Create separated page in functional programming (#184)

SUMMARY.md

@@ -40,6 +40,7 @@
   - [Deref Polymorphism](./anti_patterns/deref.md)
 
 - [Functional Programming](./functional/index.md)
+  - [Programming paradigms](./functional/paradigms.md)
 
 - [Additional Resources](./additional_resources/index.md)
   - [Design principles](./additional_resources/design-principles.md)

functional/index.md

@@ -1,66 +1,10 @@
 # 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 |
+Rust is an imperative language, but it follows many
+[functional programming](https://en.wikipedia.org/wiki/Functional_programming) paradigms.
+
+> In computer science, *functional programming* is a programming paradigm where
+> programs are constructed by applying and composing functions.
+> It is a declarative programming paradigm in which function definitions are
+> trees of expressions that each return a value, rather than a sequence of
+> imperative statements which change the state of the program.

functional/paradigms.md

@@ -0,0 +1,66 @@
+# 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 |