Why is 'not(True) * True' valid syntax, unlike 'True * not(True)'? [duplicate]

Question

Is this a consequence of the hierarchical order of operators in Python?

not(True) * True
# False
True * not(True)
# SyntaxError: invalid syntax

Answer 1

Is this a consequence of the hierarchical order of operators in Python?

Yes (although the usual term is operator precedence). Summing up and simplifying:

1. not isn't a function; it's an operator. Therefore, we don't need to write parentheses for not (True), and in fact they don't do anything here. All that happens is that the parentheses are treated as ordinary grouping parentheses - (True) is evaluated before anything else, becoming True. So, let's consider the examples without the parentheses.

2. not True * True means not (True * True). It does not mean (not True) * True, due to operator precedence. This is by design:

   >>> not 1 * 0
   True
   >>> not (1 * 0)
   True
   >>> (not 1) * 0
   0
   

   It would, the developers figured, be unexpected to write something like not 1 * 0 and get an integer result, and unexpected to write not in front of a mathematical operation and have the not only apply to the first thing in that expression.

3. Because of that same operator precedence, True * not True is a syntax error. Python parses the not by itself as the right-hand side of the *, because it hasn't yet worked out to put not True together. True * not is obviously nonsense. Or, another way of looking at it: "not followed by an expression" isn't in the list of "things that can be an operand for *".

   This is perhaps surprising because the other commonly used unary operator, - (i.e., unary negation), doesn't have this issue. But that's because the precedence is the other way around: unary negation is processed before multiplication, not after.

   The same is true for and and or combinations:

   >>> 3 * 5 and 1 # 3 * 5 is evaluated first
   1
   >>> 3 * (5 and 1)
   3
   >>> 3 or 1 * 5 # 1 * 5 is evaluated first, even though it comes later
   3
   >>> (3 or 1) * 5
   15