Q:

What is "n" in RankNTypes

I understand how forall enables us to write polymorphic function.
According to this chapter, the normal function which we generally write are Rank 1 types. And this function is of Rank 2 type:
foo :: (forall a. a -> a) -> (Char,Bool)
foo f = (f 'c', f True)

It explains like this: 

In general, a rank-n type is a function that has at least one
  rank-(n-1) argument but no arguments of even higher rank.

What does it actually mean by rank argument ?
Can somebody give an example of Rank 3 type which is similar to the above foo function.

A:

Rank is defined inductively on the structure of types:
rank (forall a. T) = max 1 (rank T)
rank (T -> U)      = max (if rank T = 0 then 0 else rank T + 1) (rank U)
rank (a)           = 0

Note how it increases by one on the left-hand side of an arrow. So:
Rank 0: Int
Rank 1: forall a. a -> Int
Rank 2: (forall a. a -> Int) -> Int
Rank 3: ((forall a. a -> Int) -> Int) -> Int

and so on.

