)
-}
-- the monoidal instance of tuple/product allows accumulating -<>- successive 'logs' -a<>c- for each computation -gx,fb

newtype Mem s a =
  Mem {
    runMem :: s -> (a,s)
  }

instance Monoid a => Monoid (Mem s a) where
  mempty = Mem $ \s -> (mempty, s)
  mappend Mem {runMem = f} Mem {runMem = g} = Mem $ \x -> let (a, b) = g x
                                                              (c, d) = f b
                                                          in (a <> c, d)


f' = Mem $ \s -> ("hi", s + 1)
main = do
  print $ runMem (f' <> mempty) 0
  print $ runMem (mempty <> f') 0
  print $ (runMem mempty 0 :: (String, Int))
  print $ runMem (f' <> mempty) 0 == runMem f' 0
print $ runMem (mempty <> f') 0 == runMem f' 0