Type classes are a type system construct that supports ad-hoc polymorphism by adding constraints to type variables in parametrically polymorphic types. They allow defining behaviors for types through implementations of type class instances. Common examples of type classes are Eq for equality and Show for string representation.

1. Type Classes
Wealthfront Engineering

2. Type Class
Type system construct that supports ad-hoc
polymorphism, achieved by adding constraints
to type variables in parametrically
polymorphic types

3. Type Class
Type system construct that supports ad-hoc
polymorphism, achieved by adding constraints
to type variables in parametrically
polymorphic types

4. Type Class
Type system construct that supports ad-hoc
polymorphism, achieved by adding constraints
to type variables in parametrically
polymorphic types

5. Type Class
Type system construct that supports ad-hoc
polymorphism, achieved by adding constraints
to type variables in parametrically
polymorphic types

6. Type Class
Type system construct that supports ad-hoc
polymorphism, achieved by adding constraints
to type variables in parametrically
polymorphic types

7. pol•y•mor•phism ¦ päli môr fizəm¦
nounthe occurrence of something in several
different forms
New Oxford American Dictionary

8. In particular:
Polymorphism is a programming language
feature that allows values of different data
types to be handled using a uniform interface

9. Several Types of Polymorphism
• Ad-hoc polymorphism
• Inclusion polymorphism
• Parametric polymorphism
• Bounded parametric polymorphism

10. Several Types of Polymorphism
• Ad-hoc polymorphism
– Operator and method overloading
• Inclusion polymorphism
• Parametric polymorphism
• Bounded parametric polymorphism

11. Several Types of Polymorphism
• Ad-hoc polymorphism
• Inclusion polymorphism
– Subtyping
• Parametric polymorphism
• Bounded parametric polymorphism

12. Several Types of Polymorphism
• Ad-hoc polymorphism
• Inclusion polymorphism
• Parametric polymorphism
– Generics
• Bounded parametric polymorphism

13. Several Types of Polymorphism
• Ad-hoc polymorphism
• Inclusion polymorphism
• Parametric polymorphism
• Bounded parametric polymorphism
– Generics with bounded wildcards

14. Ad-hoc polymorphism
Control moving through one named function is
dispatched to various other functions without
having to specify the exact function being
called

15. Ad-hoc polymorphism
String greet() {
return "Hello, World!";
}

16. Ad-hoc polymorphism
String greet(String name) {
return "Hello," + name + "!";
}

17. Ad-hoc polymorphism
String greet(int count) {
return "Hello, World" + repeat("!", count);
}

18. Ad-hoc polymorphism
> greet();
Hello, World!
> greet("Wealthfront");
Hello, Wealthfront!
> greet(3);
Hello, World!!!

19. Parametric polymorphism
A function or a data type can be written
generically so that it can handle values
identically without depending on their type

20. Parametric polymorphism
size :: a . [a] → int
size [] = 0
size (x:xs) = 1 + size xs

21. Parametric polymorphism
> size [1, 2]
2
> size ["hello", "hi", "yo"]
3

22. Bounded parametric polymorphism
A function or a data type require some
knowledge of its data types but can otherwise
work parametrically

23. Bounded parametric polymorphism
<T extends Comparable<T>> List<T> sort(List<T> list) {
return …
}

24. Type Class
Type system construct that supports ad-hoc
polymorphism, achieved by adding constraints
to type variables in parametrically
polymorphic types

25. Type Class
Type system construct that supports ad-hoc
polymorphism, achieved by adding constraints
to type variables in parametrically
polymorphic types

26. Type Class
Type system construct that supports ad-hoc
polymorphism, achieved by adding constraints
to type variables in parametrically
polymorphic types

27. Type Class
Type system construct that supports ad-hoc
polymorphism, achieved by adding constraints
to type variables in parametrically
polymorphic types

28. Type Class Eq
class Eq a where
eq :: a → a → bool
ne :: a → a → bool

29. Implementation for int
instance Eq int where
eq m n = m == n
ne m n = m != n

30. Implementation for Instrument
instance Eq Instrument where
eq x {id = xid} y {id = yid} = xid == yid
ne x {id = xid} y {id = yid} = xid != yid

31. Usage
member :: (Eq a) ⇒ a → [a] → bool
member y [] = false
member y (x:xs) = (eq x y) || member y xs

32. Ad-hoc polymorphism
member :: (Eq a) ⇒ a → [a] → bool
member y [] = false
member y (x:xs) = (eq x y) || member y xs

33. Parametric polymorphism
member :: (Eq a) ⇒ a → [a] → bool
member y [] = false
member y (x:xs) = (eq x y) || member y xs

34. Constraint on type variable
member :: (Eq a) ⇒ a → [a] → bool
member y [] = false
member y (x:xs) = (eq x y) || member y xs

35. Type Classes vs. Interfaces?
Similar, yet different:
• Implementation is separate
• Subtyping is not entailed
• Static dispatch (ad-hoc polymorphism) vs.
dynamic single dispatch

36. Return type-based dispatch
foo :: (Parseable a) ⇒ a → String → a
foo x s = x + parse s

37. Return type-based dispatch
> foo "Hello, " "World!"
Hello, World!
> foo 2 "3"
5

38. Return type-based dispatch
class String implements Parseable {
String parse() {
return this;
}
int parse() {
return Integer.parseInt(this);
}
}

39. Type Class in Scala
trait Parseable[T] {
def parse(s: String): T
}

40. Implementation in Scala for Int
implicit object ParseableInt extends Parseable[Int] {
def parse(s: String) = Integer.parseInt(s)
}

41. Usage in Scala
def foo[T: Parseable](t: T, s: String): T =
t + implicitly[Parseable[T]].parse(s)

42. Usage in Scala
> foo("Hello, ", "World!");
Hello, World! : String
> foo(2, "3");
5 : Int

43. Usage in Scala
def foo[T: Parseable](s: String): T =
implicitly[Parseable[T]].parse(s)

44. Usage in Scala
> "Hello, " + foo("World!");
Hello, World! : String
> 2 + foo("3");
5 : Int
> foo[Int]("3");
3 : Int

45. The End
FYI, Monad is a Type Class.