This is type level natural numbers. They are represented using binary encoding which means that reasonable large numbers could be represented. With default context stack depth (20) maximal number is 2^18-1 (262143).

Z           = 0
I Z         = 1
O (I Z)     = 2
I (I Z)     = 3
O (O (I Z)) = 4
...

It's easy to see that representation for each number is not unique. One could add any numbers of leading zeroes:

I Z = I (O Z) = I (O (O Z)) = 1

In order to enforce uniqueness of representation only numbers without leading zeroes are members of Nat type class. This means than types are equal if and only if numbers are equal.

Natural numbers support comparison and following operations: Next, Prev, Add, Sub, Mul. All operations on numbers return normalized numbers.

Interface type classes are reexported from TypeLevel.Number.Classes

Here is usage example for natT:

n123 :: $(natT 123)
n123 = undefined