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Functors

Avatar for Sebastian Bruckner Sebastian Bruckner
June 21, 2017
Programming
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 Functors

Avatar for Sebastian Bruckner

Sebastian Bruckner

June 21, 2017
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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. -> -> ->