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package eg
object Typeclass extends App {
// The challenge is to factor out the commonality here:
def sum(ns: List[Int]): Int = ns.foldRight(0)(_ + _)
def all(bs: List[Boolean]): Boolean = bs.foldRight(true)(_ && _)
def concat[A](ss: List[List[A]]): List[A] = ss.foldRight(List.empty[A])(_ ::: _)
// Some examples
println(sum(List(1, 2, 3))) // 6
println(all(List(true, false, true))) // false
println(concat(List(List('a', 'b'), List('c', 'd')))) // List(a, b, c, d)
// In each example we have a call to foldRight (which works on any List), using a "zero" value and a combiner
// function that are specific to the list's element type. So let's factor out the type-specific part:
trait Combiner[A] {
def combine(a: A, b: A): A
def zero: A
// With that, we can now factor out the common functionality:
def genericSum[A](as: List[A], c: Combiner[A]): A =
// Let's define a combiner for Ints, using addition as our combiner
val intCombiner = new Combiner[Int] {
def combine(a: Int, b: Int) = a + b
def zero = 0
// Try it!
println(genericSum(List(1, 2, 3), intCombiner)) // 6
// So genericSum works for any type at all, as long as you supply an appropriate Combiner for that type. This is the
// *typeclass pattern*: Combiner is the typeclass, and the genericSum method demands *evidence* that A has an
// associated instance.
// Typeclass parameters are usually implicit, so let's rewrite a little:
def genericSum2[A](as: List[A])(implicit c: Combiner[A]): A =
// Let's make our instance implicit, and declare another one:
implicit val IntCombiner = intCombiner // from above
implicit val BooleanCombiner = new Combiner[Boolean] {
def combine(a: Boolean, b: Boolean): Boolean = a && b
def zero = true
// Try it!
println(genericSum2(List(1, 2, 3))) // 6
println(genericSum2(List(true, false, true))) // false
// Ok this is pretty nice. We now have a generic function for summing stuff, we can only call it if there's an
// associated Combiner, and it has the correct static type. Try it with a List[String] and it won't compile.
// println(genericSum2(List("foo", "bar", "baz))) // won't compile
// We can even use an implicit class to add this functionality as syntax. Because the Combiner instance in the
// constructor is implicit, it's also implicit in the body of the class.
implicit class CombinerSyntax[A](as: List[A])(implicit c: Combiner[A]) {
def gsum: A = genericSum2(as) // c will be passed along because it's implicit here
// Try it!
println(List(1, 2, 3).gsum) // 6
println(List(true, false, true).gsum) // false
// But note that we never actually use `c` in the definition of CombinerSyntax; it's just there in order to be
// introduced to the implicit scope. For cases like this there is a shortcut syntax called a *context bound*.
implicit class CombinerSyntax2[A: Combiner](as: List[A]) {
def gsum2: A = genericSum2(as) // unnamed Combiner[A] is implicit here
// Create our List combiner. Note that this needs to be a def (not a val) because it has a type parameter. The
// compiler will call this method for us (!)
implicit def ListCombiner[A] = new Combiner[List[A]] {
def combine(a: List[A], b: List[A]): List[A] = a ::: b
def zero = List.empty[A]
// And try it with the new syntax!
println(List(List('a', 'b'), List('c', 'd')).gsum2) // List(a, b, c, d)
// While we're at it, let's add syntax for any combinable A as well!
implicit class ASyntax[A](a: A)(implicit c: Combiner[A]) {
def |+|(b: A) = c.combine(a, b)
// Try it!
println(1 |+| 2) // 3
println(true |+| true |+| false) // false
println(List(1, 2) |+| List(3, 4)) // List(1, 2, 3, 4)
// Ok this is where it gets crazy. If we have a Combiner[A] and a Combiner[B] can we make a Combiner[(A,B)]?
// I say we can, and the compiler will use this to construct Combiner[(A, B)] for any A and B that can be combined.
implicit def PairCombiner[A, B](implicit ca: Combiner[A], cb: Combiner[B]): Combiner[(A, B)] =
new Combiner[(A, B)] {
def combine(a: (A, B), b: (A, B)): (A, B) = (a._1 |+| b._1, a._2 |+| b._2)
def zero: (A, B) = (,
// Try it!
println((1, true) |+| (2, true) |+| (3, true)) // (6, true)
println((List('a', 'b'), 5) |+| (List('d', 'e'), 10)) // (List(a, b, d, e), 15)
// Note that summing now works for list of combinable pairs!
println(List((1, 2), (3, 4)).gsum) // (4, 6)
// But because we can combine pairs, pairs are combinable. So we can combine nested pairs too! WOW
val a = (1, ((true, 7), List('a', 'b')))
val b = (9, ((true, 8), List('c', 'd')))
println(a |+| b) // (10,((true,15),List(a, b, c, d)))
// Ok that's it for now. A few final notes:
// * Congratulations, you have done some abstract algebra! The mathy name for Combiner is "Monoid". In order to be
// correct we have to show that zero |+| a == a and a |+| zero == a. We have not done that here. With some luck
// we will do that in another example.
// * We defined the additive monoid for ints and the conjunctive monoid for booleans, but both types have consistent
// monoids for other operations. What are they?