scala212-category-theory-const-functor

Reference: https://bartoszmilewski.com/2015/01/20/functors/

preliminary

Referring my other github project could be useful (basic info concerning functors):

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

discussion

When we think about functors we are not at all concerned about accessing the values - it's completely outside of the formal scope of the functor. Functors are all about being able to transforming underlying values with functions.

• if there is possibility to access the values - we will see the transformed result
• if we cannot access them - all we care is that the manipulations compose correctly and does not change anything when composed with identity

definition

Meaningful example of a functor that does not provide us with an access to underlying values is a Const functor that completely ignores its second argument:

• data Const c a = Const c
• map :: (a -> b) -> Const c a -> Const c b

The Const data type can be thought of similarly to the const function, but as a data type.

project description

We will provide simple implementation of Const functor in Scala:

final case class Const[C, A](param: C) {
  def map[B](f: A => B): Const[C, B] = this.asInstanceOf[Const[C, B]]
}

and tests:

• creation

  val const1: Const[Int, String] = Const(1)
  val const2: Const[Int, Object] = Const(1)
  
  const1.param should be(1)
  const2.param should be(1)
  

• equals
  • same values, different dropped type

    val const1: Const[Int, String] = Const(1)
    val const2: Const[Int, Object] = Const(1)
    
    const1 should be(const2)
    

  • different values

    val const1: Const[Int, String] = Const(1)
    val const2: Const[Int, String] = Const(2)
    
    const1 should not be const2
    

  • map

    val const: Const[Int, Int] = Const(1)
    
    
    val mapped: Const[Int, String] = const.map(_ => "a")
    mapped.param should be(1)
    

Note that we provide the simplest implementation that there could be, follow https://github.com/typelevel/cats/blob/master/core/src/main/scala/cats/data/Const.scala to see much more sophisticated solution.