Type arithmetic

Type arithmetic is calculations on types using fundeps as functions.

A simple example is Peano numbers:

data Zero

data Succ a

class Add a b ab | a b -> ab, a ab -> b
instance Add Zero b b
instance (Add a b ab) => Add (Succ a) b (Succ ab)

However, many other representations of numbers are possible, including binary and balanced base three. Type arithmetic may also include type representations of boolean values and so on.