Functions

See csse1001 for course logistics — this note covers Lecture 3A’s technical content.

Today’s outline

• What a function is and how to define one
• The return statement, and how it differs from print
• Improving functions with type hints and docstrings

Learning objectives

1. User-defined functions bundle code together and are the building blocks of more sophisticated programs.
2. return hands back a value and exits a function; it is not the same as print.
3. Functions can be documented with type hints and docstrings.

What is a function?

We have already used functions — * and max, for example — each of which takes input and returns output. User-defined functions let us name and reuse our own bundles of code, just like a mathematical function such as \(f(x) = x^2+x+1\):

>>> def f(x):
...     return x**2 + x + 1
>>> f(3)
13

See python-functions for the full syntax rules (indentation, multiple parameters, the return statement, return vs. print, type hints, and docstrings) — used throughout the rest of this note.

Building up Heron’s formula

Exercise. The area of a triangle with side lengths \(a, b, c\) is \(\sqrt{s(s-a)(s-b)(s-c)}\) where \(s = \tfrac{1}{2}(a+b+c)\) (Heron’s formula). What is the area of the triangle with sides 3, 4, and 5?

As a calculator, we’d have to type this out in full, and it would be tedious to repeat for other side lengths:

>>> (0.5*(3+4+5)
...  *(0.5*(3+4+5)-3)
...  *(0.5*(3+4+5)-4)
...  *(0.5*(3+4+5)-5))**0.5
6.0

Using names and sequencing (see 2025-08-04-python-memory-model) avoids repeating the same sub-expression:

>>> a, b, c = 3, 4, 5
>>> s = (a + b + c)/2
>>> (s*(s-a)*(s-b)*(s-c))**0.5
6.0

Wrapping it in a function makes it reusable for any triangle:

>>> def heron(a, b, c):
...     s = (a + b + c)/2
...     return (s*(s-a)*(s-b)*(s-c))**0.5
>>> heron(3, 4, 5)
6.0

Improving the function

Adding type hints and a docstring (see python-functions):

>>> def triangle_area(a: float, b: float, c: float) -> float:
...     """
...     Return the area of the triangle with sides length <a>,
...     <b>, and <c>.
...     Preconditions: <a>, <b>, <c> are all nonzero positive.
...     >>> triangle_area(3, 4, 5)
...     6.0
...     """
...     s = (a+b+c)/2
...     return (s*(s-a)*(s-b)*(s-c))**0.5
>>> triangle_area(2.2, 3.3, 4.4)
3.5147323866832307

See python-pep8-style-guide for the naming, spacing, and line-length conventions expected of functions like this.

return vs. print: quick check

>>> def example(x):
...     print(1*x)
...     return 3*x
...     print(2*x)   # never runs -- return already exited the function
>>> a = example(1)
1
>>> a
3

>>> def foo(x):
...     if x > 0:
...         print("Positive")
...     if x > 10**5:
...         print("Large positive")
>>> ans = foo(10**6)
Positive
Large positive
>>> type(ans)
<class 'NoneType'>

foo above never hits a return, so it defaults to returning None even though it printed something. Contrast with a version that returns instead:

>>> def bar(x):
...     if x > 0:
...         return "Positive"
...     if x > 10**5:
...         return "Large positive"
>>> ans = bar(10**6)
>>> ans
'Positive'

bar exits at the very first return it reaches, so "Large positive" is never returned even though x > 10**5 is also true.

Exercise: the middle number

Write a function that takes three integers and returns the number that is not the largest or the smallest:

def middle_number(x: int, y: int, z: int) -> int:
    """
    Return the number that is not the largest or smallest
    among the three inputs.
    Precondition: the numbers are distinct.
    >>> middle_number(3, 1, 2)
    2
    >>> middle_number(2, 3, 1)
    2
    """
    return (x + y + z) - min(x, y, z) - max(x, y, z)

Summary

Blocks of code can be grouped into functions. Functions take zero or more inputs and hand back a single value designated by return.

Next lecture

2025-08-11-sequence-selection-and-iteration — selection.