Functions

But what can you really do with all of these different expressions? If you combine them into functions, quite a bit.

What are Functions?

As with algebra, a function is something that takes one or more inputs, does something with this input, and returns an output. Let's start with an example that takes no inputs:

$$ f() = 5 $$

This function always returns $5$. Let's see how we would implement this in Python:

def f():
    return 5

We can use this function over and over:

>>> f()
5
>>> y = f()
>>> y
5
>>> y = 6
>>> y
6
>>> f()
5

Notice that assigning y to f() will assign it to the result of calling f(), not the function itself. So, changing y to 6 doesn't change the return value of f().

Anatomy of a Function

Before we analyze the anatomy of a function, let's look at another one.

$$ g(x) = x + 2 $$

This function, in math, takes an input $x$ and returns $x+2$. In Python, this looks like:

def g(x):
    return x + 2

We can use this as follows:

>>> g(5)
7
>>> z = g(2)
>>> z
4
>>> z = 5
>>> z
5
>>> g(2)
4
>>> g(3)
5

Let's break down this function.

def g(x):           # there's a function coming called `g` that takes one input `x`
    return x + 2    # `g` returns `x+2`

Note that a function can have more than one line, but only one return statement.

def h(x):           # there's a function coming called `h` that takes one input `x`
    y = x + 2       # assign `y` to `x+2`
    return y        # `h` returns `y`

This function does that exact same thing as g, but it first assigns x+2 to a new variable before returning that new variable.

Some Built-in Functions

Python comes with a number of functions that you may find useful. We'll discover more later, but here's a few.

>>> print('Hello!')        # print the value inside the parentheses, without quotes.
Hello!
>>> print(print('Hello!')) # see the next section to understand how this is evaluated.
Hello!                     # the `print` function prints the input...
None                       # ...but note that it returns None, which is a representation of nothing.
>>> min(2, 5)              # return the minimum of two or more numbers, separated by commas.
2
>>> max(2, 5)              # return the maximum of two or more numbers, separated by commas.
5

Evaluation

The way a function is evaluated is key to understanding how it works. Essentially, Python tries to evaluate every operand before evaluating the operator. In h(x), h is the operator and x is the operand.

We'll use the functions add and mul for this example, so you can see a PEMDAS-style operation. These functions are in the operator package, which you'll learn about in a later week. For now, ignore the import statement in the example below.

>>> from operator import mul, add
>>> add(5, mul(add(5, 2), 4))
33

So what happened here?

• Well, Python tried to evaluate 5, then mul(add(5, 2), 4).
  • In evaluating the second expression, Python tried to evaluate add(5, 2) and 4.
    • In evaluating the first expression, Python tried to evaluate 5 and 2.
    • Those were already evaluated, so the innermost add function executed and returned 7.
  • Now, the mul function's parameters became 7 and 4, so the mul function executed and returned 28.
• Lastly, the outermost add function's parameters became 5 and 28, so the function executed and returned 33.