Functors

Transcript

1. Functors
2. Monoids
3. trait Monoid[A] { def empty: A def combine(one: A, another: A): A }
4. Addition: empty: 0 combine: a + b Multiplication: empty: 1 combine: a * b List: empty: Nil combine: a ++ b
5. associativity: (x |+| y) |+| z = x |+| (y |+| z) left identity: Monoid[A].empty |+| x = x right identity: x |+| Monoid[A].empty = x
6. Functors
7. // Option Some(2).map(_ * 3) === Some(6) None.map(_ * 3) === None
8. // List List(1, 2).map(_ * 3) === List(3, 6)
9. ❓
10. Functors
11. trait Functor[F[_]] { def map[A, B](fa: F[A])(f: A => B): F[B] }
12. identity: (x map identity) === x composition: (x map (v => g(f(v))) === (x map f map g)
13. Functors
14. -> -> ->