# Implementing Peano Naturals

One way to explain what natural numbers are is to do define

$0 := \left \{ \right \} \\ 1 := \left \{ \left \{ \right \}\right \} \\ 2 := \left \{ \left \{ \right \}, \left \{ \left \{ \right \} \right \}\right \} \\ \vdots$

I want to implement them using Haskell Lists like this:

 1 2 3 4 5 peano 0 = [] peano 1 = [[]] peano 2 = [[], [[]]] . . 

To do so, I write the following program:

 1 2 peano 0 = [] peano n = map peano [0..n-1] 

What can I do to fix this program?

Inspired by Peano Axioms

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