Hi,
you might want to take a look at [1]AdvancedOverlap.
However, the most simple option would be to wrap up your (Real a =>
DAlgebra a a) instance in a newtype:
> {-# LANGUAGE GeneralizedNewtypeDeriving #-}
>
> newtype FromReal a = FromReal a deriving (Eq, Ord, Read, Show, Num, Real)
>
>instance Real a => DAlgebra (FromReal a) (FromReal a) where
> conj = id
> abs2 x = x*x
Steffen
[1] http://www.haskell.org/haskellwiki/GHC/AdvancedOverlap
On 01/28/2011 04:35 AM, Frank Kuehnel 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)
Thanks for you help!
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