Difference between int and numbers.Integral in Python

Question

I'm trying to get a deeper understanding in Python's data model and I don't fully understand the following code:

>>> x = 1

>>> isinstance(x,int)
True

>>> isinstance(x,numbers.Integral)
True

>>> inspect.getmro(int)
(<type 'int'>, <type 'object'>)

>>> inspect.getmro(numbers.Integral)
(<class 'numbers.Integral'>, <class 'numbers.Rational'>, <class 'numbers.Real'>,
 <class 'numbers.Complex'>, <class 'numbers.Number'>, <type 'object'>)

Based on the above, it seems that int and number.Integral are not in the same hierarchy.

From the Python reference (2.6.6) I see

numbers.Integral - These represent elements from the mathematical set of integers (positive and negative).

What's the difference between int and numbers.Integral? Does it have something to do with the type int vs class numbers.Integral I see in the above output?

Answer 1

numbers defines a hierarchy of abstract classes that define operations possible on numeric types. See PEP 3141. The difference between int and Integral is that int is a concrete type that supports all the operations Integral defines.

Answer 2

In [34]: numbers.Integral ?
Type:           ABCMeta
Base Class:     <class 'abc.ABCMeta'>
String Form:    <class 'numbers.Integral'>
Namespace:      Interactive
File:           c:\python26\lib\numbers.py
Docstring:
    Integral adds a conversion to long and the bit-string operations.


In [35]: int ?
Type:           type
Base Class:     <type 'type'>
String Form:    <type 'int'>
Namespace:      Python builtin
Docstring:
    int(x[, base]) -> integer


In [36]: type(int) == type (numbers.Integral)
Out[36]: False

In [39]: issubclass(int, numbers.Integral)
Out[39]: True

Integral is an Abstract Base Class. int is a subclass of the ABCMeta Integral