In Scala Typeclass is a design pattern for Ad-hoc polymorphism.

1. Typeclasses
Shyamendra Solanki

2. Typical usage
 Retroactive extension
 Generic Programming
 Type level programming

3. Parametricity
 parametricity is an abstract uniformity property enjoyed by parametrically
polymorphic functions, which captures the intuition that all instances of a
polymorphic function act the same way.

4. Parametricity
def sum[A](elements: List[A]): A
It picks any value from the list.
How do we add a possibility of adding the elements?
We go one level down in abstraction, i.e. we add extra information.
def sum[A: Numeric](elements: List[A]): A
We have added information that this function is defined only when A is a Numeric.
If A is not a Numeric, it will not compile.

5. Generic Programming
In generic programming, Typeclass is used to encode a
constraint/requirement/capability on type parameter.
def sum[A: Monoid](elements: List[A]): A
def sort[A: Ord] (xs: List[A]) : List[A]
We can add multiple constraints on types.
def sum[A: Monoid: Numeric](elements: List[A]): A

6. Retroactive Extension
 the ability to extend existing software modules with new functionality without
needing to touch or re-compile the original source.

7. Retroactive Extension
 class Fruit (name: String)
 def sort[A: Ord](xs: List[A]): List[A]
 How do we make a generalized algorithm work on a particular type?
 How to make sort work on Fruit?

8. Type level programming
 Abstract Member Types
 Path Dependent Methods
 Generalized Constraints

9. In Scala Library
 trait CanBuildFrom[-From, -Elem, +To] {
 def apply(from: From): Builder[Elem, To]
 }
 trait Builder[-Elem, +To] {
 def += (elem: Elem): this.type
 def result(): To
 }

10. Typeclass Pattern
 Define the capability
 trait Semigroup[A] { def combine(a: A, b: A): A }
 Define the evidence
 Object Semigroup {
 implicit val intSemigroup = new Semigroup{
 def combine(a: Int, b: Int): Int = a + b
 }
 }

11. Typeclass Pattern
 Generic Algorithm depends on capability.
 def sum[A: Semigroup](xs: List[A]): A