What the heck is polymorphism?

Jan van Brügge on February 23, 2019

Polymorphism is the idea of defining data structures or algorithms in general, so you can use them for more than one data type. The complete answ... [Read Full]
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Nice article! It helps me a lot on contemplating about the design of my programming language.

I kind of understand every category of polymorphism you mentioned, but I still couldn’t understand how can higher-rank polymorphism is useful.

So, do you mind to provide any practical example of higher rank polymorphism (It would be better if the example you provided is actually used in industrial code, not just in the academia)

 

Yes, I've added a paragraph about the ST trick there. Another possible use case would be callback functions that receive data from your API:

withHook: (forall a. IsApiData a => a -> IO ()) -> IO ()

This allows withHook to send any data to the callback that implements the IsApiData type class

 

I'm confused, isn't this ad-hoc (or 'first-rank' I guess) as it only quantifies over a?

No, as you can see the forall is in the parenthesis, the scope does not go until the return type

herp derp, realized it myself just now, ∀x(P(x))->Q ≠ ∀x(P(x)->Q).

So this would require an an ad-hoc polymorphic function as argument, yes?

 

Thanks for this!

Regarding subtype polymorphism, I think you can use type classes to achieve something similar.
For instance, the type class for your Vehicle example would look like:

class Vehicle v where
    getWeight :: v -> Int

Each 'subtype' can then be modelled as an instance of Vehicle that implements the getWeight function accordingly.

Now I'm far from a Haskell expert, so what do you think about this relation between subtype polymorphism and type classes?

You can also view it from the other side: If you want to model a Haskell type class in Java, you would use an interface, i.e. subtype polymorphism.

For instance, if we take the Functor type class with the fmap function, we would introduce a Functor<T> interface with an fmap method. Functor instances would then be modelled as classes that implement the Functor interface.

 

Yeah, you can emulate parts of it with ad-hoc polymorphism, but it remains an approximation because type classes are more like interfaces and not like base classes. You can't do something like super.getWeight().

On the other hands interfaces (at least in Java) are not powerful enough to model type classes either. For simple type classes like Semigroup or Monoid this works perfectly:

class Semigroup a where
    (<>) :: a -> a -> a

class Semigroup a => Monoid a where
    mempty :: a

and in Java:

public interface Semigroup<T> {
    T combine(T a, T b);
}

public interface Monoid<T> extends Semigroup<T> {
    T mempty();
}

The problem is the more complicated type classes like Functor or Monad. More specifically the type classes that use higher kinded types. You see above that the a from the Monoid definition is directly used in the type signature. This means it can only have the kind Type. But take the definition of Functor for example:

class Functor f where
    fmap :: (a -> b) -> f a -> f b

The f is not directly used, but it is partially applied to another type. This means that f has kind Type -> Type, ie it is a type constructor. In Java this would mean that you would need a generic generic type, something like this:

public interface Functor<F<?>> {
    <A,B> F<B> fmap(Function<A, B> f, F<A> x);
}

which is not valid Java at all.

 

Thanks for the detailed answer!

You are right, even though the two concepts overlap a bit, there is quite some mismatch.

 

Great article Jan, I knew of only a subset of them. Haskell definitely blows my mind :D

 
 
 

It's a children's book that people like to poke fun at for its hilarious cover art. I always imagine it when I think of polymorphism and it gives me a good chuckle. Might be a bit of a non sequitur. 😁 Great article btw.

 
 

Call what a union? I don't see any way a C union could be considered polymorphic. It is basically just a convenience for casting.

Or do you mean that a union is as far as you can bring C's type system?

 

Not quite. It's implemented as a tagged union, but the power comes from building a full algebra that makes type composition trivial and very easy to reason about (thus the phrase "algebraic data type"). Their history goes back to the 1970's, so they're not much younger than C and they're older than object oriented programming.

 

Great explaination. Of Haskell and or Code Computer Programming Language's.
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