There is some magic here that I'm not quite groking. Sorry for my
slowness; but I seem to be missing a step:
This is how I'd expect liftA2 to work ( and is why I didn't use lift
in my initial response ):
*Main Control.Applicative Data.Monoid> liftA2 max Nothing (Just 1)
Nothing
I expected all the magic to be the applicative class instance that was
generated for Maximum by the GeneralizedNewtypeDeriving extension, but
why do these not work?
*Main Control.Applicative Data.Monoid> liftA2 max (Maximum Nothing)
(Maximum (Just 1))
Maximum {getMaximum = Nothing}
*Main Control.Applicative Data.Monoid> mempty `mappend` (Maximum (Just
1)) `mappend` (Maximum (Just 2) )
Maximum {getMaximum = Nothing}
When this obviously works just fine?
*Main Control.Applicative Data.Monoid> main
Stats {ct = Sum {getSum = 0}, sm = Sum {getSum = 0.0}, mn = Minimum
{getMinimum = Nothing}, mx = Maximum {getMaximum = Nothing}}
Stats {ct = Sum {getSum = 1}, sm = Sum {getSum = 1.0}, mn = Minimum
{getMinimum = Just 1.0}, mx = Maximum {getMaximum = Just 1.0}}
Stats {ct = Sum {getSum = 1}, sm = Sum {getSum = 2.0}, mn = Minimum
{getMinimum = Just 2.0}, mx = Maximum {getMaximum = Just 2.0}}
Stats {ct = Sum {getSum = 2}, sm = Sum {getSum = 3.0}, mn = Minimum
{getMinimum = Just 1.0}, mx = Maximum {getMaximum = Just 2.0}}
Sorry if I am missing something obvious and this question is really silly!
On Mon, Dec 12, 2011 at 5:18 PM, Dean Herington & Elizabeth Lacey
At 8:21 AM +1000 12/12/11, Ben Kolera wrote:
That is just because you are calling min and max against the Maybe rather than on the values inside of your maybes. Max is working because there is an instance of Ord for Maybe and
Nothing > Just n > Just ( n + 1 )
You have the right idea, but replace `>` above by `<`.
This is certainly not the most elegant solution ( I am a beginner, too ) but here is what I would do:
instance Monoid Stats where mempty = Stats 0 Nothing Nothing 0 mappend (Stats sm1 mn1 mx1 len1) (Stats sm2 mn2 mx2 len2) = Stats (sm1 + sm2) (chooseMaybe min mn1 mn2) (chooseMaybe max mx1 mx2) (len1 + len2)
chooseMaybe _ Nothing Nothing = Nothing chooseMaybe _ (Just a) Nothing = Just a chooseMaybe _ Nothing (Just b) = Just b chooseMaybe f (Just a) (Just b) = Just $ f a b
Hopefully this quick answer can get you on your way to solving your problem and we can both learn a better way of doing it when someone optimises my solution. ;)
You've got the principle just right. Here's a way to cast it that makes it apparent that `Stats` is a monoid in a "componentwise" fashion.
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
import Data.Monoid import Control.Applicative
-- | Monoid under minimum. newtype Minimum a = Minimum { getMinimum :: Maybe a } deriving (Eq, Ord, Functor, Applicative, Read, Show)
instance Ord a => Monoid (Minimum a) where mempty = Minimum Nothing mappend = liftA2 min
-- | Monoid under maximum. newtype Maximum a = Maximum { getMaximum :: Maybe a } deriving (Eq, Ord, Functor, Applicative, Read, Show)
instance Ord a => Monoid (Maximum a) where mempty = Maximum Nothing mappend = liftA2 max
data Stats = Stats { ct :: Sum Int, sm :: Sum Double, mn :: Minimum Double, mx :: Maximum Double } deriving (Eq, Show, Read)
instance Monoid Stats where mempty = Stats mempty mempty mempty mempty mappend (Stats ct1 sm1 mn1 mx1) (Stats ct2 sm2 mn2 mx2) = Stats (ct1 `mappend` ct2) (sm1 `mappend` sm2) (mn1 `mappend` mn2) (mx1 `mappend` mx2)
mkStats v = Stats (Sum 1) (Sum v) (Minimum (Just v)) (Maximum (Just v))
st0, st1, st2, st3 :: Stats
st0 = mempty st1 = mkStats 1 st2 = mkStats 2 st3 = st1 `mappend` st2
main = mapM_ print [st0, st1, st2, st3]