On Thu, Jan 27, 2011 at 10:09 PM, Frank Kuehnel <kuehnelf@gmail.com> wrote:

Hi Antoine,

I've turned on the OverlappingInstances option

this is what I get, when I execute

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.html#instance-overlap

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

Antoine

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

On Thu, Jan 27, 2011 at 9:35 PM, Frank Kuehnel <vincef13@mac.com> wrote:

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

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

Thanks for you help!

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