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Today's Topics:
1. Re: Fwd: Averaging a string of numbers
(Dean Herington & Elizabeth Lacey)
----------------------------------------------------------------------
Message: 1
Date: Mon, 12 Dec 2011 02:18:40 -0500
From: Dean Herington & Elizabeth Lacey <[email protected]>
Subject: Re: [Haskell-beginners] Fwd: Averaging a string of numbers
To: Ben Kolera <[email protected]>, [email protected]
Message-ID: <a06240800cb0b587b87a9@[10.0.1.3]>
Content-Type: text/plain; charset="us-ascii" ; format="flowed"
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]
------------------------------
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