# Functional Usage of Rust

Rust is an imperative language, but it follows many functional programming paradigms.
One of the biggest hurdles to understanding functional programs when coming from an imperative background is the shift in thinking.
Imperative programs describe __how__ to do something, whereas declarative programs describe __what__ to do.
Let's sum the numbers from 1 to 10 to show this.

## Imperative

```rust
let mut sum = 0;
for i in 1..11 {
    sum += i;
}
println!("{}", sum);
```

With imperative programs, we have to play compiler to see what is happening.
Here, we start with a `sum` of `0`.
Next, we iterate through the range from 1 to 10.
Each time through the loop, we add the corresponding value in the range.
Then we print it out.

| `i` | `sum` |
|:---:|:-----:|
|   1 |     1 |
|   2 |     3 |
|   3 |     6 |
|   4 |    10 |
|   5 |    15 |
|   6 |    21 |
|   7 |    28 |
|   8 |    36 |
|   9 |    45 |
|  10 |    55 |

This is how most of us start out programming. We learn that a program is a set of steps.

## Declarative

```rust
println!("{}", (1..11).fold(0, |a, b| a + b));
```

Whoa! This is really different! What's going on here? Remember that with declarative programs
we are describing __what__ to do, rather than __how__ to do it.
`fold` is a function that [composes](https://en.wikipedia.org/wiki/Function_composition) functions. The name is a convention from Haskell.

Here, we are composing functions of addition (this closure: `|a, b| a + b)`) with a range from 1 to 10.
The `0` is the starting point, so `a` is `0` at first.
`b` is the first element of the range, `1`. `0 + 1 = 1` is the result.
So now we `fold` again, with `a = 1`, `b = 2` and so `1 + 2 = 3` is the next result.
This process continues until we get to the last element in the range, `10`.

| `a` | `b` | result |
|:---:|:---:|:------:|
|   0 |   1 |      1 |
|   1 |   2 |      3 |
|   3 |   3 |      6 |
|   6 |   4 |     10 |
|  10 |   5 |     15 |
|  15 |   6 |     21 |
|  21 |   7 |     28 |
|  28 |   8 |     36 |
|  36 |   9 |     45 |
|  45 |  10 |     55 |