\index{boolean expression} \index{expression!boolean} \index{logical operator} \index{operator!logical}
A boolean expression is an expression that is either
true or false. The following examples use the operator ==,
which compares two operands and produces True if they are
equal and False otherwise:
>>> 5 == 5
True
>>> 5 == 6
False
True and False are special values that belong
to the class bool; they are not strings:
\index{True special value} \index{False special value} \index{special value!True} \index{special value!False} \index{bool type} \index{type!bool}
>>> type(True)
<class 'bool'>
>>> type(False)
<class 'bool'>
The == operator is one of the comparison
operators; the others are:
x != y # x is not equal to y
x > y # x is greater than y
x < y # x is less than y
x >= y # x is greater than or equal to y
x <= y # x is less than or equal to y
x is y # x is the same as y
x is not y # x is not the same as y
Although these operations are probably familiar to you, the Python
symbols are different from the mathematical symbols for the same
operations. A common error is to use a single equal sign
(=) instead of a double equal sign (==).
Remember that = is an assignment operator and
== is a comparison operator. There is no such thing as
=< or =>.
\index{comparison operator} \index{operator!comparison}
\index{logical operator} \index{operator!logical}
There are three logical operators: and,
or, and not. The semantics (meaning) of these
operators is similar to their meaning in English. For example,
x > 0 and x < 10
is true only if x is greater than 0 and less than 10.
\index{and operator} \index{or operator} \index{not operator} \index{operator!and} \index{operator!or} \index{operator!not}
n%2 == 0 or n%3 == 0 is true if either of the conditions
is true, that is, if the number is divisible by 2 or 3.
Finally, the not operator negates a boolean expression, so
not (x > y) is true if x > y is false.
>>> x = 1
>>> y = 2
>>> x > y
False
>>> not (x > y)
True
Strictly speaking, the operands of the logical operators should be boolean expressions, but Python is not very strict. Any nonzero number is interpreted as "true."
>>> 17 and True
True
This flexibility can be useful in some situations, but there are some subtleties to it that might be confusing. You might want to avoid it until you are sure you know what you are doing.
\index{conditional statement} \index{statement!conditional} \index{if statement} \index{statement!if} \index{conditional executions}
In order to write useful programs, we almost always need the ability to
check conditions and change the behavior of the program accordingly.
Conditional statements give us this ability. The
simplest form is the if statement:
if x > 0 :
print('x is positive')
The boolean expression after the if statement is called the
condition. We end the if statement with a
colon character (:) and the line(s) after the if statement are indented.
If the logical condition is true, then the indented statement gets executed. If the logical condition is false, the indented statement is skipped.
\index{condition} \index{compound statement} \index{statement!compound}
if statements have the same structure as function
definitions or for loops^[We will learn about functions in Chapter 4 and loops in Chapter 5.].
The statement consists of a
header line that ends with the colon character (:) followed by an
indented block. Statements like this are called compound
statements because they stretch across more than one line.
if x > y:
print(x)
print(y)
There is no limit on the number of statements that can appear in the
body, but there must be at least one. Occasionally, it is useful to have
a body with no statements (usually as a place holder for code you haven't
written yet). In that case, you can use the pass statement to pass the Python interpreter check,
which does nothing.
\index{pass statement} \index{statement!pass}
if x < 0 :
pass # need to handle negative values, do nothing for now.
If you enter an if statement in the Python interpreter, the
prompt will change from three chevrons (>>>) to three dots (...) to indicate you are
in the middle of a block of statements, as shown below:
>>> x = 3
>>> if x < 10:
... print('Small')
...
Small
>>>
When using the Python interpreter, you must leave a blank line at the end of a block, otherwise Python will return an error:
>>> x = 3
>>> if x < 10:
... print('Small')
... print('Done')
File "<stdin>", line 3
print('Done')
^
SyntaxError: invalid syntax
A blank line at the end of a block of statements is not necessary when writing and executing a script, but it may improve readability of your code.
\index{alternative execution} \index{else keyword} \index{keyword!else}
A second form of the if statement is alternative
execution, in which there are two possibilities and the
condition determines which one gets executed. The syntax looks like
this:
if x % 2 == 0:
print('x is even')
else:
print('x is odd')
If the remainder when x is divided by 2 is 0, then we know
that x is even, and the program displays a message to that
effect. If the condition is false, the second set of statements is
executed.
Since the condition must either be true or false, exactly one of the alternatives will be executed. The alternatives are called branches, because they are branches in the flow of execution.
\index{branch}
\index{chained conditional} \index{conditional!chained}
Sometimes there are more than two possibilities and we need more than two branches. One way to express a computation like that is a chained conditional:
if x < y:
print('x is less than y')
elif x > y:
print('x is greater than y')
else:
print('x and y are equal')
elif is an abbreviation of "else if." Again, exactly one
branch will be executed.
There is no limit on the number of elif statements. If
there is an else clause, it has to be at the end, but there
doesn't have to be one.
\index{elif keyword} \index{keyword!elif}
if choice == 'a':
print('Bad guess')
elif choice == 'b':
print('Good guess')
elif choice == 'c':
print('Close, but not correct')
Each condition is checked in order. If the first is false, the next is checked, and so on. If one of them is true, the corresponding branch executes, and the statement ends. Even if more than one condition is true, only the first true branch executes.
\index{nested conditional} \index{conditional!nested}
One conditional can also be nested within another. We could have written the three-branch example like this:
if x == y:
print('x and y are equal')
else:
if x < y:
print('x is less than y')
else:
print('x is greater than y')
The outer conditional contains two branches. The first branch contains a
simple statement. The second branch contains another if
statement, which has two branches of its own. Those two branches are
both simple statements, although they could have been conditional
statements as well.
Although the indentation of the statements makes the structure apparent, nested conditionals become difficult to read very quickly. In general, it is a good idea to avoid them when you can.
Logical operators often provide a way to simplify nested conditional statements. For example, we can rewrite the following code using a single conditional:
if 0 < x:
if x < 10:
print('x is a positive single-digit number.')
The print statement is executed only when we pass
both conditionals. We can get the same effect with the
and operator:
if 0 < x and x < 10:
print('x is a positive single-digit number.')
Earlier we saw a code segment where we used the input and
int functions to read and parse an integer number entered
by the user. We also saw how treacherous doing this could be:
>>> prompt = "What is the air velocity of an unladen swallow?\n"
>>> speed = input(prompt)
What is the air velocity of an unladen swallow?
What do you mean, an African or a European swallow?
>>> int(speed)
ValueError: invalid literal for int() with
base 10: 'What do you mean, an African or a European swallow?'
>>>
When we are executing these statements in the Python interpreter, we get a new prompt from the interpreter, think "oops", and move on to our next statement.
However if you place this code in a Python script and this error occurs, your script immediately stops in its tracks with a traceback. It does not execute the following statement.
\index{traceback}
Here is a sample program to convert a Fahrenheit temperature to a Celsius temperature:
\index{fahrenheit} \index{celsius} \index{temperature conversion}
\VerbatimInput{../code3/fahren.py}
If we execute this code and give it invalid input, it simply fails with an unfriendly error message:
python fahren.py
Enter Fahrenheit Temperature:72
22.22222222222222
python fahren.py
Enter Fahrenheit Temperature:fred
Traceback (most recent call last):
File "fahren.py", line 2, in <module>
fahr = float(inp)
ValueError: could not convert string to float: 'fred'
There is a conditional execution structure built into Python to handle
these types of expected and unexpected errors called "try / except". The
purpose of try and except is that you know that
some sequence of instruction(s) may have a problem and you want to add
some statements to be executed if an error occurs. These extra
statements (the except block) are ignored if there is no error.
You can think of the try and except feature in
Python as an "insurance policy" on a sequence of statements.
We can rewrite our temperature converter as follows:
\VerbatimInput{../code3/fahren2.py}
Python starts by executing the sequence of statements in the
try block. If all goes well, it skips the
except block and proceeds. If an exception occurs in the
try block, Python jumps out of the try block
and executes the sequence of statements in the except
block.
python fahren2.py
Enter Fahrenheit Temperature:72
22.22222222222222
python fahren2.py
Enter Fahrenheit Temperature:fred
Please enter a number
Handling an exception with a try statement is called
catching an exception. In this example, the
except clause prints an error message. In general, catching
an exception gives you a chance to fix the problem, or try again, or at
least end the program gracefully.
\index{short circuit}
When Python is processing a logical expression such as
x >= 2 and (x/y) > 2, it evaluates the expression from left to right.
Because of the definition of and, if x is less
than 2, the expression x >= 2 is False and so
the whole expression is False regardless of whether
(x/y) > 2 evaluates to True or
False.
When Python detects that there is nothing to be gained by evaluating the rest of a logical expression, it stops its evaluation and does not do the computations in the rest of the logical expression. When the evaluation of a logical expression stops because the overall value is already known, it is called short-circuiting the evaluation.
\index{guardian pattern} \index{pattern!guardian}
While this may seem like a fine point, the short-circuit behavior leads to a clever technique called the guardian pattern. Consider the following code sequence in the Python interpreter:
>>> x = 6
>>> y = 2
>>> x >= 2 and (x/y) > 2
True
>>> x = 1
>>> y = 0
>>> x >= 2 and (x/y) > 2
False
>>> x = 6
>>> y = 0
>>> x >= 2 and (x/y) > 2
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ZeroDivisionError: division by zero
>>>
The third calculation failed because Python was evaluating
(x/y) and y was zero, which causes a runtime
error. But the first and the second examples did not fail because in the first calculation y was non zero and in the second one the first part of
these expressions x >= 2 evaluated to False so
the (x/y) was not ever executed due to the
short-circuit rule and there was no error.
We can construct the logical expression to strategically place a guard evaluation just before the evaluation that might cause an error as follows:
>>> x = 1
>>> y = 0
>>> x >= 2 and y != 0 and (x/y) > 2
False
>>> x = 6
>>> y = 0
>>> x >= 2 and y != 0 and (x/y) > 2
False
>>> x >= 2 and (x/y) > 2 and y != 0
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ZeroDivisionError: division by zero
>>>
In the first logical expression, x >= 2 is
False so the evaluation stops at the and. In
the second logical expression, x >= 2 is True
but y != 0 is False so we never reach
(x/y).
In the third logical expression, the y != 0 is after the
(x/y) calculation so the expression fails with an error.
In the second expression, we say that y != 0 acts as a
guard to insure that we only execute (x/y)
if y is non-zero.
\index{debugging} \index{traceback}
The traceback Python displays when an error occurs contains a lot of information, but it can be overwhelming. The most useful parts are usually:
-
What kind of error it was, and
-
Where it occurred.
Syntax errors are usually easy to find, but there are a few gotchas. Whitespace errors can be tricky because spaces and tabs are invisible and we are used to ignoring them.
\index{whitespace}
>>> x = 5
>>> y = 6
File "<stdin>", line 1
y = 6
^
IndentationError: unexpected indent
In this example, the problem is that the second line is indented by one
space. But the error message points to y, which is
misleading. In general, error messages indicate where the problem was
discovered, but the actual error might be earlier in the code, sometimes
on a previous line.
In general, error messages tell you where the problem was discovered, but that is often not where it was caused.
body : The sequence of statements within a compound statement. \index{body}
boolean expression
: An expression whose value is either True or False.
\index{boolean expression}
\index{expression!boolean}
branch : One of the alternative sequences of statements in a conditional statement. \index{branch}
chained conditional : A conditional statement with a series of alternative branches. \index{chained conditional} \index{conditional!chained}
comparison operator
: One of the operators that compares its operands: ==,
!=, >, <, >=, and <=.
conditional statement : A statement that controls the flow of execution depending on some condition. \index{conditional statement} \index{statement!conditional}
condition : The boolean expression in a conditional statement that determines which branch is executed. \index{condition}
compound statement : A statement that consists of a header and a body. The header ends with a colon (:). The body is indented relative to the header. \index{compound statement}
guardian pattern : Where we construct a logical expression with additional comparisons to take advantage of the short-circuit behavior. \index{guardian pattern} \index{pattern!guardian}
logical operator
: One of the operators that combines boolean expressions:
and, or, and not.
nested conditional : A conditional statement that appears in one of the branches of another conditional statement. \index{nested conditional} \index{conditional!nested}
traceback : A list of the functions that are executing, printed when an exception occurs. \index{traceback}
short circuit : When Python is part-way through evaluating a logical expression and stops the evaluation because Python knows the final value for the expression without needing to evaluate the rest of the expression. \index{short circuit}
Exercise 1: Rewrite your pay computation to give the employee 1.5 times the hourly rate for hours worked above 40 hours.
Enter Hours: 45
Enter Rate: 10
Pay: 475.0
Exercise 2: Rewrite your pay program using try and
except so that your program handles non-numeric input
gracefully by printing a message and exiting the program. The following
shows two executions of the program:
Enter Hours: 20
Enter Rate: nine
Error, please enter numeric input
Enter Hours: forty
Error, please enter numeric input
Exercise 3: Write a program to prompt for a score between 0.0 and 1.0. If the score is out of range, print an error message. If the score is between 0.0 and 1.0, print a grade using the following table:
Score Grade
>= 0.9 A
>= 0.8 B
>= 0.7 C
>= 0.6 D
< 0.6 F
Enter score: 0.95
A
Enter score: perfect
Bad score
Enter score: 10.0
Bad score
Enter score: 0.75
C
Enter score: 0.5
F
Run the program repeatedly as shown above to test the various different values for input.