In this article, we’re going to look at a common programming pattern and discuss how we can refactor our code when we notice this pattern. 🏗
We’ll be discussing how to make code with this shape a little more descriptive:
1 2 3 4 5 

An Example: Primality
Here’s a function that checks whether a given number is prime by trying to divide it by all numbers below it:
1 2 3 4 5 

Note: a square root makes this faster and our code breaks below 2
but we’ll ignore those issues here
This function:
 loops from 2 to the given number
 returns
False
as soon as a divisor is found  returns
True
if no divisor was found
This primality check is asking “do any numbers evenly divide the candidate number”.
Note that this function returns as soon as it finds a divisor, so it only iterates all the way through the number range when the candidate number is prime.
Let’s take a look at how we can rewrite this function using all
.
What’s all
?
Python has a builtin function all
that returns True
if all items are truthy
1 2 3 4 5 6 7 8 

You can think of truthy as meaning nonempty or nonzero (Python chat on truthiness). For our purposes, we’ll treat it as pretty much the same as True
.
The all
builtin function is equivalent to this:
1 2 3 4 5 

Notice the similarity between all
and our is_prime
function? Our is_prime
function is similar, but they’re not quite the same structure.
The all
function checks for the truthiness of element
, but we need something a little more than that: we need to check a condition on each element (whether it’s a divsior).
Using all
Our original is_prime
function looks like this:
1 2 3 4 5 

If we want to use all
in this function, we need an iterable (like a list) to pass to all
.
If we wanted to be really silly, we could make such a list of boolean values like this:
1 2 3 4 5 6 7 8 

We could simplify this function like this:
1 2 3 4 5 

I know this is probably doesn’t seem like progress, but bear with me for a few more steps…
List comprehensions
If you’re familiar with list comprehensions, this code structure might look a little familiar. We’re creating one iterable from another which is exactly what list comprehensions are good for.
Let’s copypaste our way into a list comprehension (see my article on how to write list comprehensions):
1 2 3 4 5 6 

That’s quite a bit shorter, but there’s a problem: we’re building up an entire list just to loop over it once!
This is less efficient than our original approach, which only looped all the way when candidate
was prime.
Let’s fix this inefficiency by turning our list comprehension into a generator expression.
Generator expressions
A generator expression is like a list comprehension, but instead of making a list it makes a generator (Python chat on generators).
A generator is a lazy iterable: generators don’t compute the items they contain until you loop over them. We’ll see what that means in a moment.
We can turn our list comprehension into a generator expression by changing the brackets to parentheses:
1 2 3 4 5 6 

Now our code doesn’t create a list to loop over. Instead it provides us with a generator that allows us to compute the divisibility of each number onebyone.
We can make this code even more readable by putting that generator expression inside the function call (notice that we can drop the second set of parentheses):
1 2 3 4 5 

Note that because our generator is lazy, we stop computing divisibilities as soon as our all
function finds a divisible number. So we end up calculating candidate % n != 0
only as many times as we did in our original function.
Recap
So we started with a for
loop, an if
statement, a return
statement for stopping once we find a divisor, and a return
statement for the case where our number had no divisors (when it’s prime).
1 2 3 4 5 

We turned all that into a generator expression passed to the all
function.
1 2 3 4 5 

I prefer this second approach (a generator expression with all
) because I find it more descriptive.
We’re checking to see whether “all numbers in a range are not divisors of our candidate number”. That sounds quite a bit more like English to me than “loop over all numbers in a range and return False if a divisor is found otherwise return True”.
If you don’t find the behavior of all
intuitive, you might find it easier to understand (and more Englishlike) when used with if
:
1 2 3 4 

You can always reformat your code to use an if
statement if you find it more readable.
any
or all
We’ve been working with the all
function, but I haven’t mentioned it’s counterpart: the any
function. Let’s take a look at how all
and any
compare.
These two expressions:
1 2 3 4 5 6 7 8 

Are equivalent to these two expressions (because of DeMorgan’s Laws):
1 2 3 4 5 6 7 8 

So this code:
1 2 3 4 5 

Is featureidentical to this code:
1 2 3 4 5 

Both of them stop as soon as they find a divisor.
I find the use of all
more readable here, but I wanted to mention that any
would work just as well.
Cheat sheet for refactoring with any
and all
All that explanation above was valuable, but how can we use this new knowledge to refactor our own code? Here’s a cheat sheet for you.
Anytime you see code like this:
1 2 3 4 5 

You can replace that code with this:
1 2 3 4 

Anytime you see code like this:
1 2 3 4 5 

You can replace it with this:
1 2 3 4 

Note that break
is used in the code above because we’re not returning from a function. Using return
(like we did in is_prime
) is another way to stop our loop early.
Python’s any
and all
functions were made for use with generator expressions (discussion here and here). You can use any
and all
without generator expressions, but I don’t find a need for that as often.
Quick note: any(item == 'something' for item in iterable)
is the same as 'something' in iterable
. Don’t use all
/any
for checking containment, use in
.
Code style is a process
As you discover new Python idioms and new language features are invented, your code style will evolve. Your preferred code style may never stop evolving. Code style is not concrete: it’s a process.
I hope I’ve inspired you to embrace the use of any
/all
with generator expressions for improved readability and code clarity.
If you’d like to get practice with the any
and all
functions right now, sign up for Python Morsels using the form below to get an exercise that benefits from using one of these two functions.
I made Python Morsels to help experienced programmers level up their Python skills every week. For more details on it, see the Python Morsels website.