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Peano arithmetic

mathematics A system for representing natural numbers

inductively using only two symbols, "0" (zero) and "S"

(successor).

This could be expressed as a recursive data type with the

following Haskell definition:

data Peano = Zero | Succ Peano

The number three, usually written "SSS0", would be Succ (Succ

(Succ Zero)). Addition of Peano numbers can be expressed as a

simple syntactic transformation: