Chapter 3 Functions
In the context of programming, a function is a named sequence of statements that performs a computation. When you define a function, you specify the name and the sequence of statements. Later, you can “call” the function by name.
3.1 Function calls
We have already seen one example of a function call:
>>> type(42) <class 'int'>
>>> int('32') 32 >>> int('Hello') ValueError: invalid literal for int(): Hello
int can convert floating-point values to integers, but it doesn’t round off; it chops off the fraction part:
>>> int(3.99999) 3 >>> int(-2.3) -2
>>> float(32) 32.0 >>> float('3.14159') 3.14159
>>> str(32) '32' >>> str(3.14159) '3.14159'
3.2 Math functions
Before we can use the functions in a module, we have to import it with an import statement:
>>> import math
This statement creates a module object named math. If you display the module object, you get some information about it:
>>> math <module 'math' (built-in)>
The module object contains the functions and variables defined in the module. To access one of the functions, you have to specify the name of the module and the name of the function, separated by a dot (also known as a period). This format is called dot notation.
>>> ratio = signal_power / noise_power >>> decibels = 10 * math.log10(ratio) >>> radians = 0.7 >>> height = math.sin(radians)
The first example uses
The second example finds the sine of radians. The variable name radians is a hint that sin and the other trigonometric functions (cos, tan, etc.) take arguments in radians. To convert from degrees to radians, divide by 180 and multiply by π:
>>> degrees = 45 >>> radians = degrees / 180.0 * math.pi >>> math.sin(radians) 0.707106781187
>>> math.sqrt(2) / 2.0 0.707106781187
So far, we have looked at the elements of a program—variables, expressions, and statements—in isolation, without talking about how to combine them.
One of the most useful features of programming languages is their ability to take small building blocks and compose them. For example, the argument of a function can be any kind of expression, including arithmetic operators:
x = math.sin(degrees / 360.0 * 2 * math.pi)
And even function calls:
x = math.exp(math.log(x+1))
Almost anywhere you can put a value, you can put an arbitrary expression, with one exception: the left side of an assignment statement has to be a variable name. Any other expression on the left side is a syntax error (we will see exceptions to this rule later).
>>> minutes = hours * 60 # right >>> hours * 60 = minutes # wrong! SyntaxError: can't assign to operator
3.4 Adding new functions
So far, we have only been using the functions that come with Python, but it is also possible to add new functions. A function definition specifies the name of a new function and the sequence of statements that run when the function is called.
Here is an example:
def print_lyrics(): print("I'm a lumberjack, and I'm okay.") print("I sleep all night and I work all day.")
def is a keyword that indicates that this is a function
definition. The name of the function is
The first line of the function definition is called the header; the rest is called the body. The header has to end with a colon and the body has to be indented. By convention, indentation is always four spaces. The body can contain any number of statements.
The strings in the print statements are enclosed in double quotes. Single quotes and double quotes do the same thing; most people use single quotes except in cases like this where a single quote (which is also an apostrophe) appears in the string.
All quotation marks (single and double) must be “straight quotes”, usually located next to Enter on the keyboard. “Curly quotes”, like the ones in this sentence, are not legal in Python.
>>> def print_lyrics(): ... print("I'm a lumberjack, and I'm okay.") ... print("I sleep all night and I work all day.") ...
To end the function, you have to enter an empty line.
>>> print(print_lyrics) <function print_lyrics at 0xb7e99e9c> >>> type(print_lyrics) <class 'function'>
The syntax for calling the new function is the same as for built-in functions:
>>> print_lyrics() I'm a lumberjack, and I'm okay. I sleep all night and I work all day.
Once you have defined a function, you can use it inside another
function. For example, to repeat the previous refrain, we could write
a function called
def repeat_lyrics(): print_lyrics() print_lyrics()
And then call
>>> repeat_lyrics() I'm a lumberjack, and I'm okay. I sleep all night and I work all day. I'm a lumberjack, and I'm okay. I sleep all night and I work all day.
But that’s not really how the song goes.
3.5 Definitions and uses
Pulling together the code fragments from the previous section, the whole program looks like this:
def print_lyrics(): print("I'm a lumberjack, and I'm okay.") print("I sleep all night and I work all day.") def repeat_lyrics(): print_lyrics() print_lyrics() repeat_lyrics()
This program contains two function definitions:
As you might expect, you have to create a function before you can run it. In other words, the function definition has to run before the function gets called.
As an exercise, move the last line of this program to the top, so the function call appears before the definitions. Run the program and see what error message you get.
Now move the function call back to the bottom
and move the definition of
3.6 Flow of execution
To ensure that a function is defined before its first use, you have to know the order statements run in, which is called the flow of execution.
Execution always begins at the first statement of the program. Statements are run one at a time, in order from top to bottom.
Function definitions do not alter the flow of execution of the program, but remember that statements inside the function don’t run until the function is called.
A function call is like a detour in the flow of execution. Instead of going to the next statement, the flow jumps to the body of the function, runs the statements there, and then comes back to pick up where it left off.
That sounds simple enough, until you remember that one function can call another. While in the middle of one function, the program might have to run the statements in another function. Then, while running that new function, the program might have to run yet another function!
Fortunately, Python is good at keeping track of where it is, so each time a function completes, the program picks up where it left off in the function that called it. When it gets to the end of the program, it terminates.
In summary, when you read a program, you don’t always want to read from top to bottom. Sometimes it makes more sense if you follow the flow of execution.
3.7 Parameters and arguments
Some of the functions we have seen require arguments. For example, when you call math.sin you pass a number as an argument. Some functions take more than one argument: math.pow takes two, the base and the exponent.
def print_twice(bruce): print(bruce) print(bruce)
This function assigns the argument to a parameter named bruce. When the function is called, it prints the value of the parameter (whatever it is) twice.
This function works with any value that can be printed.
>>> print_twice('Spam') Spam Spam >>> print_twice(42) 42 42 >>> print_twice(math.pi) 3.14159265359 3.14159265359
>>> print_twice('Spam '*4) Spam Spam Spam Spam Spam Spam Spam Spam >>> print_twice(math.cos(math.pi)) -1.0 -1.0
You can also use a variable as an argument:
>>> michael = 'Eric, the half a bee.' >>> print_twice(michael) Eric, the half a bee. Eric, the half a bee.
The name of the variable we pass as an argument (michael) has
nothing to do with the name of the parameter (bruce). It
doesn’t matter what the value was called back home (in the caller);
3.8 Variables and parameters are local
def cat_twice(part1, part2): cat = part1 + part2 print_twice(cat)
>>> line1 = 'Bing tiddle ' >>> line2 = 'tiddle bang.' >>> cat_twice(line1, line2) Bing tiddle tiddle bang. Bing tiddle tiddle bang.
>>> print(cat) NameError: name 'cat' is not defined
3.9 Stack diagrams
To keep track of which variables can be used where, it is sometimes useful to draw a stack diagram. Like state diagrams, stack diagrams show the value of each variable, but they also show the function each variable belongs to.
Each function is represented by a frame. A frame is a box with the name of a function beside it and the parameters and variables of the function inside it. The stack diagram for the previous example is shown in Figure 3.1.
The frames are arranged in a stack that indicates which function
called which, and so on. In this example,
Each parameter refers to the same value as its corresponding argument. So, part1 has the same value as line1, part2 has the same value as line2, and bruce has the same value as cat.
If an error occurs during a function call, Python prints the
name of the function, the name of the function that called
it, and the name of the function that called that, all the
way back to
For example, if you try to access cat from within
Traceback (innermost last): File "test.py", line 13, in __main__ cat_twice(line1, line2) File "test.py", line 5, in cat_twice print_twice(cat) File "test.py", line 9, in print_twice print(cat) NameError: name 'cat' is not defined
This list of functions is called a traceback. It tells you what program file the error occurred in, and what line, and what functions were executing at the time. It also shows the line of code that caused the error.
The order of the functions in the traceback is the same as the order of the frames in the stack diagram. The function that is currently running is at the bottom.
3.10 Fruitful functions and void functions
Some of the functions we have used, such as the math functions, return
results; for lack of a better name, I call them fruitful
functions. Other functions, like
When you call a fruitful function, you almost always want to do something with the result; for example, you might assign it to a variable or use it as part of an expression:
x = math.cos(radians) golden = (math.sqrt(5) + 1) / 2
When you call a function in interactive mode, Python displays the result:
>>> math.sqrt(5) 2.2360679774997898
But in a script, if you call a fruitful function all by itself, the return value is lost forever!
>>> result = print_twice('Bing') Bing Bing >>> print(result) None
The value None is not the same as the string
>>> type(None) <class 'NoneType'>
3.11 Why functions?
It may not be clear why it is worth the trouble to divide a program into functions. There are several reasons:
In some ways debugging is like detective work. You are confronted with clues and you have to infer the processes and events that led to the results you see.
Debugging is also like an experimental science. Once you have an idea about what is going wrong, you modify your program and try again. If your hypothesis was correct, you can predict the result of the modification, and you take a step closer to a working program. If your hypothesis was wrong, you have to come up with a new one. As Sherlock Holmes pointed out, “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.” (A. Conan Doyle, The Sign of Four)
For some people, programming and debugging are the same thing. That is, programming is the process of gradually debugging a program until it does what you want. The idea is that you should start with a working program and make small modifications, debugging them as you go.
For example, Linux is an operating system that contains millions of lines of code, but it started out as a simple program Linus Torvalds used to explore the Intel 80386 chip. According to Larry Greenfield, “One of Linus’s earlier projects was a program that would switch between printing AAAA and BBBB. This later evolved to Linux.” (The Linux Users’ Guide Beta Version 1).
Write a function named
>>> right_justify('monty') monty
Hint: Use string concatenation and repetition. Also,
Python provides a built-in function called len that
returns the length of a string, so the value of
A function object is a value you can assign to a variable
or pass as an argument. For example,
def do_twice(f): f() f()
Here’s an example that uses
def print_spam(): print('spam') do_twice(print_spam)
Note: This exercise should be done using only the statements and other features we have learned so far.
Solution: http://thinkpython2.com/code/grid.py. Credit: This exercise is based on an exercise in Oualline, Practical C Programming, Third Edition, O’Reilly Media, 1997.
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