1. High Wizardry in the Land
of Scala
Daniel Spiewak

3. Agenda
• Higher-Kinds
• Typeclasses
• Type-Level Encodings
• Continuations

4. Higher-Kinds
• What is a “kind system”?

5. Higher-Kinds
• What is a “kind system”?
• What is a “type system”?

6. A type system is a tractable syntactic method for
proving the absence of certain program behaviors
by classifying phrases according to the kinds of
values they compute. – Benjamin Pierce

7. val i: Int = 42
val j: Int = 21
val s: String = "foo"
val f: Int => String = { _.toString }
val xs: List[Int] = List(1, 1, 2, 3, 5, 8)

8. Values

9. Types
Values

10. ???
Types
Values

11. Kinds
Types
Values

12. Higher-Kinds
• Type systems classify values
• Kind systems classify types
• Values are to types as types are to kinds

13. type Int :: *
type String :: *
type (Int => String) :: *
type List[Int] :: *

14. type List :: ???
type Function1 :: ???

15. type List :: * => *
type Function1 :: (* × *) => *

16. // id : Int => Int
def id(x: Int) = x
// Id :: * => *
type Id[A] = A

17. // id : ((Int => Int), Int) => Int
def id(f: Int => Int, x: Int) = f(x)
// Id :: ((* => *) × *) => *
type Id[A[_], B] = A[B]

18. val map: Map[Option[Any], List[Any]] = Map(
Some("foo") -> List("foo", "bar", "baz"),
Some(42) -> List(1, 1, 2, 3, 5, 8),
Some(true) -> List(true, false, true, true))
// ugly cast!
val xs: List[String] =
map(Some("foo")).asInstanceOf[List[String]]
// ditto!
val ys: List[Int] =
map(Some(42)).asInstanceOf[List[Int]]

19. val map: HOMap[Option, List] = HOMap[Option, List](
Some("foo") -> List("foo", "bar", "baz"),
Some(42) -> List(1, 1, 2, 3, 5, 8),
Some(true) -> List(true, false, true, true))
// blissful type safety!
val xs: List[String] = map(Some("foo"))
// ditto!
val ys: List[Int] = map(Some(42))

20. // HOMap :: ((* => *) × (* => *)) => *
class HOMap[K[_], V[_]](delegate: Map[K[Any], V[Any]]) {
def apply[A](key: K[A]): V[A] =
delegate(key.asInstanceOf[K[Any]]).asInstanceOf[V[A]]
}
object HOMap {
def apply[K[_], V[_]](tuples: (K[Any], V[Any])*) =
new HOMap[K, V](Map(tuples: _*))
}
(credit: Jorge Ortiz)

21. Higher-Kinds
• Kind systems classify types
• Values are to types as types are to kinds
• “Higher” kinds are the kinds of type
constructors
• Type functions
• Use any time one type is logically a function
of another

22. Typeclasses
• Forget everything you know about classes
• (it won’t help you anyway)
• Instead of “class”, think “category”
• If you’ve ever looked at Haskell…

24. sum(List(1, 2, 3, 4)) // => 10
sum(List(3.14, 2.72)) // => 5.86
sum(List("me", "you")) // shouldn't compile!

25. trait Num[A] {
val zero: A
def add(x: A, y: A): A
}
def sum[A](nums: List[A])(tc: Num[A]) =
nums.foldLeft(tc.zero)(tc.add)

26. object IntNum extends Num[Int] {
val zero = 0
def add(x: Int, y: Int) = x + y
}
object DoubleNum extends Num[Double] {
val zero = 0d
def add(x: Double, y: Double) = x + y
}

27. // works!
sum(List(1, 2, 3, 4))(IntNum)
sum(List(3.14, 2.72))(DoubleNum)

28. Typeclasses
• This is functional, but ugly
• We have to explicitly provide the relevant
instance of Num[A]

29. Typeclasses
• This is functional, but ugly
• We have to explicitly provide the relevant
instance of Num[A]

30. def sum[A](nums: Seq[A])(tc: Num[A]) =
nums.foldLeft(tc.zero)(tc.add)

31. def sum[A](nums: Seq[A])(implicit tc: Num[A]) =
nums.foldLeft(tc.zero)(tc.add)

32. object IntNum extends Num[Int] {
val zero = 0
def add(x: Int, y: Int) = x + y
}
object DoubleNum extends Num[Double] {
val zero = 0d
def add(x: Double, y: Double) = x + y
}

33. implicit object IntNum extends Num[Int] {
val zero = 0
def add(x: Int, y: Int) = x + y
}
implicit object DoubleNum extends Num[Double] {
val zero = 0d
def add(x: Double, y: Double) = x + y
}

34. sum(List(1, 2, 3, 4))(IntNum)
sum(List(3.14, 2.72))(DoubleNum)

35. sum(List(1, 2, 3, 4))
sum(List(3.14, 2.72))

36. Typeclasses
• Typeclasses are categories of types
• If you have a set of types with well-defined
commonalities, think about typeclasses
• Collections in 2.8
• Numeric in 2.8

37. Type-Level Encodings
• Kinds make our types into superheroes
• Typeclasses allow us to abstract over types
• How can we abuse our new-found power?

38. Type-Level Encodings
• Kinds make our types into superheroes
• Typeclasses allow us to abstract over types
• How can we abuse our new-found power?
• Maybe…data structures at the type level?

39. Type-Level Encodings
• HList is a linked-list implemented in types
• …and values
• Sort of like Tuple, but unbounded

40. import HList._
val xs = 42 :: "foo" :: 3.14 :: HNil
xs.head // => 42: Int
xs.tail.head // => "foo": String

41. val xs1 = 42 :: false :: HNil
val xs2 = "Hello" :: "World" :: HNil
val xs = xs1 ++ xs2
xs.head // => 42: Int
xs.tail.tail.head // => "Hello": String

42. object HList {
sealed trait HList {
type Head
type Tail <: HList
type Append[L <: HList] <: HList
def head: Head
def tail: Tail
def ++[L <: HList](xs: L): Append[L]
}
// ...
}

43. val x: List[Int] = ...
val y: List[Int] = ...
x ++ y
x 1 2 3 4
y 5 6 7 8 9

44. val x: List[Int] = ...
val y: List[Int] = ...
x ++ y
x 2 3 4
y 5 6 7 8 9

45. val x: List[Int] = ...
val y: List[Int] = ...
x ++ y
x 3 4
y 5 6 7 8 9

46. val x: List[Int] = ...
val y: List[Int] = ...
x ++ y
x 4
y 5 6 7 8 9

47. val x: List[Int] = ...
val y: List[Int] = ...
x ++ y
x’
y 5 6 7 8 9

48. val x: List[Int] = ...
val y: List[Int] = ...
x ++ y
x’ 4
y 5 6 7 8 9

49. val x: List[Int] = ...
val y: List[Int] = ...
x ++ y
x’ 3 4
y 5 6 7 8 9

50. val x: List[Int] = ...
val y: List[Int] = ...
x ++ y
x’ 2 3 4
y 5 6 7 8 9

51. val x: List[Int] = ...
val y: List[Int] = ...
x ++ y
x’ 1 2 3 4
y 5 6 7 8 9

52. object HList {
// ...
final class HNil extends HList {
type Head = Nothing
type Tail = Nothing
type Append[L <: HList] = L
def head = error("Head of an empty HList")
def tail = error("Tail of an empty HList")
def ::[A](a: A) = HCons(a, this)
def ++[L <: HList](xs: L) = xs
}
val HNil = new HNil
}

53. object HList {
// ...
case class HCons[A, B <: HList](head: A, tail: B)
extends HList {
type Head = A
type Tail = B
type Append[L <: HList] =
HCons[Head, Tail#Append[L]]
def ::[C](c: C) = HCons(c, this)
def ++[L <: HList](xs: L) =
head :: (tail ++ xs)
}
type ::[A, B <: HList] = HCons[A, B]
}

54. Type-Level Encodings
• What about an nth(Int) function?

55. Type-Level Encodings
• What about an nth(Int) function?
• Not today!
• Church Numerals
• λ-Calculus

56. Type-Level Encodings
• What about an nth(Int) function?
• Not today!
• Church Numerals
• λ-Calculus
• We could do a lot more
• Just not in a 45 minute talk

57. Continuations
• Actually, delimited continuations
• Very different from plain continuations!
• Not like callcc
• Not considered harmful
• …though they can simulate goto!

58. case class JumpException(i: Int)
extends RuntimeException
val res = try {
val i = 42
println("before")
throw JumpException(i) // basically: `break`
val j: Int = i / 2
println("after")
println(j + 2)
j // needed for type checker
} catch {
case JumpException(i) => i
}
println("outside")

59. val (res, func) = {
val i = 42
println("before")
(i, { j: Int =>
println("after")
println(j + 2)
})
}
println("outside")
func(res / 2)
func(res / 6)

60. val (res, func) = reset {
val i = 42
println("before")
val j = shift { (k: Int => Unit) => (i, k) }
println("after")
println(j + 2)
}
println("outside")
func(res / 2)
func(res / 6)

61. val (res, func) = reset {
val i = 42
println("before")
val j = shift { (k: Int => Unit) => (i, k) }
println("after")
println(j + 2)
}
println("outside")
func(res / 2)
func(res / 6)

62. val (res, func) = reset {
val i = 42
println("before")
val j = shift { (k: Int => Unit) => (i, k) }
println("after")
println(j + 2)
}
println("outside")
func(res / 2)
func(res / 6)

63. val (res, func) = reset {
val i = 42
println("before")
val j = shift { (k: Int => Unit) => (i, k) }
println("after")
println(j + 2)
}
println("outside")
func(res / 2)
func(res / 6)

64. def gen() = {
var x = 1
var y = 1
while (true) {
shift { (k: Unit => Result) => Result(x, k) }
y += x
x = y - x
}
}
val res = reset {
gen()
error("It never ends that way, too!"): Result
}
val fib: Stream[Int] = res.toStream
(credit: PEP-255)

65. def gen() = {
var x = 1
var y = 1
while (true) {
shift { (k: Unit => Result) => Result(x, k) }
y += x
x = y - x
}
}
val res = reset {
gen()
error("It never ends that way, too!"): Result
}
val fib: Stream[Int] = res.toStream
(credit: PEP-255)

66. Continuations
• This is cool and all, but what’s it good for?

67. Continuations
• This is cool and all, but what’s it good for?
• Not as much as you would think

68. reset {
for (i <- 0 to 10) {
shift { (k: Unit => Unit) => i }
}
}

69. reset {
for (i <- 0 to 10) {
shift { (k: Unit => Unit) => i }
}
}

70. Continuations
• This is cool and all, but what’s it good for?
• Not as much as you would think
• Nonblocking I/O
• Multi-page wizards
• Framework support is needed

71. Conclusion
• Higher-Kinds • Type Encodings
• Classify types • Are really cool!
• Typeclasses • Continuations
• Categorize types • Powerful
• ...but useless

72. Questions?