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. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

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

On 20/07/14 09:57, Niklas Haas wrote:

Hmm, to be honest I'm not sure if this is effectively any different from what you had in your original example.

Does this work as expected w.r.t type inferencing and instance selection? _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

Yes, it works as expected, e.g, now I have instances of FourierTrasformable for List [Double] and for HMatrix.Vector Double, and the following works well:

fft (toComplex [1,2,3,4 :: Double]) [10.0 :+ 0.0,(-2.0) :+ 2.0,(-2.0) :+ 0.0,(-2.0) :+ (-2.0)] fft (toComplex $ vector [1,2,3,4]) fromList [10.0 :+ 0.0,(-2.0) :+ 2.0,(-2.0) :+ 0.0,(-2.0) :+ (-2.0)]

I think (if I understand well) this is because the constraints (RealSignalType (ComplexSignalType s) ~ s) in the Complexable class definition and (csx ~ ComplexSignalType s, ComplexSignal csx) in the fft definition makes a one-by-one dependency between s and csx. -- 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

On Mon, Jul 21, 2014 at 2:52 PM, Niklas Haas wrote:

You can drop the forall csx. bit, for what it's worth, since csx is an unbound variable either way (and hence implicitly quantified).

Also, the "ComplexSignal csx" constraint is redundant, since the Complexable superclass constraint includes it. In other words, you can write: class (Complexable s) ⇒ FourierTransformable s where fft :: (csx ~ ComplexSignalType s) ⇒ csx → csx

On 21/07/14 16:09, Niklas Haas wrote:

On Mon, 21 Jul 2014 15:39:08 -0400, adam vogt wrote:

...

Also, the "ComplexSignal csx" constraint is redundant, since the Complexable superclass constraint includes it. In other words, you can write:

class (Complexable s) ⇒ FourierTransformable s where fft :: (csx ~ ComplexSignalType s) ⇒ csx → csx In fact, this type should now even be equivalent to:

class Complexable s => FourierTransformable s where fft :: ComplexSignalType s -> ComplexSignalType s _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe Yes, it was redundant, and now it looks better. Thanks!

-- 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