Expand Traits, add associated types (#1815)

This breaks the "Traits" slide into three smaller sub-slides. It also
addresses part of #1511 by explicitly addressing associated types.

---------

Co-authored-by: Martin Geisler <martin@geisler.net>

src/SUMMARY.md

@@ -80,6 +80,8 @@
 - [Methods and Traits](methods-and-traits.md)
   - [Methods](methods-and-traits/methods.md)
   - [Traits](methods-and-traits/traits.md)
+    - [Implmementing Traits](methods-and-traits/traits/implementing.md)
+    - [Associated Types](methods-and-traits/traits/associated-types.md)
   - [Deriving](methods-and-traits/deriving.md)
   - [Exercise: Generic Logger](methods-and-traits/exercise.md)
     - [Solution](methods-and-traits/solution.md)

src/methods-and-traits/traits.md

@@ -1,5 +1,5 @@
 ---
-minutes: 8
+minutes: 10
 ---
 
 # Traits
@@ -7,40 +7,12 @@ minutes: 8
 Rust lets you abstract over types with traits. They're similar to interfaces:
 
 ```rust,editable
-struct Dog {
-    name: String,
-    age: i8,
-}
-struct Cat {
-    lives: i8,
-}
-
 trait Pet {
+    /// Return a sentence from this pet.
     fn talk(&self) -> String;
 
-    fn greet(&self) {
-        println!("Oh you're a cutie! What's your name? {}", self.talk());
-    }
-}
-
-impl Pet for Dog {
-    fn talk(&self) -> String {
-        format!("Woof, my name is {}!", self.name)
-    }
-}
-
-impl Pet for Cat {
-    fn talk(&self) -> String {
-        String::from("Miau!")
-    }
-}
-
-fn main() {
-    let captain_floof = Cat { lives: 9 };
-    let fido = Dog { name: String::from("Fido"), age: 5 };
-
-    captain_floof.greet();
-    fido.greet();
+    /// Print a string to the terminal greeting this pet.
+    fn greet(&self);
 }
 ```
 
@@ -49,10 +21,7 @@ fn main() {
 - A trait defines a number of methods that types must have in order to implement
   the trait.
 
-- Traits are implemented in an `impl <trait> for <type> { .. }` block.
-
-- Traits may specify pre-implemented (provided) methods and methods that users
-  are required to implement themselves. Provided methods can rely on required
-  methods. In this case, `greet` is provided, and relies on `talk`.
+- In the "Generics" segment, next, we will see how to build functionality that
+  is generic over all types implementing a trait.
 
 </details>

src/methods-and-traits/traits/associated-types.md

@@ -0,0 +1,37 @@
+# Associated Types
+
+Associated types allow are placeholder types which are filled in by the trait
+implementation.
+
+```rust,editable
+#[derive(Debug)]
+struct Meters(i32);
+#[derive(Debug)]
+struct MetersSquared(i32);
+
+trait Multiply {
+    type Output;
+    fn multiply(&self, other: &Self) -> Self::Output;
+}
+
+impl Multiply for Meters {
+    type Output = MetersSquared;
+    fn multiply(&self, other: &Self) -> Self::Output {
+        MetersSquared(self.0 * other.0)
+    }
+}
+
+fn main() {
+    println!("{:?}", Meters(10).multiply(&Meters(20)));
+}
+```
+
+<details>
+
+- Associated types are sometimes also called "output types". The key observation
+  is that the implementer, not the caller, chooses this type.
+
+- Many standard library traits have associated types, including arithmetic
+  operators and `Iterator`.
+
+</details>

src/methods-and-traits/traits/implementing.md

@@ -0,0 +1,42 @@
+# Implementing Traits
+
+```rust,editable
+trait Pet {
+    fn talk(&self) -> String;
+
+    fn greet(&self) {
+        println!("Oh you're a cutie! What's your name? {}", self.talk());
+    }
+}
+
+struct Dog {
+    name: String,
+    age: i8,
+}
+
+impl Pet for Dog {
+    fn talk(&self) -> String {
+        format!("Woof, my name is {}!", self.name)
+    }
+}
+
+fn main() {
+    let fido = Dog { name: String::from("Fido"), age: 5 };
+    fido.greet();
+}
+```
+
+<details>
+
+- To implement `Trait` for `Type`, you use an `impl Trait for Type { .. }`
+  block.
+
+- Unlike Go interfaces, just having matching methods is not enough: a `Cat` type
+  with a `talk()` method would not automatically satisfy `Pet` unless it is in
+  an `impl Pet` block.
+
+- Traits may provide default implementations of some methods. Default
+  implementations can rely on all the methods of the trait. In this case,
+  `greet` is provided, and relies on `talk`.
+
+</details>