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# Programming paradigms
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One of the biggest hurdles to understanding functional programs when coming from
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an imperative background is the shift in thinking. Imperative programs describe
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**how** to do something, whereas declarative programs describe **what** to do.
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Let's sum the numbers from 1 to 10 to show this.
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## Imperative
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```rust
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let mut sum = 0;
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for i in 1..11 {
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sum += i;
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}
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println!("{sum}");
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```
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With imperative programs, we have to play compiler to see what is happening.
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Here, we start with a `sum` of `0`. Next, we iterate through the range from 1
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to 10. Each time through the loop, we add the corresponding value in the range.
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Then we print it out.
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| `i` | `sum` |
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| :-: | :---: |
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| 1 | 1 |
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| 2 | 3 |
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| 3 | 6 |
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| 4 | 10 |
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| 5 | 15 |
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| 6 | 21 |
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| 7 | 28 |
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| 8 | 36 |
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| 9 | 45 |
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| 10 | 55 |
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This is how most of us start out programming. We learn that a program is a set
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of steps.
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## Declarative
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```rust
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println!("{}", (1..11).fold(0, |a, b| a + b));
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```
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Whoa! This is really different! What's going on here? Remember that with
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declarative programs we are describing **what** to do, rather than **how** to do
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it. `fold` is a function that
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[composes](https://en.wikipedia.org/wiki/Function_composition) functions. The
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name is a convention from Haskell.
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Here, we are composing functions of addition (this closure: `|a, b| a + b`) with
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a range from 1 to 10. The `0` is the starting point, so `a` is `0` at first. `b`
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is the first element of the range, `1`. `0 + 1 = 1` is the result. So now we
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`fold` again, with `a = 1`, `b = 2` and so `1 + 2 = 3` is the next result. This
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process continues until we get to the last element in the range, `10`.
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| `a` | `b` | result |
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| :-: | :-: | :----: |
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| 0 | 1 | 1 |
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| 1 | 2 | 3 |
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| 3 | 3 | 6 |
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| 6 | 4 | 10 |
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| 10 | 5 | 15 |
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| 15 | 6 | 21 |
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| 21 | 7 | 28 |
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| 28 | 8 | 36 |
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| 36 | 9 | 45 |
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| 45 | 10 | 55 |
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