[Haskell-cafe] more generic class instances?

[Nickolay Kudasov]

I mentioned in my last email that you can do that with extra type parameter.
Apparently, it’s much simpler but my code needs some improvement:

{-# LANGUAGE GeneralizedNewtypeDeriving #-}
​
{-# LANGUAGE RankNTypes #-}
newtype Constant a = Constant a deriving (Eq, Ord, Num, Enum)
data Linear    a = Linear    a (Constant a)data Quadratic a =
Quadratic a (Linear a)data Arbitrary a = Arbitrary (forall n. Integral
n => n -> a)
class PartialSum term where
  partialSum :: (Integral a, Num b) => a -> term b -> b
instance PartialSum Constant where
  partialSum n (Constant c) = fromIntegral n * c
instance PartialSum Linear where
  partialSum n (Linear k c) = k * fromIntegral (n * (n + 1) `div` 2) +
partialSum n c
instance PartialSum Quadratic where
  partialSum n (Quadratic k l) = k * fromIntegral (n * (n + 1) * (2 *
n + 1) `div` 6)  + partialSum n l
instance PartialSum Arbitrary where
  partialSum n (Arbitrary f) = sum $ map f [1..n]

This gives you appropriate behavior:

-- integerspartialSum 10 $ Linear 1 0partialSum 10 $ Arbitrary (2^)--
floatspartialSum 10 $ Arbitrary (\n -> 1.5 * fromIntegral n ::
Float)partialSum 10 $ Arbitrary (sqrt . fromIntegral)-- complex (from
Data.Complex)partialSum 10 $ Arbitrary (\n -> fromIntegral n^2 :+
fromIntegral n)

Nick


2013/11/2 Christopher Howard <christopher.howard at frigidcode.com>

> Thanks for the continued help. The only issue with your recently described
> approach is that, as near as I can tell, it requires the terms to be
> integral.
>
>
> data Arbitrary a = Arbitrary (a -> a)
>
> class PartialSum term where
>
>   partialSum :: (Integral a) => a -> term a -> a
>
> instance PartialSum Arbitrary where
>
>   partialSum n (Arbitrary f) = sum $ map f [1..n]
>
> I cannot, for example, do
>
> h> partialSum 10 (Arbitrary (\x -> 1.5 * x :: Float))
>
> <interactive>:88:1:
>
>     No instance for (Integral Float)
>
>       arising from a use of `partialSum'
>
>     Possible fix: add an instance declaration for (Integral Float)
>
>     In the expression:
>
>       partialSum 10 (Arbitrary (\ x -> 1.5 * x :: Float))
>
>     In an equation for `it':
>
>         it = partialSum 10 (Arbitrary (\ x -> 1.5 * x :: Float))
>
> h> partialSum 10 (Arbitrary (\ x -> (1 % 5) * x))
>
> <interactive>:100:1:
>
>     No instance for (Integral (Ratio a0))
>
>       arising from a use of `partialSum'
>
>     Possible fix: add an instance declaration for (Integral (Ratio a0))
>
>     In the expression: partialSum 10 (Arbitrary (\ x -> (1 % 5) * x))
>
>     In an equation for `it':
>
>         it = partialSum 10 (Arbitrary (\ x -> (1 % 5) * x))
>
>
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