scala212-cats-category-theory-composing-functors

Reference: https://bartoszmilewski.com/2015/01/20/functors/
Reference: https://typelevel.org/cats/typeclasses/functor.html

preface

Basic info about functors:

• https://github.com/mtumilowicz/java11-category-theory-optional-is-not-functor
• https://github.com/mtumilowicz/java11-category-theory-reader-functor

project description

We have optionList:Option[List[Int]] = Option(List(1, 2, 3)) and we want to square the elements.

• pure Scala

  def square(i: Int) = i * i
  val optionList = Option(List(1, 2, 3))
  
  optionList.map(_ . map(square)) should be (Some(List(1, 4, 9)))
  

• Scala + Cats
  • Option is a functor
  • List is a functor
  • Composition of two functors, when acting on objects, is just the composition of their respective object mappings.

  def square(i: Int) = i * i
  val optionList = Option(List(1, 2, 3))
  
  Functor[Option].compose[List].map(optionList)(square) should be (Some(List(1, 4, 9)))