[Haskell-beginners] Weighted average

[Daniel Fischer]

Am Montag, 3. November 2008 22:41 schrieb Michael Snoyman:
> Hi everyone,
>
> I'm trying to set up some type safe functions for doing weighted averages
> and sum of products. The example I give below is to try and calculate the
> average miles per gallon for a collections of vehicles. Unfortunately, I am
> unable to get my weightedAverage function to work, seemingly due to an
> ambiguity for which instance to use. I think that the issue is that my
> "class Multiplicable" should only have two parameters, as opposed to the
> three it currently has. However, I can't figure out how to get that to
> work.
>
> Any help is greatly appreciated. Thank you,
> Michael
>
> ----------------------------------
>
> {-# LANGUAGE MultiParamTypeClasses #-}
>
> import Prelude hiding (sum, product)
>
> class Addable a where
>     add :: a -> a -> a
>     zero :: a
>
>     sum :: [a] -> a
>     sum = foldr add zero
>
> class Multiplicable a b c where
>     mult :: a -> b -> c

Use functional dependencies {-# LANGUAGE FunctionalDependencies #-},

class Multiplicable a b c | a b -> c where ...

which states that the result type of multiplication is determined by the 
argument types

or type families

>
>     product :: [a] -> [b] -> [c]
>     product x y = map (\(x1, y1) -> x1 `mult` y1) $ zip x y

product = zipWith mult

>
> sumProduct :: (Addable c, Multiplicable a b c) => [a] -> [b] -> c
> sumProduct x y = sum $ product x y
>
> weightedAverage x y = (sumProduct y x) `divide` (sum y)
>
> class Dividable a b c where
>     divide :: c -> a -> b

FunDep here, too, but which one?

>
> newtype MilesPerGallon = MilesPerGallon Double deriving Show
> newtype Gallon = Gallon Double deriving Show
> newtype Mile = Mile Double deriving Show
>
> instance Addable Gallon where
>     add (Gallon x) (Gallon y) = Gallon $ x + y
>     zero = Gallon 0
>
> instance Addable Mile where
>     add (Mile x) (Mile y) = Mile $ x + y
>     zero = Mile 0
>
> instance Multiplicable Gallon MilesPerGallon Mile where
>     mult (Gallon x) (MilesPerGallon y) = Mile $ x * y
>
> instance Dividable Gallon MilesPerGallon Mile where
>     divide (Mile x) (Gallon y) = MilesPerGallon $ x / y
>
> milesPerGallon :: [MilesPerGallon]
> milesPerGallon = map MilesPerGallon [35, 25, 29, 20, 52]
>
> gallons :: [Gallon]
> gallons = map Gallon [500, 190, 240, 100, 600]
>
> totalGallons :: Gallon
> totalGallons = sum gallons
>
> totalMiles :: Mile
> totalMiles = sumProduct gallons milesPerGallon
>
> totalMilesPerGallon :: MilesPerGallon
> totalMilesPerGallon = totalMiles `divide` totalGallons
> -- I would like some way to get the following line to replace the previous
> --totalMilesPerGallon = weightedAverage milesPerGallon gallons
>
> main = do
>     putStrLn $ "Total gallons of gas used: " ++ show totalGallons
>     putStrLn $ "Total miles traveled: " ++ show totalMiles
>     putStrLn $ "Average miles per gallon: " ++ show totalMilesPerGallon