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# Pure functions
Throughout Lustre's documentation you may come across references to _purity_ or
_pure functions_. Lustre makes some fundamental assumptions around purity in your
programs so it's important to know what it means!
## Functions as formulas
Outside of programming, the concept of a "function" exists in mathematics too.
There, they are sometimes referred to as _formulas_ and you might have already
encountered them in school, something like:
```
f(x) = 3x
```
Or "a function over `x` is equal to `3` times `x`". Let's jump back to Gleam and
write that function again:
```gleam
fn f(x) {
3 * x
}
```
Functions like this are _pure_. They take an input, perform some computation, and
return an output. The output is _only_ determined by the input, and the function
doesn't change anything about the outside world like writing to a file or making
an HTTP request.
**Lustre assumes your `init`, `update`, and `view` functions are pure** and breaking
this assumption can lead to unexpected behaviour. It is _really_ important to
make sure these functions are pure!
## Functions as procedures
Of course, what sets programming apart from mathematics is that we _can_ have
side effects in our programs. You may sometimes see functions that perform side
effects referred to as _procedures_, and they are useful too!
Lustre may expect your `init`, `update`, and `view` functions to be pure, but
that doesn't mean _Gleam_ does. To learn more about how Lustre handles side
effects and procedures, check out the [side effects guide](https://hexdocs.pm/lustre/guide/03-side-effects.html).
## Other resources
Here are some other resources from around the Web that you might also find useful:
- [Keeping components pure](https://react.dev/learn/keeping-components-pure) from
the React docs.
- [Pure functions](https://elmprogramming.com/pure-functions.html) from the
"Beginning Elm" book.
- [Pure functions](https://en.wikipedia.org/wiki/Pure_function) from Wikipedia.
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