class: center, middle, inverse # Functions --- ## Functions 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. We have already seen one example of a function call: ``` >>> type(42) <class 'int'> ``` The name of the function is `type`. The expression in parentheses is called the **argument** of the function. The **result**, for this function, is the type of the argument. --- ## The `int` Function It is common to say that a function __takes__ an **argument** and __returns__ a **result**. The result is also called the **return value**. Python provides functions that convert values from one type to another. The `int` function takes any value and converts it to an integer, if it can, or complains otherwise: ``` >>> int('32') 32 >>> int('Hello') ValueError: invalid literal for int(): Hello ``` --- ## `int` and `float` `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` converts integers and strings to floating-point numbers: ``` >>> float(32) 32.0 >>> float('3.14159') 3.14159 ``` --- ## `str` `str` converts its argument to a string: ``` >>> str(32) '32' >>> str(3.14159) '3.14159' ``` --- ## Math Functions Python has a math **module** that provides most of the familiar mathematical functions. A module is a file that contains a collection of related 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)> ``` --- ## Math Functions 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) ``` --- ## Math Functions To convert from degrees to radians, divide by 180 and multiply by pi: ``` >>> degrees = 45 >>> radians = degrees / 180.0 * math.pi >>> math.sin(radians) 0.707106781187 ``` The expression `math.pi` gets the variable pi from the math module. Its value is a floating point approximation of pi, accurate to about 15 digits. If you know trigonometry, you can check the previous result by comparing it to the square root of two divided by two: ``` >>> math.sqrt(2) / 2.0 0.707106781187 ``` --- ## Composition 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)) ``` --- ## Composition 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. ``` >>> minutes = hours * 60 # right >>> hours * 60 = minutes # wrong! SyntaxError: can't assign to operator ``` --- ## 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. ``` 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 `print_lyrics`. The rules for function names are the same as for variable names: letters, numbers and underscore are legal, but the first character can’t be a number. You can’t use a keyword as the name of a function, and you should avoid having a variable and a function with the same name. --- ## Adding New Functions ``` def print_lyrics(): print("I'm a lumberjack, and I'm okay.") print("I sleep all night and I work all day.") ``` The empty parentheses after the name indicate that this function doesn’t take any arguments. 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. --- ## Defining Functions in Interactive Mode If you type a function definition in interactive mode, the interpreter prints dots `...` to let you know that the definition isn’t complete: ``` >>> 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. --- ## Calling Your New 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 repeat_lyrics: ``` def repeat_lyrics(): print_lyrics() print_lyrics() ``` And then call repeat_lyrics: ``` >>> repeat_lyrics() ``` --- ## Putting Everything Together... Here's a whole program: ``` 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() ``` Function definitions get executed just like other statements, but the effect is to create function objects. The statements inside the function do not run until the function is called, and the function definition generates no output. --- ## Flow of Execution 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. 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. --- ## Flow of Execution 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. --- ## 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. Inside the function, the arguments are assigned to variables called **parameters**. Here is a definition for a function that takes an argument: ``` 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. --- ## Arguments Our 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 ``` --- ## Arguments The same rules of composition that apply to built-in functions also apply to programmer-defined functions, so we can use any kind of expression as an argument for `print_twice`: ``` >>> print_twice('Spam '*4) Spam Spam Spam Spam Spam Spam Spam Spam >>> print_twice(math.cos(math.pi)) -1.0 -1.0 ``` The argument is evaluated before the function is called, so in the examples the expressions 'Spam '*4 and math.cos(math.pi) are only evaluated once. --- ## Arguments 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); here in `print_twice`, we call everybody `bruce`. --- ## Variables and Parameters are Local When you create a variable inside a function, it is **local**, which means that it only exists inside the function. For example: ``` def cat_twice(part1, part2): cat = part1 + part2 print_twice(cat) ``` This function takes two arguments, concatenates them, and prints the result twice. Here is an example that uses it: ``` >>> line1 = 'Bing tiddle ' >>> line2 = 'tiddle bang.' >>> cat_twice(line1, line2) Bing tiddle tiddle bang. Bing tiddle tiddle bang. ``` --- ## Scope When `cat_twice` terminates, the variable `cat` is destroyed. If we try to print it, we get an exception: ``` >>> print(cat) NameError: name 'cat' is not defined ``` Parameters are also local. For example, outside `print_twice`, there is no such thing as bruce. The places in your program where a variable exists is called it's **scope**. --- ## Stack Trace 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 the beginning. For example, if you try to access `cat` from within `print_twice`, you get a `NameError`: ``` 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 ``` `__main__` is a special name for the whole program, or the biggest scope. When you create a variable outside of any function, it belongs to `__main__`. --- ## Value-Returning Functions and Void Functions Some of the functions we have used, such as the math functions, return results. Other functions, like print_twice, perform an action but don’t return a value. They are called **void functions**. When you call a value-returning 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 ``` --- ## Return Values in Interactive Mode When you call a function in interactive mode, Python displays the result: ``` >>> math.sqrt(5) 2.2360679774997898 ``` But in a script, if you don't do something with the return value from a function, it is lost forever! ``` math.sqrt(5) ``` This script computes the square root of 5, but since it doesn’t store or display the result, it is not very useful. --- ## Void Functions Void functions might display something on the screen or have some other effect, but they don’t have a return value. If you assign the result to a variable, you get a special value called `None`. ``` >>> result = print_twice('Bing') Bing Bing >>> print(result) None ``` The value `None` is not the same as the string `'None'`. It is a special value that has its own type: ``` >>> type(None) <class 'NoneType'> ``` --- ## Why Functions? - Creating a new function gives you an opportunity to name a group of statements, which makes your program easier to read and debug. - Functions can make a program smaller by eliminating repetitive code. Later, if you make a change, you only have to make it in one place. - Dividing a long program into functions allows you to debug the parts one at a time and then assemble them into a working whole. - Well-designed functions are often useful for many programs. Once you write and debug one, you can reuse it. --- class: center, middle, inverse # Vocabulary --- ## Vocabulary function: A named sequence of statements that performs some useful operation. Functions may or may not take arguments and may or may not produce a result. function definition: A statement that creates a new function, specifying its name, parameters, and the statements it contains. function object: A value created by a function definition. The name of the function is a variable that refers to a function object. header: The first line of a function definition. body: The sequence of statements inside a function definition. --- ## Vocabulary parameter: A name used inside a function to refer to the value passed as an argument. function call: A statement that runs a function. It consists of the function name followed by an argument list in parentheses. argument: A value provided to a function when the function is called. This value is assigned to the corresponding parameter in the function. local variable: A variable defined inside a function. A local variable can only be used inside its function. return value: The result of a function. If a function call is used as an expression, the return value is the value of the expression. --- ## Vocabulary void function: A function that always returns None. None: A special value returned by void functions. module: A file that contains a collection of related functions and other definitions. import statement: A statement that reads a module file and creates a module object. module object: A value created by an import statement that provides access to the values defined in a module. --- ## Vocabulary dot notation: The syntax for calling a function in another module by specifying the module name followed by a dot (period) and the function name. composition: Using an expression as part of a larger expression, or a statement as part of a larger statement. flow of execution: The order statements run in. stack diagram: A graphical representation of a stack of functions, their variables, and the values they refer to. stack trace: A list of the functions that are executing, printed when an exception occurs.