Peano arithmetic

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Peano arithmetic

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:

plus Zero n = n plus (Succ m) n = Succ (plus m n)