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+---
+marp: true
+math: mathjax
+paginate: true
+backgroundImage: url('../pics/background_moonbit.png')
+---
+
+<!--
+```moonbit
+enum Tree[T] {
+  Empty
+  Node(T, Tree[T], Tree[T])
+}
+
+struct Queue[T] {
+  mut array: Array[T]
+  mut start: Int
+  mut end: Int
+  mut length: Int
+}
+```
+-->
+
+# Modern Programming Ideology
+
+## Traits
+
+### MoonBit Open Course Team
+
+---
+
+# Recapitulation
+
+- Balanced Binary Search Trees (Chapter 6)
+  - Define a more general balanced BST, capable of storing various data types.
+  ```moonbit no-check
+  enum Tree[T] {
+    Empty
+    Node(T, Tree[T], Tree[T])
+  }
+
+  // We need a comparison function to determine the order of values
+  // -1: less than; 0: equal to; 1: greater than
+  fn insert[T](self: Tree[T], value: T, compare: (T, T) -> Int) -> Tree[T]
+  fn delete[T](self: Tree[T], value: T, compare: (T, T) -> Int) -> Tree[T]
+  ```
+- Circular Queues (Chapter 8)
+  - Initialize the array with the default value of the type.
+  ```moonbit no-check
+  fn make[T]() -> Queue[T] {
+    { array: Array::make(5, T::default()), start: 0, end: 0, length: 0 }
+  }
+  ```
+
+---
+
+# Methods
+
+Some functions may associate with a type `T`.
+- Compare two `T` values: `fn T::compare(self: T, other: T) -> Int`
+- Get the default value of `T`: `fn T::default() -> T`
+- Get the string representation of a `T` value: `fn T::to_string(self: T) -> String`
+- ...
+
+Such functions are called the **methods** of `T`.
+
+---
+
+# Traits
+
+Traits declare a list of operations to be supplied if a type wants to implement it.
+
+```moonbit
+trait Compare {
+  compare(Self, Self) -> Int
+  // `Self` refers to the type that implements the trait.
+}
+trait Default {
+  default() -> Self
+}
+```
+
+- The trait system in MoonBit is structural.
+  - There is no need to implement a trait explicitly.
+  - Types with the required methods automatically implements a trait.
+
+---
+
+# Traits
+
+- In generic functions, we use traits as bounds to specify what methods a type supports.
+  - `<type>: <trait>` requires `<type>` to be bound by `<trait>`;
+  - The methods of a trait can then be called via `<type>::<method>()`.
+
+```moonbit no-check
+fn make[T: Default]() -> Queue[T] { // `T` should support the `default` method.
+  { 
+    array: Array::make(5, T::default()), // The return type of `default` is `T`.
+    start: 0,  end: 0,  length: 0 
+  } 
+}
+```
+
+- With traits, we can timely detect errors caused by calling missing methods.
+![height:150px](../pics/no_method.png)
+
+---
+
+# Traits
+
+```moonbit
+fn insert[T : Compare](tree : Tree[T], value : T) -> Tree[T] {
+  // Since `T` is bound by `Compare`, it should support the `compare` method.
+  match tree {
+    Empty => Node(value, Empty, Empty) 
+    Node(v, left, right) =>  
+      if T::compare(value, v) == 0 { // We can call `compare` here.
+        tree
+      } else if T::compare(value, v) < 0 { // We can call `compare` here.
+        Node(v, insert(left, value), right)
+      } else {
+        Node(v, left, insert(right, value))
+      }
+  }
+}
+```
+
+---
+
+# Definition of Methods
+
+- Methods can be defined using the syntax `fn <type>::<method>(...) -> ...`.
+
+```moonbit
+struct BoxedInt { value : Int }
+
+fn BoxedInt::default() -> BoxedInt {
+  // By defining the `default` method, the `Default` trait is now implemented.
+  { value : Int::default() }
+  // The default value can be defined by boxing the default value of `Int`.
+}
+```
+```moonbit no-check
+fn init {
+  let array: Queue[BoxedInt] = make()
+}
+```
+
+---
+
+# Method Chaining
+
+- In addition to `<type>::<method>(<expr>, ...)`, we can as well call the method using `<expr>.<method>(...)`, given `<expr>` is of type `<type>`.
+
+```moonbit
+fn BoxedInt::plus_one(b: BoxedInt) -> BoxedInt {
+  { value : b.value + 1 }
+}
+fn plus_two(self: BoxedInt) -> BoxedInt {
+  // `<type>::` can be omitted when the parameter name is `self`.
+  { value : self.value + 2}
+}
+
+fn init {
+  let _five = { value: 1 }.plus_one().plus_one().plus_two()
+  // This avoids multiple nesting of method calls.
+  let _five = plus_two(plus_one(plus_one({value: 1})))
+}
+```
+
+---
+
+# Automatically Derive Builtin Traits
+
+- Some simple builtin traits can be automatically derived by adding `derive(<traits>)` after the type definition.
+
+```moonbit no-check
+struct BoxedInt { value : Int } derive(Default, Eq, Compare, Debug)
+```
+
+- The member data types should have implemented the same traits.
+
+---
+
+# Using Traits to Implement a Map
+
+- A map is a collection of key-value pairs.
+  - Each **key** corresponds to a **value**.
+  - Example: `{ 0 -> "a", 5 -> "Hello", 7 -> "a"}`.
+
+```moonbit no-check
+type Map[Key, Value]
+
+// Create a map
+fn make[Key, Value]() -> Map[Key, Value]
+// Add a key-value pair, or update the corresponding value of a key
+fn put[Key, Value](map: Map[Key, Value], key: Key, value: Value) -> Map[Key, Value]
+// Get the corresponding value of a key
+fn get[Key, Value](map: Map[Key, Value], key: Key) -> Option[Value]
+```
+
+---
+
+# Using Traits to Implement a Map
+
+- A simple implementation:
+  - Store key-value pairs using a list of pairs.
+  - Add/update a key-value pair by inserting the pair to the beginning of the list.
+  - Search the list from the beginning until the first matching key is found.
+- We need to compare the key we are looking for with the keys stored in the list.
+  - The `Key` type should implement the `Eq` trait.
+  ```moonbit no-check
+  fn get[Key: Eq, Value](map: Map[Key, Value], key: Key) -> Option[Value]
+  ```
+
+---
+
+# Using Traits to Implement a Map
+
+- Store key-value pairs using a list of pairs.
+```moonbit
+// Define `Map[Key, Value]` to be `List[(Key, Value)]`
+type Map[Key, Value] List[(Key, Value)]
+
+fn make[Key, Value]() -> Map[Key, Value] { 
+  Map(Nil)
+}
+
+fn put[Key, Value](map: Map[Key, Value], key: Key, value: Value) -> Map[Key, Value] { 
+  let Map(original_map) = map
+  Map( Cons( (key, value), original_map ) )
+}
+```
+
+---
+
+# Using Traits to Implement a Map
+
+- Store key-value pairs using a list of pairs.
+```moonbit
+fn get[Key: Eq, Value](map : Map[Key, Value], key : Key) -> Option[Value] {
+  fn aux(list : List[(Key, Value)]) -> Option[Value] {
+    match list {
+      Nil => None
+      Cons((k, v), tl) => if k == key {
+        // `Key` is bound by `Eq`, so we can call `==` directly.
+        Some(v)
+      } else {
+        aux(tl)
+      }
+    }
+  }
+
+  aux(map.0) // Use `.0` to get the value.
+}
+```
+
+---
+
+# Custom Operators
+
+- Operators can be customized by defining methods with specific names and types.
+
+```moonbit
+fn BoxedInt::op_equal(i: BoxedInt, j: BoxedInt) -> Bool {
+  i.value == j.value
+}
+fn BoxedInt::op_add(i: BoxedInt, j: BoxedInt) -> BoxedInt {
+  { value: i.value + j.value }
+}
+
+fn init {
+  let _ = { value: 10 } == { value: 100 } // false
+  let _ = { value: 10 } + { value: 100 } // { value: 110 }
+}
+```
+
+---
+
+# Custom Operators
+
+- Operators can be customized by defining methods with specific names and types.
+
+```moonbit
+// map [ key ]
+fn Map::op_get[Key: Eq, Value](map: Map[Key, Value], key: Key) -> Option[Value] {
+  get(map, key)
+}
+// map [ key ] = value
+fn Map::op_set[Key: Eq, Value](map: Map[Key, Value], key: Key, value: Value) -> Map[Key, Value] {
+  put(map, key, value)
+}
+
+fn init {
+  let empty: Map[Int, Int] = make()
+  let one = { empty[1] = 1 } // let one = Map::op_set(empty, 1, 1)
+  let _ = one[1] // let _ = Map::op_get(one, 1)
+}
+```
+
+---
+
+# Summary
+
+- In this chapter, we learned how to
+  - Define traits and use them to bound type parameters
+  - Implement methods and custom operators
+  - Implement a simple map using traits in MoonBit