Presentation slide from St. Louis Lambda Lounge presentation on August 5th 2010.

1. Grokking Monads in Scala St. Louis Lambda Lounge August 5, 2010 Tim Dalton Senior Software Engineer Object Computing Inc.

2. Monads Are… Just a monoid in the category of endofunctors. Like “duh”!

6. Scala &quot;For comprehensions&quot; for (i <- 1 to 5) yield i scala.collection.immutable.IndexedSeq[Int] = Vector(1, 2, 3, 4, 5) for (i <- 1 to 5 if i % 2 == 0) yield i scala.collection.immutable.IndexedSeq[Int] = Vector(2, 4) for (i <-1 to 5 if i % 2 == 0) { print (i + &quot; &quot; ) } 2 4 for (i <-1 to 5 if i % 2 == 0; j <- 1 to 5 if j % 2 != 0) yield ( i * j ) scala.collection.immutable.IndexedSeq[Int] = Vector(2, 6, 10, 4, 12, 20) for (i <-1 to 5 if i % 2 == 0; j <- 1 to 5 if j % 2 != 0; k <- 1 to 5) yield ( i * j / k ) scala.collection.immutable.IndexedSeq[Int] = Vector(2, 1, 0, 0, 0, 6, 3, 2, 1, 1, 10, 5, 3, 2, 2, 4, 2, 1, 1, 0, 12, 6, 4, 3, 2, 20, 10, 6, 5, 4)

7. De-sugarized For comprehensions (1 to 5).map(identity) scala.collection.immutable.IndexedSeq[Int] = Vector(1, 2, 3, 4, 5) (1 to 5).filter{_ % 2 == 0}.map(identity) scala.collection.immutable.IndexedSeq[Int] = Vector(2, 4) (1 to 5).filter{_ % 2 == 0}.foreach { i => print (i + &quot; &quot; ) } 2 4 (1 to 5).filter{_ % 2 == 0}.flatMap { i => (1 to 5).filter{_ % 2 != 0}.map{ j => i * j } } scala.collection.immutable.IndexedSeq[Int] = Vector(2, 6, 10, 4, 12, 20) (1 to 5).filter{_ % 2 == 0}.flatMap { i => (1 to 5).filter{_ % 2 != 0}.flatMap{ j => (1 to 5).map{ k => i * j / k } } } scala.collection.immutable.IndexedSeq[Int] = Vector(2, 1, 0, 0, 0, 6, 3, 2, 1, 1, 10, 5, 3, 2, 2, 4, 2, 1, 1, 0, 12, 6, 4, 3, 2, 20, 10, 6, 5, 4)

9. Simplest Monad – Identity case class Identity[A](value:A) { def map[B](f:(A) => B) = Identity(f(value)) def flatMap[B](f:(A) => Identity[B]) = f(value) }

11. AST Evaluator – Identity object IdentityEvaluator extends EvaluatorTrait[Term, Identity[Int]] { def eval(term: Term) = term match { case Constant(x) => Identity(x) case Divide(a,b) => for (bp <- eval(b); ap <- eval(a)) yield (ap/bp) } println(eval(Divide(Divide(Constant(1972),Constant(2)), Constant(23)))) Identity(42) println(eval(Divide(Constant(1),Constant(0)))) Exception in thread &quot;main&quot; java.lang.ArithmeticException: / by zero

13. Usefulness of Option val areaCodes = Map( &quot;Fenton&quot; -> 636, &quot;Florissant&quot; -> 314, &quot;Columbia&quot; -> 573 ) val homeTowns = Map( &quot;Moe&quot; -> &quot;Columbia&quot;, &quot;Larry&quot; -> &quot;Fenton&quot;, &quot;Curly&quot; -> &quot;Florissant&quot;, &quot;Schemp&quot; -> &quot;St. Charles” ) def personAreaCode(person:String) = for (homeTown <- homeTowns.get(person); areaCode <- areaCodes.get(homeTown)) yield (areaCode)

14. Usefulness of Option println(personAreaCode(&quot;Moe&quot;)) Some(573) println(personAreaCode(&quot;Schemp&quot;)) None println(personAreaCode(&quot;Joe&quot;)) None println( for (areaCode <- areaCodes if areaCode._2 == 314; stoogeHome <- homeTowns if stoogeHome._2 == areaCode._1) yield stoogeHome._1 ) List(Curly) Look Mom, No null checks !!!

15. AST Evaluator - Option object OptionDivide extends ((Option[Int], Option[Int]) => Option[Int]) { def apply(a:Option[Int], b:Option[Int]) = for (bp <- b; ap <- if (bp != 0) a else None) yield (ap/bp) } object OptionEvaluator extends EvaluatorTrait[Term, Option[Int]] { def eval(term: Term) = term match { case Constant(x) => Some(x) case Divide(a,b) => OptionDivide(eval(a), eval(b)) } }

16. AST Evaluator - Option println(eval(Divide(Divide(Constant(1972),Constant(2)), Constant(23)))) Some(42) println(eval(Divide(Constant(1),Constant(0)))) None

17. “ Wonkier” Monad – State object State { def unit[S,A](a:A) = new State((s:S) => (s, a)) } case class State[S, A](val s:S => (S, A)) { def map[B](f: A => B): State[S,B] = flatMap((a:A) => State.unit(f(a))) def flatMap[B](f: A => State[S,B]): State[S,B] = State((x:S) => { val (a,y) = s(x) f(y).s(a) }) }

18. State Monad val add = (x:Int, y:Int) => State[List[String], Int]((s:List[String]) => { ((x + &quot; + &quot; + y + &quot; = &quot; + (x + y)) :: s, (x + y)) }) val sub = (x:Int, y:Int) => State[List[String], Int]((s:List[String]) => { ((x + &quot; - &quot; + y + &quot; = &quot; + (x - y)) :: s, (x - y)) }) val f = for (x1 <- add(2 , 2); x2 <- sub(x1, 5); x3 <- add(x2, 2)) yield (x3) val result = f.s(Nil) println(&quot;log = &quot; + result._1.reverse) log = List(2 + 2 = 4, 4 - 5 = -1, -1 + 2 = 1) println(&quot;result = &quot; + result._2) result = 1

19. State Monad – No Sugar val f = add(2,2).flatMap{ x1 => sub(x1, 5).flatMap { x2 => add(x2,2) } }.map(identity) val result = f.s(Nil) println(&quot;log = &quot; + result._1.reverse) log = List(2 + 2 = 4, 4 - 5 = -1, -1 + 2 = 1) println(&quot;result = &quot; + result._2) result = 1

20. AST Evaluator - State object StateEvaluator extends EvaluatorTrait[Term, State[Int, Option[Int]]] { def eval(term: Term) = term match { case Constant(x) => State((s:Int) => (s + x, Some(x))) case Divide(a,b) => for ( evala <- eval(a); evalb <- eval(b)) yield OptionDivide(evala, evalb) } println(eval(Divide(Divide(Constant(1972),Constant(2)), Constant(23))).s(0)) (1997,Some(42)) println(eval(Divide(Constant(20),Constant(0))).s(0)) (20,None)

22. Discussion Can monads ever be “mainstream” ?

23. Links James Iry – “Monads are Elephants” http://james-iry.blogspot.com/2007/09/monads-are-elephants-part-1.html http://james-iry.blogspot.com/2007/10/monads-are-elephants-part-2.html http://james-iry.blogspot.com/2007/10/monads-are-elephants-part-3.html Philip Wadler’s Monad Papers http://homepages.inf.ed.ac.uk/wadler/topics/monads.html Brian Beckman Monad Videos http://channel9.msdn.com/shows/Going+Deep/Brian-Beckman-Dont-fear-the-Monads/ http://channel9.msdn.com/shows/Going+Deep/Brian-Beckman-The-Zen-of-Expressing-State-The-State-Monad/