Re: [Haskell-cafe] [Haskell-beginners] Multi-parameter type classes and ambiguous type variables...

On Sat, Mar 21, 2015 at 8:37 PM, Sumit Sahrawat, Maths & Computing, IIT (BHU) wrote:

This might be better answered at the haskell-cafe. Sending to cafe.

On 21 March 2015 at 03:09, Stuart Hungerford wrote:

...

Hi,

As a learning exercise I'm modelling some algebraic structures as Haskell typeclasses. Some of these are multi-parameter type classes. Here's a very simplified version of the type class relationships:

class MM a where one :: a

class AM a where zero :: a

class (AM a, MM a) => SR a

class (AM a) => AG a where inv :: a -> a

class (SR a) => R a where neg :: a -> a

class (R r, AG g) => M r g where sca :: r -> g -> g

check :: (Eq g, M r g) => g -> Bool check x = sca one x == x

The problem I have is that GHC is finding the "r" type variable in the "check" function ambiguous. Given my still limited Haskell knowledge I'm not surprised this is happening. What I would like to know is how experienced Haskellers handle this situation in practice: is there an idiomatic way of disambiguating "r" or is it a sign of poor type class design?

In the type signature: check :: (Eq g, M r g) => g -> Bool you fix the type `g`, but not the type `r`. This causes an ambiguity in the program because if you had e.g. instance M Float Vector where ... instance M Int Vector where ... both in the same program, and you passed a Vector to `check`, GHC won't know which instance to choose. To solve this ambiguity, either fix `r` with an extra parameter: check :: (Eq g, M r g) => r -> g -> Bool check one' x = sca one' x == x Or declare that `r` is uniquely determined by `g` using a *functional dependency*: class (R r, AG g) => M r g | g -> r where sca :: r -> g -> g Or equivalently, using *associated types*: class (AG g, R (Scalar g)) => M g where type Scalar g :: * sca :: Scalar g -> g -> g check :: (Eq g, M g) => g -> Bool check x = -- as before A Google search for these two terms should yield plenty of tutorials and examples. (By the way, I'd suggest using longer names like "Ring" and "AdditiveGroup" instead, as they're easier to read.) Chris

...

Thanks,

Stu _______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners

-- Regards

Sumit Sahrawat

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