Will it Blend? - ScalaSyd February 2015

Sometimes merging or appending collections together doesn't work as expected.

Video: http://goo.gl/hQxxqz
Code: http://goo.gl/aQUifC

Transcript

1. Will it Blend? February 2015 @filippovitale
3. value value value Map Set key value key value key value List v v v v
4. List
5. Immutable Collection Hierarchy Traversable Seq List http://docs.scala-lang.org/tutorials/FAQ/collections.html
6. Immutable Collection Hierarchy Traversable Seq List http://docs.scala-lang.org/tutorials/FAQ/collections.html def ++[B] (that:Traversable[B]) :Traversable[B]
7. Blending Lists List(1, 2, 3) ++ List(4, 5, 6) == ???
8. Blending Appending Lists List(1, 2, 3) ++ List(4, 5, 6) == List(1, 2, 3, 4, 5, 6) http://www.scala-lang.org/api/current/#scala.collection.immutable.List http://docs.scala-lang.org/overviews/collections/seqs.html def ++[B](that: Traversable[B]): List[B] Returns a new list containing the elements from the left hand operand followed by the elements from the right hand operand.
9. Set
10. Immutable Collection Hierarchy Traversable Seq Set List HashSet http://docs.scala-lang.org/tutorials/FAQ/collections.html
11. Blending Sets Set(1, 2, 3) ++ Set(4, 5, 6) == ???
12. Blending Adding Sets Set(1, 2, 3) ++ Set(4, 5, 6) == Set(5, 1, 6, 2, 3, 4) http://www.scala-lang.org/api/current/#scala.collection.immutable.Set http://docs.scala-lang.org/overviews/collections/sets.html def ++[B](that: Traversable[B]): Set[B] Returns a new set containing the elements from the left hand operand followed by the elements from the right hand operand.
13. Blending Adding Sets Set(1, 2, 3) ++ Set(4, 5, 6) == Set(5, 1, 6, 2, 3, 4) Set(1, 2) ++ Set(2, 3) == Set(1, 2, 3)
16. Map
17. Immutable Collection Hierarchy Traversable Seq Set Map List HashSet HashMap http://docs.scala-lang.org/tutorials/FAQ/collections.html
18. Blending Adding Maps Map() ++ Map("a" -> 1) == Map("a" -> 1) http://www.scala-lang.org/api/current/#scala.collection.immutable.Map http://docs.scala-lang.org/overviews/collections/maps.html def ++[B](that: Traversable[(A, B)]): Map[A, B] Returns a new map containing the elements from the left hand operand followed by the elements from the right hand operand.
19. Blending Adding Maps Map("a" -> Set(1, 2)) ++ Map("a" -> Set(2, 3)) == ??? http://www.scala-lang.org/api/current/#scala.collection.immutable.Map http://docs.scala-lang.org/overviews/collections/maps.html def ++[B](that: Traversable[(A, B)]): Map[A, B] Returns a new map containing the elements from the left hand operand followed by the elements from the right hand operand.
20. Map("a" -> Set(1, 2)) ++ Map("a" -> Set(2, 3)) == ??? 1: Map("a" -> Set(1, 2)) 2: Map("a" -> Set(1, 2, 3)) 3: Map("a" -> Set(2, 3)) 4: RuntimeException 5: Compiler Error What is the result of “blending” those Maps?
21. Map("a" -> Set(1, 2)) ++ Map("a" -> Set(2, 3)) == ??? 1: 2: 3: Map("a" -> Set(2, 3)) 4: 5: What is the result of “blending” those Maps?
22. Map("a" -> Set(1, 2)) ??? Map("a" -> Set(2, 3)) Map("a" -> Set(1, 2, 3))
26. Map with values as Set (of Int) “a” Set(1, 2) “key b” Set(4, 7, 5) “key c” Set(9, 4) “a” Set(2, 3) “key c” Set(3, 4) “key d” Set(5, 6) val ma: Map[String, Set[Int]] val mb: Map[String, Set[Int]]
27. Map with values as Set (of Int) “a” Set(1, 2) “a” Set(2, 3) “a” Set(1, 2) ++ Set(2, 3)
28. Map with values as Set (of Int) “a” Set(1, 2) “a” Set(2, 3) “a” Set(1, 2, 3)
29. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { for ((k, v) <- mb) { ??? } }
30. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { val result = mutable.Map() ++ ma for ((k, v) <- mb) { ??? } result.toMap }
31. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { val result = mutable.Map() ++ ma mb foreach { case (k, v) => ??? } result.toMap }
32. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { val result = mutable.Map() ++ ma mb foreach { case (k, v) => if (result.contains(k)) result += k -> (result(k) ++ v) else result += k -> v } result.toMap }
33. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { } (ma /: mb) { case (result,(k, v)) => if (result.contains(k)) result + (k -> (result(k) ++ v)) else result + (k -> v) } val result = mutable.Map() ++ ma mb foreach { case (k, v) => if (result.contains(k)) result += k -> (result(k) ++ v) else result += k -> v } result.toMap
34. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { } (ma /: mb) { case (result,(k, v)) => if (result.contains(k)) result + (k -> (result(k) ++ v)) else result + (k -> v) } val result = mutable.Map() ++ ma mb foreach { case (k, v) => if (result.contains(k)) result += k -> (result(k) ++ v) else result += k -> v } result.toMap mb.foldLeft(ma) { ... }
35. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { } (ma /: mb) { case (result,(k, v)) => if (result.contains(k)) result + (k -> (result(k) ++ v)) else result + (k -> v) } val result = mutable.Map() ++ ma mb foreach { case (k, v) => if (result.contains(k)) result += k -> (result(k) ++ v) else result += k -> v } result.toMap
36. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { } (ma /: mb) { case (result,(k, v)) => if (result.contains(k)) result + (k -> (result(k) ++ v)) else result + (k -> v) } val result = mutable.Map() ++ ma mb foreach { case (k, v) => if (result.contains(k)) result += k -> (result(k) ++ v) else result += k -> v } result.toMap
37. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { (ma /: mb) { case (result,(k, v)) => if (result.contains(k)) result + (k -> (result(k) ++ v)) else result + (k -> v) } }
38. (ma /: mb) { case (result,(k, v)) => result + (k -> { result.get(k) match { case Some(vr) => vr ++ v case None => v } }
39. (ma /: mb) { case (result,(k, v)) => result + (k -> { result.get(k) match { case Some(vr) => vr ++ v case None => v } // .map(_ ++ v).getOrElse(v) // // // }}
40. (ma /: mb) { case (result,(k, v)) => result + (k -> { result.get(k) match { case Some(vr) => vr ++ v case None => v } // .map(_ ++ v).getOrElse(v) // .some(_ ++ v).none(v) // // }}
41. (ma /: mb) { case (result,(k, v)) => result + (k -> { result.get(k) match { case Some(vr) => vr ++ v case None => v } // .map(_ ++ v).getOrElse(v) // .some(_ ++ v).none(v) // .fold(v)(_ ++ v) // }}
42. (ma /: mb) { case (result,(k, v)) => result + (k -> { result.get(k) match { case Some(vr) => vr ++ v case None => v } // .map(_ ++ v).getOrElse(v) // .some(_ ++ v).none(v) // .fold(v)(_ ++ v) // .cata(_ ++ v, v) }}
43. (ma /: mb) { case (result,(k, v)) => result + (k -> { result.get(k) match { case Some(vr) => vr ++ v case None => v } // .map(_ ++ v).getOrElse(v) // .some(_ ++ v).none(v) // .fold(v)(_ ++ v) // .cata(_ ++ v, v) }} http://stackoverflow.com/questions/5328007/why-doesnt-option-have-a-fold-method http://en.wikipedia.org/wiki/Catamorphism “Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire”
44. (ma /: mb) { case (result,(k, v)) => result + (k -> { result.get(k) match { case Some(vr) => vr ++ v case None => v } // .map(_ ++ v).getOrElse(v) // .some(_ ++ v).none(v) // .fold(v)(_ ++ v) // .cata(_ ++ v, v) }} http://stackoverflow.com/questions/5328007/why-doesnt-option-have-a-fold-method http://en.wikipedia.org/wiki/Catamorphism “Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire”
45. (ma /: mb) { case (result, (k, v)) => result + (k -> result.get(k).cata(_ ++ v, v)) } val result = mutable.Map() ++ ma mb foreach { case (k, v) => result += (k -> result.get(k).cata(_ ++ v, v)) }
49. What if we change Data Structure?
50. def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = (ma /: mb) { case (result, (k, v)) => result + (k -> result.get(k).cata(_ ++ v, v)) } Map[String, Set[Int]] Map[String, Map[Int, Set[Int]]]
51. def blend(ma: Map[String, Map[Int, Set[Int]]], mb: Map[String, Map[Int, Set[Int]]]) : Map[String, Map[Int, Set[Int]]] = (ma /: mb) { case (result, (k, v)) => result + ??? // { ??? => { ??? } } } Map[String, Set[Int]] Map[String, Map[Int, Set[Int]]]
52. trait Blendable[A] { def blend(ma: A, mb: A): A } new Blendable[...] { def blend(ma: ..., mb: ...): ... = ??? }
53. trait Blendable[A] { def blend(ma: A, mb: A): A } new Blendable[...] { def blend(ma: ..., mb: ...): ... = ??? } x10 Developer
54. What is the meaning of “Blending”? (in my world)
55. What blended “as expected”? List using the ++ binary operator Set using the ++ binary operator List(1, 2, 3) ++ List(4, 5, 6) == List(1, 2, 3, 4, 5, 6) Set(1, 2) ++ Set(2, 3) == Set(1, 2, 3)
56. (List, ++) (Set, ++) (1 blend 2) == ??? What about Int?
57. (List, ++) (Set, ++) (Int, +) (1 blend 2) == 1 + 2 == 3 What about Int?
58. (List, ++) (Set, ++) (Int, +) (String, +) ("ab" blend "cd") == ("ab" + "cd") == "abcd" String
59. (List, ++) (Set, ++) (Int, +) (String, +) (Map[...], Blendable[...].blend) Blendable[Map[String, Set[Int]]].blend(ma, mb) Map[String, Set[Int]]
60. What can Mathematicians tell us here?
61. Warning Category Theory ahead ☣
62. What is a Semigroup? Michael Barr, Charles Wells - Category Theory for Computing Science Semigroups “A semigroup is a set S together with an associative binary operation m: S × S → S”
63. Closure Property http://en.wikipedia.org/wiki/Closure_(mathematics) trait Semigroup[T] { def op(a: T, b: T): T } For all a, b in T, the result of the operation a ⋅ b is also in T: ∀a, b ∈ T : a∙b ∈ T
64. http://en.wikipedia.org/wiki/Closure_(mathematics) trait Semigroup[T] { def op(a: T, b: T): T } def op(a: Boolean, b: Boolean): Boolean def op(a: Int, b: Int): Boolean ✓ ✘ Closure Property
65. Associative Property http://en.wikipedia.org/wiki/Associative_property trait Semigroup[T] { def op(a: T, b: T): T } For all a, b, and c in T, the equation (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c) holds: ∀a, b, c ∈ T : (a∙b)∙c = a∙(b∙c) (a op b) op c == a op (b op c)
66. What is a Semigroup? Michael Barr, Charles Wells - Category Theory for Computing Science Semigroups “A semigroup is a set S together with an associative binary operation m: S × S → S”
67. Scalaz and Semigroup
68. Scalaz and Semigroup import scalaz.std.set._
69. Scalaz and Semigroup implicit def setSemigroup[A]:Semigroup[Set[A]] = new Semigroup[Set[A]] { def append(f1: Set[A], f2: => Set[A]) = f1 ++ f2 }
70. Scalaz and Semigroup implicit def setSemigroup[A]:Semigroup[Set[A]] = new Semigroup[Set[A]] { def append(f1: Set[A], f2: => Set[A]) = f1 ++ f2 } op
71. Scalaz and Semigroup import scalaz.syntax.semigroup._ import scalaz.std.list._ Set(1, 2) |+| Set(2, 3) res0: scala.collection.immutable.Set[Int] = Set(1, 2, 3)
72. Scalaz and Semigroup import scalaz.syntax.semigroup._ import scalaz.std.list._ List(1, 2) |+| List(3, 4) res0: scala.collection.immutable.List[Int] = List(1, 2, 3, 4)
73. Scalaz and Semigroup import scalaz.syntax.semigroup._ import scalaz.std.string._ "a" |+| "b" |+| "c" res0: String = abc
74. /** * A semigroup in type F must satisfy two laws: * * - '''closure''': `∀ a, b in F, append(a, b)` is also in `F`. * - '''associativity''': `∀ a, b, c` in `F`, the equation * `append(append(a, b), c) = append(a, append(b , c))` holds. */ trait SemigroupLaw { def associative(f1: F, f2: F, f3: F)(implicit F: Equal[F]): Boolean = F.equal(append(f1, append(f2, f3)), append(append(f1, f2), f3)) }
75. import scalaz.scalacheck.ScalazProperties._ semigroup.laws[Int].check + semigroup.associative: OK, passed 100 tests.
76. import scalaz.scalacheck.ScalazProperties._ semigroup.laws[String].check semigroup.laws[Set[Int]].check semigroup.laws[List[String]].check semigroup.laws[Map[Int, Int]].check + semigroup.associative: OK, passed 100 tests. + semigroup.associative: OK, passed 100 tests. + semigroup.associative: OK, passed 100 tests. + semigroup.associative: OK, passed 100 tests.
77. import scalaz.scalacheck.ScalazProperties._ semigroup.laws[Map[String, Set[Int]]].check
78. import scalaz.scalacheck.ScalazProperties._ semigroup.laws[Map[String, Set[Int]]].check + semigroup.associative: OK, passed 100 tests.
79. Map("a" -> Set(1, 2)) |+| Map("a" -> Set(2, 3))
80. Map("a" -> Set(1, 2)) |+| Map("a" -> Set(2, 3)) res0: ...immutable.Map[...] = Map(a -> Set(1, 2, 3))
81. Map("a" -> Set(1, 2)) |+| Map("a" -> Set(2, 3)) “Some data structures form interesting semigroups as long as the types of the elements they contain also form semigroups.” “adapted” from: Functional Programming in Scala - Part 3 - Chapter 10 Monoids
82. Map("a" -> Map("aa" -> Map("aaa" -> Map("aaaa" -> List(1, 3), "aaab" -> List(2, 4))))) |+| Map("a" -> Map("aa" -> Map("aaa" -> Map("aaaa" -> List(5, 7), "aaab" -> List(6, 8))))) Map(a->Map(aa->Map(aaa->Map(aaaa->List(1, 3, 5, 7), aaab->List(2, 4, 6, 8)))))
83. Map("a" -> 1, "b" -> 4) |+| Map("a" -> 2)
84. Map("a" -> 1, "b" -> 4) |+| Map("a" -> 2) res0: ...immutable.Map[...] = Map(a -> 3, b -> 4)
85. 1.some |+| 2.some res0: Option[Int] = Some(3) 1.some |+| none[Int] res1: Option[Int] = Some(1)
86. implicit def optionMonoid[A: Semigroup]: ... def append(f1: Option[A], f2: => Option[A]) = (f1, f2) match { case (Some(a1), Some(a2)) => Some(Semigroup[A].append(a1, a2)) case (Some(a1), None) => f1 case (None, sa2 @ Some(a2)) => sa2 case (None, None) => None } }
87. Customised Semigroup case class MeetupOrganiser(name: String, meetup: String, yowCommunityAward: Int) val jed = MeetupOrganiser("Jed", "scalasyd", 1) val mark = MeetupOrganiser("Mark", "scalasyd", 0) val leo = MeetupOrganiser("Leonardo", "clj-syd", 0)
88. Customised Semigroup case class MeetupOrganiser(name: String, meetup: String, yowCommunityAward: Int) implicit val meetupOrganiserSemigroup = new Semigroup[MeetupOrganiser] { def append(f1: MeetupOrganiser, f2: => MeetupOrganiser): MeetupOrganiser = if (f1.yowCommunityAward >= f2.yowCommunityAward) f1 else f2 }
89. Customised Semigroup implicit val meetupOrganiserArbitrary: Arbitrary[MeetupOrganiser] = Arbitrary(for { n <- arbitrary[String] m <- arbitrary[String] r <- arbitrary[Int] } yield MeetupOrganiser(n, m, r)) implicit val meetupOrganiserEqual: Equal[MeetupOrganiser] = Equal.equal(_ == _) semigroup.laws[MeetupOrganiser].check + semigroup.associative: OK, passed 100 tests.
90. Customised Semigroup mark |+| leo res0: MeetupOrganiser = MeetupOrganiser(Mark,scalasyd,0) mark |+| leo |+| jed res1: MeetupOrganiser = MeetupOrganiser(Jed,scalasyd,1) NonEmptyList(mark, leo, jed).suml1 res2: MeetupOrganiser = MeetupOrganiser(Jed,scalasyd,1)
92. Computer programming as an art (1974)
93. Map[String, Set[Int]]
95. Thanks! February 2015 @filippovitale
96. Questions? February 2015 @filippovitale