Continuation Passing Style - example converted to scala from haskell; this time without the $ op

cps_without_dollar_op.scala

//https://en.wikibooks.org/wiki/Haskell/Continuation_passing_style#Passing_continuations

val add: Int => Int => Int = {x => { y => x + y}}
//add(1)(2)
//Function.uncurried(add)(1, 2)

def addCps[R]: Int => Int => ((Int => R) => R) = {x => { y =>
  def lambda[K]: (Int => K) => K = {k: (Int => K) => k(add(x)(y))}
  lambda
}}

val square: Int => Int = { x => x * x }
//square(2)

def squareCps[R]: Int => ((Int => R) => R) = { x =>
  def lambda[K]: (Int => K) => K = { k: (Int => K) => k(square(x)) }
  lambda
}

val pythagoras: Int => Int => Int = {x => {y => add(square(x))(square(y))}}

//pythagoras(2)(3)
//Function.uncurried(pythagoras)(2, 3)

def pythagorasCps[R]: Int => Int => ((Int => R) => R) = {x => {y =>
  def lambda[K]: (Int => K) => K = {k: (Int => K) =>
    val `x^2`: (Int => K) => K = squareCps[K](x)
    val `y^2`: (Int => K) => K = squareCps[K](y)

    `x^2`{xSquared => 
      `y^2`{ySquared =>
        addCps[K](xSquared)(ySquared)(k)
      }
    }
  }
  lambda
}}

val sCps: (Int => Unit) => Unit = squareCps[Unit](2)
sCps({a => println(a)})

val aCps: (Int => Unit) => Unit = addCps[Unit](1)(2)
aCps({a =>
  val b = a*13
  println(b)
})

val pCsp: (Int => Unit) => Unit = pythagorasCps[Unit](3)(4)
pCsp(println)

// https://scastie.scala-lang.org/Yaneeve/BVYFqjG0SsG4kDcdx7i5uQ