多态类型有什么用途？

Question

Polymorphic kinds are an extension to Haskell's type system, supported by UHC, allowing

data A x y = A (y x)

to be typed (kinded?) as a -> (a -> *) -> * . What are they useful for?

Answer 1

One possible usage example can be using conal's TypeCompose for composing monad transformers in point-free style.

type MyT = StateT Foo :. MaybeT :. ContT Bar

(just as an example, I have no idea what one's going to do with those foos and bars..)

Instead of:

type MyT m = StateT Foo (MaybeT (ContT Bar m))

(this would have the same result apart from newtype -wrappers)

Currently you'll need to duplicate the combinators code for different kinds, and this extension abolishes the repetition and allows using one piece of code to rule them all.

Answer 2

Adding Polymorphic Kinds to GHC

The background to this question would be the motivation in general for a more expressive kind system .

That is, the overall reason to add polymorphic kinds to Haskell is to improve the experience of type level programming . Currently type level programming in Haskell proceeds in a essentially untyped " kind " level. A richer kind language will make type level programming in Haskell, in general, easier.

A more concrete example would be to remove the (dynamic) Typeable constraint from generics of the SYB style ( citation ), as well as improving overall support for higher-kinded generic programming..

Answer 3

They are useful for defining functions that operate over data constructors with arbitrary arity, of course!

A concrete example could be a function that, given a data constructor with arbitrary arity, returns a new data constructor that wraps the given constructor in Some().