Truth Value Testing

By default, an object is considered true unless its class defines either a __bool__() method that returns False or a __len__() method that returns zero, when called with the object. Here are most of the built-in objects considered false:

• constants defined to be false: None and False.
• zero of any numeric type: 0, 0.0, 0j, Decimal(0), Fraction(0, 1)
• empty sequences and collections: '', (), [], {}, set(), range(0)

>>> class A:
...   def __bool__(self):
...     return False
... 
>>> a = A()
>>> 
>>> bool(a)
False

>>> class B:
...   pass
... 
>>> b = B()
>>> bool(b)
True

• __bool__
  Called to implement truth value testing and the built-in operation bool(); should return False or True. When this method is not defined, __len__() is called, if it is defined, and the object is considered true if its result is nonzero. If a class defines neither __len__() nor __bool__(), all its instances are considered true.

• __len__()
  Called to implement the built-in function len(). Should return the length of the object, an integer >= 0. Also, an object that doesn’t define a __bool__() method and whose __len__() method returns zero is considered to be false in a Boolean context.

Boolean Operations

• x or y : if x is false, then y, else x
  This is a short-circuit operator, so it only evaluates the second argument if the first one is false.

• x and y: if x is false, then x, else y
  This is a short-circuit operator, so it only evaluates the second argument if the first one is true.

• not x: if x is false, then True, else False

Note that neither and nor or restrict the value and type they return to False and True, but rather return the last evaluated argument. This is sometimes useful, e.g., if s is a string that should be replaced by a default value if it is empty, the expression s or 'foo' yields the desired value. Because not has to create a new value, it returns a boolean value regardless of the type of its argument (for example, not 'foo' produces False rather than ''.

>>> 2 or 3
2
>>> 2 and 3
3

>>> s = ''
>>> s or 'foo'
'foo'
>>> not 'foo'
False

Comparisons

• There are eight comparison operations in Python.
  <, <=, >, >=, ==, !=, is, is not

• x < y <= z is equivalent to x < y and y <= z, except that y is evaluated only once (but in both cases z is not evaluated at all when x < y is found to be false).

• The <, <=, > and >= operators will raise a TypeError exception when comparing a complex number with another built-in numeric type, when the objects are of different types that cannot be compared, or in other cases where there is no defined ordering.

• Instances of a class cannot be ordered with respect to other instances of the same class, or other types of object, unless the class defines enough of the methods __lt__(), __le__(), __gt__(), and __ge__()

• rich comparison methods

object.__lt__(self, other)    ; x<y calls x.__lt__(y)
object.__le__(self, other)    ; x<=y calls x.__le__(y) 
object.__eq__(self, other)    ; x==y calls x.__eq__(y)
object.__ne__(self, other)    ; x!=y calls x.__ne__(y)
object.__gt__(self, other)    ; x>y calls x.__gt__(y)
object.__ge__(self, other)    ; x>=y calls x.__ge__(y).

A rich comparison method may return the singleton NotImplemented if it does not implement the operation for a given pair of arguments. By convention, False and True are returned for a successful comparison. However, these methods can return any value.

By default, __ne__() delegates to __eq__() and inverts the result unless it is NotImplement.

• Identity comparisons

The operators is and is not test for object identity: x is y is true if and only if x and y are the same object. Object identity is determined using the id() function. x is not y yields the inverse truth value.

>>> a = []
>>> b = [] 
>>> id(a) == id(b)
False
>>> a is b
False
>>> a is not b
True

>>> a = b = []
>>> id(a) == id(b)
True
>>> a is b
True

Numeric Types

There are three distinct numeric types: integers, floating point numbers, and complex numbers. In addition, Booleans are a subtype of integers.

• some operations

x/y : quotient of x and y
x//y : floored quotient of x and y
x % y: remainder of x / y
pow(x, y): x to the power y
x**y : x to the power y

>>> 1 // 2
0
>>> -1 // 2
-1

>>> 0**0
1
>>> 0**1
0
>>> 1**0
1
>>> 2**0
1

• inf v.s. nan

inf: positive infinity
-inf: negative infinity
nan: Not a Number

>>> a_inf = float('inf')
>>> b_nan = float('nan')

>>> 0 * a_inf
nan
>>> 2 * a_inf
inf
>>> -2 * a_inf
-inf
>>> 1 / a_inf
0.0

>>> import math
>>> math.isnan(b_nan)
True
>>> math.isinf(a_inf)
True

>>> b_nan == b_nan
False
>>> a_inf == a_inf
True