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Meaning of PEANO ARITHMETIC

 
Computing Dictionary
 
 Definition: 

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)

 

 

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