Blazing Fast, Pure Effects without Monads — LambdaConf 2018

1
Blazing Fast, Pure
Effects without
Monads
LambdaConf 2018
By John A. De Goes — @jdegoes

2
1991 1998 2018 - April
Eugenio Moggi John Hughes Flavio Brasil
F R O M M O N A D S T O A R R O W S
A brief history of effects leading to KleisliIO.
KleisliIO
2018 - June
Notions of
computation
and monads
Generalizing
monads to
arrows
TraneIO:
Arrows & tasks
in Scala

3
THE TRINITY OF FP
Total
Deterministic
Free of Side-effects

4
THE TRINITY OF FUNCTIONAL PROGRAMMING
Total
Deterministic
f : A => B
a ∈ A ⇒ f(a) ∈ B

5
Total
Deterministic
def notTotal1(a: Int): String = null
def notTotal2(a: Int): String =
throw new Error(" ")
def notTotal3(a: Int): String = notTotal3(a)

6
Total
Deterministic
f : A => B
b1 = f(a) ∧ b2 = f(a) ⇒ b1 = b2

7
Total
Deterministic
def notDeterministic1(a: Int): String =
if (Math.random() > 0.5) "Hello"
else "Goodbye"
scala.io.StdIn.readLine()
(System.nanoTime() + a).toString

8
Total
Deterministic
f : A => B
f’s only computational effect is computing B

9
Total
Deterministic
def notEffectFree1(a: Int): String =
{ println("Hello"); a.toString }
def notEffectFree2(a: Int): String = {
val _ = scala.io.StdIn.readLine()
a.toString
}
def notEffectFree3(a: Int): String =
{ Logger.log(a); (a * a).toString }

10
THE RICHES OF PURITY
Type Reasoning
Equality Reasoning

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Type Reasoning
Equality Reasoning
def foo1[A](a: A): A
def foo2[A](a: A, f: A => A): A
def foo3[A, B](f: (A => A) => B): B

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Type Reasoning
Equality Reasoning
def println(line: String): Unit
def readLine(): String

13
Type Reasoning
Equality Reasoning
def f = (x: Int) => x * x
val b = f(a)
val c = b + b
// c = b + b
// c = f(a) + f(a)
// c = (a * a) + (a * a)
// c = 2 * a * a

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Type Reasoning
Equality Reasoning
def readLine = scala.io.StdIn.readLine()
val a = readLine
val b = a + a
// b = a + a
// b = readLine + readLine
// !?!?! readLine + readLine !=
// { val a = readLine; a + a }

15
MONADIC EFFECTS
Effects Into Values
Values Into Effects
The Cost of Value Effects

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EFFECTS INTO VALUES
println
IO[Unit]
String
def println(line: String): IO[Unit]

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EFFECTS INTO VALUES
IO[A]
Immutable value produced by the effect
Immutable value describing the effect

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EFFECTS INTO VALUES
sealed trait IO[A] {
def map[B](f: A => B): IO[B] =
flatMap((a: A) => IO.point(f(a)))
def flatMap[B](f: A => IO[B]): IO[B] =
FlatMap(this, f)
}
object IO {
def point[A](a: A): IO[A] = Point(a)
}
final case class PrintLn(line: String) extends IO[Unit]
final case class ReadLine() extends IO[String]
final case class FlatMap[A, B](fa: IO[A], f: A => IO[B]) extends IO[B]
final case class Point[A](a: A) extends IO[A]

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val name = readLine()
println("Hello " + name + ", how are you?")
EFFECTS INTO VALUES
println
IO[Unit]
def readLine: IO[String]
def println(line: String): IO[Unit]
val program =
for {
name <- readLine
_ <- println("Hello " + name + ", how are you?")
} yield ()
readLine
IO[String]
String
Unit

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VALUES INTO EFFECTS
def unsafePerformIO(io: IO[A]): A = io match {
case PrintLn(line) => println(line)
case ReadLine() => readLine()
case FlatMap(fa, f) =>
unsafePerformIO(f(unsafePerformIO(fa)))
case Point(a) => a
}

22
THE COST OF VALUE EFFECTS
println
F[Unit]
class SS {
for {
name <- readLine
_ <- println("Hello " + name +
", how are you?")
} yield ()
readLine
F[String]
String
Unit

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readLine.flatMap(name =>
printLn("Hello, " + name +
", how are you?"))
Allocations
Allocation
Megamorphic
Dispatch

24
1 Statement in Procedural
Programming
4 Extra Allocations, 1 Extra
Megamorphic Dispatch in
Functional Programming
=

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IO.sync {
App.main()
}
Monolith Composed
Pure Values

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Future

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KLEISLI EFFECTS
Effects Into Values
Values Into Effects
The Cost of Value Effects

29
EFFECTS INTO VALUES
println
FunctionIO[String, Unit]
val println: FunctionIO[String, Unit]

30
EFFECTS INTO VALUES
FunctionIO[A, B]
Immutable input value to the function
Immutable value describing the effectful function
Immutable output value from the function

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EFFECTS INTO VALUES
final case class FunctionIO[A, B](apply0: A => IO[B])
extends (A => IO[B]) {
def apply(a: A): IO[B] = apply0(a)
def andThen[C](f: FunctionIO[B, C]): FunctionIO[A, C] =
FunctionIO(a => apply(a).flatMap(f.apply))
}
object FunctionIO {
def lift[A, B](f: A => B): FunctionIO[A, B] =
FunctionIO(IO.point.compose(f))
}

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val name = readLine()
println("Hello " + name + ", how are you?")
EFFECTS INTO VALUES
val readLine: FunctionIO[Unit, String]
val println: FunctionIO[String, Unit]
val program =
readLine
.andThen(lift((name: String) => "Hello, " + name +
", how are you?"))
.andThen(println)
readLine
FunctionIO[Unit, String]
<anonymous>
FunctionIO[String,String]
println

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VALUES INTO EFFECTS
val program: FunctionIO[Unit, Unit]
unsafePerformIO(program())

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THE COST OF EFFECT VALUES
readLine.andThen(lift((name: String) =>
"Hello, " + name + ", how are you?"))
.andThen(println)
readLine
FunctionIO[Unit, String]
<anonymous>
FunctionIO[String,String]
println

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Megamorphic
Dispatches
final case class FunctionIO[A, B](apply: A => IO[B])
readLine.andThen(println)
Allocations Allocations

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1 Statement in Procedural
Programming
6 Extra Allocations, 3 Extra
Megamorphic Dispatches in
=

37
THE PROMISE OF KLEISLIIO
sealed trait FunctionIO[A, B] extends (A => IO[B]) { ... }
final class Pure[A, B](val apply0: A => IO[B])
extends FunctionIO[A, B] {
def apply(a: A): IO[B] = apply0(a)
}
final class Impure[A, B](val apply0: A => B)
extends FunctionIO[A, B] {
def apply(a: A): IO[B] = IO.point(apply0(a))
}
val readLine: FunctionIO[Unit, String] =
new Impure(_ => scala.io.StdIn.readLine())
val printLn: FunctionIO[String, Unit] = new Impure(println)

38
THE PROMISE OF KLEISLIIO
class Impure[A, B](val apply0: A => B)
1 Invocation in Procedural
Programming
0 Extra Allocations,
1 Extra Dispatch in
=

39
KLEISLIIO
Running KleisliIO
Constructing KleisliIO
Composing KleisliIO
Introducing KleisliIO
Optimizing KleisliIO
Testing KleisliIO

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KLEISLIIO
sealed trait KleisliIO[E, A, B] extends (A => IO[E, B]) { ... }
object KleisliIO {
class KleisliIOError[E](error: E) extends Throwable {
def unsafeCoerce[E2] = error.asInstanceOf[E2]
}
class Pure[E, A, B](apply0: A => IO[E, B]) extends KleisliIO[E, A, B] {
override final def apply(a: A): IO[E, B] = apply0(a)
}
class Impure[E, A, B](val apply0: A => B) extends KleisliIO[E, A, B] {
override final def apply(a: A): IO[E, B] =
IO.suspend {
try IO.now[E, B](apply0(a))
catch {
case e: KleisliIOError[_] => IO.fail[E, B](e.unsafeCoerce[E])
}
}
}
...
}

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RUNNING KLEISLIIO
val printLn: KleisliIO[IOException, String, Unit]
printLn("Hello, world!") // IO[IOException, Unit]

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CONSTRUCTING PURE KLEISLIIO
object KleisliIO {
...
def pure[E, A, B](f: A => IO[E, B]):
KleisliIO[E, A, B] = ???
...
}
val printLn: KleisliIO[Void, String, Unit] =
KleisliIO.pure((a: String) => IO.sync(println(a)))

43
CONSTRUCTING IMPURE KLEISLIIO
object KleisliIO {
...
def impure[E, A, B](catcher: PartialFunction[Throwable, E])(f: A => B)
...
}
val IOExceptions: PartialFunction[Throwable, IOException] = {
case io : IOException => io
}
val printLn: KleisliIO[Void, String, Unit] =
KleisliIO.impure(IOExceptions)(println)

44
CONSTRUCTING IMPURE KLEISLIIO
object KleisliIO {
...
def impureVoid[A, B](f: A => B): KleisliIO[Void, A, B] = ???
...
}
val printLn: KleisliIO[Void, String, Unit] = KleisliIO.impureVoid(println)

45
CONSTRUCTING KLEISLIIO
object KleisliIO {
...
def identity[E, A]: KleisliIO[E, A, A] = ???
...
}
A A
KleisliIO.identity[Void, Int](1) // IO.point(1)

46
COMPOSING KLEISLIIO
trait KleisliIO[E, A, B] extends (A => IO[E, B])
{
...
def >>>[C](that: KleisliIO[E, B, C]):
KleisliIO[E, A, C] = ???
...
}
...
A B C
A C
readLine >>> printLn

47
COMPOSING KLEISLIIO
A
B
C
(B, C) => D
A D
trait KleisliIO[E, A, B] extends (A => IO[E, B]) {
...
def zipWith[C, D](that: KleisliIO[E, A, C])(f: (B, C) => D):
KleisliIO[E, A, D] = ???
...
}
readLine.zipWith(readLine)((l1, l2) => l1 + l2)

48
COMPOSING KLEISLIIO
...
def &&&[C]( that: KleisliIO[E, A, C]):
KleisliIO[E, A, (B, C)] = ???
...
}
A
B
C
A (B,C)
readLine &&& readLine

49
COMPOSING KLEISLIIO
...
def |||[C](that: KleisliIO[E, C, B]):
KleisliIO[E, Either[A, C], B]
...
}
A
B
C
Either[A, C] D
(fancyPrintLn |||
standardPrintLn)(Left("Fancied!"))

50
COMPOSING KLEISLIIO
...
def first: KleisliIO[E, A, (B, A)] =
this &&& KleisliIO.identity[E, A]
...
}
A B
A (B, A)
readLine >>> printLn.first // (Unit, String)

51
COMPOSING KLEISLIIO
...
def second: KleisliIO[E, A, (A, B)] =
KleisliIO.identity[E, A] &&& this
...
}
A B
A (A, B)
readLine >>> printLn.second // (String, Unit)

52
COMPOSING KLEISLIIO
...
def left[C]:
KleisliIO[E, Either[A, C], Either[B, C]] = ???
...
}
Either[A, C] Either[B, C]
A B
printLn.left[String]( Left("Hello")) //
Left[Unit]

53
COMPOSING KLEISLIIO
...
def right[C]:
KleisliIO[E, Either[A, C], Either[B, C]] = ???
...
}
Either[A, C] Either[B, C]
A B
printLn.right[String]( Right("Hello")) // Right[Unit]

54
COMPOSING KLEISLIIO
trait KleisliIO[E, A, B] extends (A => IO[E, B])
{
...
def asEffect: KleisliIO[E, A, A] =
self.first >>> KleisliIO._2
...
}
A A
B
printLn.asEffect // String

55
COMPOSING KLEISLIIO
object KleisliIO {
...
def test[E, A](cond: KleisliIO[E, A, Boolean]):
KleisliIO[E, A, Either[A, A]] = ???
...
}
test(KleisliIO.lift(_ > 2))(4) // IO[Void, Either[Int,
Int]]
cond
A Bool
A Either[A, A]
Right(a)Left(a)

56
COMPOSING KLEISLIIO
object KleisliIO {
...
def ifThenElse[E, A, B](cond : KleisliIO[E, A, Boolean])
(then0: KleisliIO[E, A, B])(else0: KleisliIO[E, A, B]):
KleisliIO[E, A, B] =
test[E, A](cond) >>> (then0 ||| else0)
...
}
ifThenElse(KleisliIO.lift(_ == "John"))(printLn)(const(()))
A B
else0 then0
A BA B
cond
A Bool

57
COMPOSING KLEISLIIO
object KleisliIO {
...
def whileDo[E, A](check: KleisliIO[E, A, Boolean])
(body : KleisliIO[E, A, A]): KleisliIO[E, A, A] = ???
...
}
A A
A Boolean
A Abody
check
readLine >>> whileDo(lift(_ != “John”)) {
KleisliIO.point(“Wrong name”) >>> printLn >>> readLine
}

58
OPTIMIZING KLEISLIIO
final def compose[E, A, B, C](second: KleisliIO[E, B, C], first: KleisliIO[E, A, B]):
KleisliIO[E, A, C] =
(second, first) match {
case (second: Impure[_, _, _], first: Impure[_, _, _]) =>
new Impure(second.apply0.compose(first.apply0))
case _ =>
new Pure((a: A) => first(a).flatMap(second))
}

59
final def ifThenElse[E, A, B](cond: KleisliIO[E, A, Boolean])
(then0: KleisliIO[E, A, B])(else0: KleisliIO[E, A, B]): KleisliIO[E, A, B] =
(cond, then0, else0) match {
case (cond: Impure[_, _, _], then0: Impure[_, _, _], else0: Impure[_, _, _]) =>
new Impure[E, A, B](a => if (cond.apply0(a)) then0.apply0(a) else else0.apply0(a))
case _ => test[E, A](cond) >>> (then0 ||| else0)
}

60
final def whileDo[E, A](check: KleisliIO[E, A, Boolean])(body: KleisliIO[E, A, A]): KleisliIO[E, A, A] =
(check, body) match {
case (check: Impure[_, _, _], body: Impure[_, _, _]) =>
new Impure[E, A, A]({ (a0: A) =>
val cond = check.apply0
val update = body.apply0
var a = a0
while (cond(a)) { a = update(a) }
a
})
case _ =>
lazy val loop: KleisliIO[E, A, A] =
KleisliIO.pure((a: A) =>
check(a).flatMap((b: Boolean) =>
if (b) body(a).flatMap(loop) else IO.now(a)))
loop
}

61
TESTING KLEISLIIO - ARRAY FILL
Output: An array filled with 10,000 elements in increasing order.

62
def arrayFill(array: Array[Int]): KleisliIO[Void, Int] = {
val condition = KleisliIO.lift(i => i < array.length)
val update = KleisliIO.impureVoid{ i =>
array.update(i, i); i + 1 }
KleisliIO.whileDo(condition)(update)
}
def arrayFill(array: Array[Int])(i: Int): IO[Unit] =
if (i >= array.length) IO.unit
else IO(array.update(i, i)).flatMap(_ => arrayFill(array)(i + 1))
KleisliIO Array Fill Monadic Array Fill

63
7958.946 ops/s
3622.744 ops/s
3689.406 ops/s
Array Fill
2.18x Faster!

64
TESTING KLEISLIIO - BUBBLE SORT
Input: Array of 10000 element with reversed order
Output: bubbleSort(array)
bubbleSort(array):
i <- 1 to 10000
j <- i + 1 to 9999
lessThanEqual = array(i) <= array(j)
if (!lessThanEqual) swap(array, i, j)

65
val sort: KleisliIO[Void, Int, Unit] =
KleisliIO
.whileDo(outerLoopCheck)(
innerLoopStart >>>
KleisliIO.whileDo(innerLoopCheck)(
extractIJIndexValue >>>
KleisliIO.ifNotThen(lessThanEqual)(swapIJ) >>>
extractIJAndIncrementJ
) >>>
extractIAndIncrementI
)
sort(0)
def outerLoop(i: Int): IO[Unit] =
if (i >= array.length - 1) IO.unit
else innerLoop(i, i + 1).flatMap(_ => outerLoop(i + 1))
def innerLoop(i: Int, j: Int): IO[Unit] =
if (j >= array.length) IO.unit
else IO((array(i), array(j))).flatMap {
case (ia, ja) =>
val maybeSwap = if (lessThanEqual0(ia, ja)) IO.unit
else swapIJ(i, ia, j, ja)
maybeSwap.flatMap(_ => innerLoop(i, j + 1))
}
outerLoop(0)
KleisliIO Bubble sort Monadic Bubble sort

66
58.811 ops/s
41.545 ops/s
33.229 ops/s
1.57x Faster!
Bubble Sort

67
W H E R E F R O M H E R E
A brief roadmap for KleisliIO.
?
Infinite
Composition
Recursion
Combinator
Low-Cost
Propagation

68
THANK YOU!
Thanks to the staff, volunteers, and speakers of
LambdaConf, and to Wiem Zine El Abidine for
help with the development and
implementation of KleisliIO.
Follow me @jdegoes
Follow Wiem @wiemzin
Join Scalaz at gitter.im/scalaz/scalaz

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Blazing Fast, Pure Effects without Monads — LambdaConf 2018