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Type arithmetic

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Revision as of 20:48, 1 February 2006

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.