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

On 26/06/2012, Nathan Howell wrote:

On Tue, Jun 26, 2012 at 3:19 PM, Tillmann Rendel wrote:

...

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: ...

Better yet, use foldMap:

import Data.Monoid import Data.Foldable 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)

instance Foldable Tree where foldMap f (Leaf x) = f x foldMap f (Branch s t) = foldMap f s <> foldMap f t

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 . foldMap Product _ -> getSum . foldMap Sum

print . getResult $ val

Yet better yet:

{-# LANGUAGE DeriveFunctor, DeriveFoldable #-}

import Data.Monoid; import Data.Foldable; import System.Environment

data Tree a = Leaf a | Branch (Tree a) (Tree a) deriving (Functor, Foldable);

...

(^_^) -- Strake