# [Haskell-cafe] tricky recursive type instance method

Antoine Latter aslatter at gmail.com
Fri Jan 28 05:00:27 CET 2011

```On Thu, Jan 27, 2011 at 9:35 PM, Frank Kuehnel <vincef13 at 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!
>
> _______________________________________________