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# Polymorphism

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# Higher Kinded Types

# Higher Ranked Polymorphism

All types are implicitly qualified. A good explanation for this lives here. In haskell syntax:

-- this is implicitly adding a universal qualifier
f :: a -> a -> b
-- the qualifier:
f :: forall a b. a -> a -> b

Higher ranked polymorphism is simply allowing us to accept arguments and return polymorphic functions. For example, rank 2 polymorphism allows us to return functions containing a forall.

f :: (forall a. a) -> (forall b. b)

The level of nested qualification determines the “ranked”-ness of the polymorphism. For example, the following function would be of rank 3:

f :: (Int -> (forall a. a)) -> Int

TODO transformers/why this is useful

# SystemF