[Haskell-cafe] Martin Odersky on "What's wrong with Monads"

[Nathan Howell]

On Tue, Jun 26, 2012 at 3:19 PM, Tillmann Rendel
<rendel at informatik.uni-marburg.de> wrote:
> A function to add up all integers in a tree:
>
>  amount:: Tree -> Integer
>  amount (Leaf x) = x
>  amount (Branch t1 t2) = amountt1 + amountt2
>
> All fine so far. Now, consider the following additional requirement: "If the
> command-line flag --multiply is set, the function amount computes the
> product instead of the sum."
>
> How would you implement this requirement in Haskell without changing the
> line "amount (Leaf x) = x"?

One option is to encode the desired behavior at the type level. By
extended the data type slightly and adding a Functor instance,
selecting between a product and a sum can be done using their Monoid
newtypes:

import Data.Monoid
import System.Environment

data Tree a = Leaf a | Branch (Tree a) (Tree a)

instance Functor Tree where
  f `fmap` Leaf x = Leaf (f x)
  f `fmap` Branch x y = Branch (fmap f x) (fmap f y)

amount :: Monoid a => Tree a -> a
amount (Leaf x) = x
amount (Branch t1 t2) = amount t1 <> amount t2

main :: IO ()
main = do
  args <- getArgs

  let val :: Tree Int
      val = Branch (Leaf 8) (Leaf 18)

  let getResult :: Tree Int -> Int
      getResult = case args of
        ["--multiply"] -> getProduct . amount . fmap Product
        _              -> getSum     . amount . fmap Sum

  print . getResult $ val