Peano Natural Numbers in Python

peano.py

'''
Peano Natural Numbers ( https://en.wikipedia.org/wiki/Peano_axioms )
'''

class Nat(object):
    def __init__(self, prev=None):
        self.prev = prev
    
    def __eq__(self, other) -> bool:
        if self.prev is None and other.prev is None:
            return True
        elif self.prev is None and other.prev is not None:
            return False
        elif other.prev is None and self.prev is not None:
            return False
        return self.prev == other.prev
    
    def __add__(self, other):
        if other == Nat():
            return self
        elif other.prev == Nat():
            return Nat(self)
        return Nat(self) + other.prev
    
    def __sub__(self, other):
        if other == Nat():
            return self
        elif other.prev == Nat():
            if self.prev is None:
                raise Exception('Not allowed in Natural Number Set')
            return self.prev
        else:
            return self.prev - other.prev
    
    def _to_repr(self):
        if self.prev is None:
            return 0
        else:
            return self.prev._to_repr() + 1
        
    def __repr__(self):
        return f'Nat({self._to_repr()})'
        
Zero = Nat()
AnotherZero = Nat()
One = Nat(Zero)
AnotherOne = Nat(AnotherZero)
Two = Nat(AnotherOne)

print('0 == 0', Zero == Zero, Zero == AnotherZero)
print('1 != 0', Zero == One, AnotherZero == One, AnotherZero == AnotherOne)
print('1 == 1', One == One, One == AnotherOne, AnotherOne == One)
print('Zero, One', Zero, AnotherZero, One, AnotherOne)
print(Two + Two, Two + Zero, Two + One + Two)
print(Two + Two - AnotherOne)
print(One - Two)