[Haskell-cafe] tricky recursive type instance method

[Frank Kuehnel]

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 <kuehnelf at 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 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!
>>>> 
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>>>> 
>> 
>> 

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