Re: [Haskell-cafe] tricky recursive type instance method

Thanks Antoine, indeed , instance DAlgebra Integer Integer where ... disambiguates it enough, then it works!! Is there a way to use instance DAlgebra (Real a) (Real a) where ... in some sort?? I know it doesn't compile! On Jan 27, 2011, at 8:33 PM, Antoine Latter wrote:

On Thu, Jan 27, 2011 at 10:09 PM, Frank Kuehnel wrote:

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Hi Antoine,

I've turned on the OverlappingInstances option

this is what I get, when I execute

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conj ((C 1 2) :: (Complex Int))

Overlapping instances for DAlgebra (Complex Float) (Complex Float) arising from a use of `conj' Matching instances: instance [overlap ok] Real a => DAlgebra a a -- Defined at Clifford.hs:21:10-31 instance [overlap ok] (Real r, Num a, DAlgebra a r) => DAlgebra (Complex a) r

I'm guessing GHC can't pick which instance to use, because neither one follows the rules for being more specific than the other. I tried to read the manual on it, but I don't have a clear answer for you: http://www.haskell.org/ghc/docs/7.0.1/html/users_guide/type-class-extensions...

If I change the `DAlgebra a a` instance to `DAlgebra Integer Integer` I can get examples to work fine.

Antoine

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On Jan 27, 2011, at 8:00 PM, Antoine Latter wrote:

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On Thu, Jan 27, 2011 at 9:35 PM, Frank Kuehnel wrote:

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Hi folks,

how do I make this work: I want a division algebra over a field k, and I want to define the conjugation of complex numbers, i.e. conj (C 1 2) but also the conjugation of tensors of complex numbers conj (C (C 1 2) (C 1 4))

ghci load that stuff butt barfs on a simple

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conj (C 1 2)

with instance Real a => DAlgebra a a -- Defined at Clifford.hs:20:10-31 instance (Real r, Num a, DAlgebra a r) => DAlgebra (Complex a) r

here's the code:

-- for a normed division algebra we need a norm and conjugation! class DAlgebra a k | a -> k where -- need functional dependence because conj doesn't refer to k conj :: a -> a abs2 :: a -> k

-- real numbers are a division algebra instance Real a => DAlgebra a a where conj = id abs2 x = x*x

-- Complex numbers form a normed commutative division algebra data Complex a = C a a deriving (Eq,Show)

instance Num a => Num (Complex a) where fromInteger a = C (fromInteger a) 0 (C a b)+(C a' b') = C (a+a') (b+b') (C a b)-(C a' b') = C (a-a') (b-b') (C a b)*(C a' b') = C (a*a'-b*b') (a*b'+b*a')

instance (Real r, Num a, DAlgebra a r) => DAlgebra (Complex a) r where conj (C a b) = C a (conj (-b)) abs2 (C a b) = (abs2 a) + (abs2 b)

What error are you getting in GHCi? It wasn't immediately clear from your email, but maybe I missed it.

It looks like you have overlapping instances between `DAlgebra a a` and `DAlgebra (Complex a) r`, so if that's what you want you'll need to making sure you have the OverlappingInstances extension turned on.

You might run in to other issues further on.

Antoine

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Thanks for you help!

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