scala212-category-theory-contravariant-op-functor

Reference: http://hackage.haskell.org/package/contravariant-1.5/docs/Data-Functor-Contravariant.html
Reference: https://ocharles.org.uk/blog/guest-posts/2013-12-21-24-days-of-hackage-contravariant.html
Reference: https://bartoszmilewski.com/2015/02/03/functoriality/

preview

Referring my other github projects could be helpful:

• Functor's basics: https://github.com/mtumilowicz/java11-category-theory-optional-is-not-functor
• Functor related to Op: https://github.com/mtumilowicz/java11-category-theory-reader-functor

functor intuition

class Functor f where
  map :: (a -> b) -> f a -> f b

• Functor is a sort of "producer of output": if f is a functor, then f a represents a "producer" of type a
• Functor can have its type adapted
• Using a function a->b we can modify output to type b (using map)
• Three easy examples of functors (and modification of output):
  1. Option[A]: using map we can adapt potentially None[A] to None[B]
  2. List[A]: using map we can adapt List[A] to List[B]
  3. Reader[R, A] (r -> a) - we can think about it as a functions taking r as input and producing a; using map we can convert output to b

map allows us to change the output, but we are unable to change the input - and that's where contravariance comes in

contravariance

class Contravariant f where
  contramap :: (b -> a) -> f a -> f b

• For contravariant f, f a represents input
• Using a function b -> a we can modify input to type b (using contramap)
• Notice that a contravariant functor is just a regular functor from the opposite category (category with reversed morphisms)

project description

We provide example of contravariant functor with tests.

• haskell is more expressive:

  type Op r a = a -> r
  
  instance Contravariant (Op r) where
      -- (b -> a) -> Op r a -> Op r b
      contramap f g = g . f
  

• and the Scala code comes here:

  trait Op[R, A] extends (A => R) {
    def map[B](f: B => A): Op[R, B] = this.compose(f).apply
  }
  

  • Notice that the function f inserts itself before the contents of Op - the function g.
• tests:
  • we have function counting list's size, and we want to modify it to accept Set:

    val sizer: Op[Int, List[String]] = _.size
    
    sizer.map((set: Set[String]) => set.toList).apply(Set()) should be(0)
    sizer.map((set: Set[String]) => set.toList).apply(Set("a")) should be(1)
    sizer.map((set: Set[String]) => set.toList).apply(Set("a", "b", "c")) should be(3)
    

  • we have predicate to check if a given int is even, and we want to transform it to accept ints given as a string

    val isEven: Op[Boolean, Int] = _ % 2 == 0
    
    isEven.contramap((s: String) => s.toInt).apply("2") should be(true)
    isEven.contramap((s: String) => s.toInt).apply("3") should be(false)