[Haskell-cafe] Problems with type family in a class

[Leza Morais Lutonda]

On 17/07/14 02:32, Niklas Haas wrote:
> The reason you're getting this error is because all you know about your
> instance is that the type of fft is :: [Complex Double] -> [Complex
> Double].
>
> Since by definition this [Complex Double] is ComplexSignalType sx, all
> we know about the associated instance (parametrized by sx) is that
> ComplexSignalType sx ~ [Complex Double]. Since ComplexSignalType is a
> type family, it's not injective, so this does not suffice to uniquely
> identify our actual instance (sx, here called s0 by GHC).
>
> For example, we could have a second instance:
>
> instance Complexable () where
>    type ComplexSignalType () = [Complex Double]
>
> instance FourierTransformable () where
>    fft = error "oops"
>
> And with this instance, fft would also be [Complex Double] -> [Complex
> Double] but the behavior of would clearly be different to your actually
> intended function.
>
> If you think your signal function is bijective, you could use a two-way
> functional dependency like this:
>
> class Complexable sx cx | sx -> cx, cx -> sx
>
> class Complexable sx cx => FourierTransformable sx cx where
>    fft :: cx -> cx
>
> Or if you want to avoid the overhead of redesigning Complexable you
> could even do something like this:
>
> class (cx ~ ComplexSignalType sx, Complexable sx) => FourierTransformable sx cx | cx -> sx where
>    fft :: cx -> cx
>
> Either way, if instance selection should be possible based solely on the
> type of ‘cx’, then ‘cx’ must imply everything contained in the instance
> head.
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Thanks for the explanation, Niklas, now I understand (I'm understanding) 
type families and I left with:

class (Signal s,
        ComplexSignal (ComplexSignalType s),
        RealSignalType (ComplexSignalType s) ~ s) ⇒ Complexable s where

         type ComplexSignalType s

class (Complexable s) ⇒ FourierTransformable s where
         fft  ⦂ ∀ csx. (csx ~ ComplexSignalType s, ComplexSignal csx) ⇒ csx → csx


Maybe more complex than normal?

Thanks again.

-- 
Leza Morais Lutonda, Lemol-C
http://lemol.github.io


50 Aniversario de la Cujae. Inaugurada por Fidel el 2 de diciembre de 1964  http://cujae.edu.cu