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Polimorfismo cosa?

The document discusses Scala collections and provides examples of methods available in the Traversable trait. It shows how collections like List, Set and Map can be combined using the ++ operator, with List concatenating elements and Set/Map merging elements. It also demonstrates how to implement a blend function to merge Maps with Set values in an immutable way using foldLeft.

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Settembre 2015 @filippovitale Polimorfismo parametrico, polimorfismo su misura e polimorfismo cosa?
3 semplici Data Structure
Seq Set Map package scala.collection
Seq Set Map package scala.collection v v v v
Seq Set Map package scala.collection valueA valueB valueC
Seq Set Map package scala.collection key value key value key value
Seq Set Map package scala.collection base trait per implementazioni mutable e immutable
package scala.collection Seq Set Map package scala.collection.mutable ArrayBuffer HashSet HashMap
package scala.collection.mutable ArrayBuffer HashSet HashMap “Mutability is an optimisation – perhaps premature”
package scala.collection Seq Set package scala.collection.immutable Map List HashSet HashMap package scala.collection.mutable ArrayBuffer HashSet HashMap http://docs.scala-lang.org/tutorials/FAQ/collections.html
package scala.collection.immutable List HashSet HashMap Immutabilità implica: - equational reasoning - sharing with referential integrity - thread safety - …
“When you get used to immutable data, ya kinda forget how to use mutable data in a sensible way.” – Jessica Kerr
package scala.collection Traversable Seq Set Map
Quali metodi offre Traversable?
Metodi offerti da Traversable isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString
isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString Metodi offerti da Traversable def map[B](f: A => B)
isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString Metodi offerti da Traversable def foreach(f: (A) => Unit): Unit def map[B](f: A => B)
Metodi offerti da Traversable isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString
isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString Metodi offerti da Traversable def foldLeft[B](z: B)(f: (B, A) => B): B
isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString Metodi offerti da Traversable def foldLeft[B](z: B)(f: (B, A) => B): B def /:[B](z: B)(op: (B, A) => B): B = foldLeft(z)(op)
isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString Metodi offerti da Traversable def foldLeft[B](z: B)(f: (B, A) => B): B def /:[B](z: B)(op: (B, A) => B): B = foldLeft(z)(op)
Theorems for free! – http://ttic.uchicago.edu/~dreyer/course/papers/wadler.pdf
Parametricity – http://yowconference.com.au/slides/yowlambdajam2014/Morris-ParametricityTypesAreDocumentation.pdf
Unire Strutture Dati
Metodi offerti da Traversable isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString
Metodi offerti da Traversable isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString def ++[B](that: Traversable[B]): Traversable[B]
Metodi offerti da Traversable isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString def ++[B](that: Traversable[B]): Traversable[B] Traversable Seq List
List(1, 2, 3) ++ List(4, 5, 6) == ???
List(1, 2, 3) ++ List(4, 5, 6) == List(1, 2, 3, 4, 5, 6)
Metodi offerti da Traversable isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString def ++[B](that: Traversable[B]): Traversable[B] Traversable Set HashSet
Set(1, 2, 3) ++ Set(4, 5, 6) == ???
Set(1, 2, 3) ++ Set(4, 5, 6) == Set(5, 1, 6, 2, 3, 4)
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)
Metodi offerti da Traversable isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString def ++[B](that: Traversable[B]): Traversable[B] Traversable Map HashMap
Map("a" -> 1) ++ Map("b" -> 2) == Map("a" -> 1, "b" -> 2)
E in casi più complessi?
Map[String, Set[Int]]
Map[String, Set[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)
Map("a" -> Set(1, 2)) ++ Map("a" -> Set(2, 3)) == ???
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
Map("a" -> Set(1, 2)) ++ Map("a" -> Set(2, 3)) == ??? 1: 2: 3: Map("a" -> Set(2, 3)) 4: 5:
Map("a" -> Set(1, 2)) ??? Map("a" -> Set(2, 3)) Map("a" -> Set(1, 2, 3))
Metodi offerti da Traversable isEmpty size hasDefiniteSize ++ map flatMap filter remove partition groupBy foreach reduceRightOpt head headOption tail last lastOption init take drop slice takeWhile forall exists count find foldLeft /: foldRight : reduceLeft reduceLeftOpt reduceRight dropWhile span splitAt toArray toList toIterable toSeq toStream sortWith mkString toString Seq Set Map ✔ ✔ ✘
Quando vuoi un lavoro fatto bene…
“a” Set(1, 2) “a” Set(2, 3) “a” Set(1, 2) ++ Set(2, 3)
“a” Set(1, 2) “a” Set(2, 3) “a” Set(1, 2, 3)
def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]]
def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = { mb foreach { case (k, v) => ??? } }
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 }
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 }
Implementazione con Map immutable
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
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) } }
(ma /: mb) { case (result,(k, v)) => result + (k -> { result.get(k) match { case Some(vr) => vr ++ v case None => v } }
(ma /: mb) { case (result,(k, v)) => result + (k -> { result.get(k) match { case Some(vr) => vr ++ v case None => v } // .map(_ ++ v).getOrElse(v) }}
(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) }}
(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) }}
(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) }} “FP with Bananas, Lenses, Envelopes and Barbed Wire” – http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125 http://en.wikipedia.org/wiki/Catamorphism
(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
(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
(ma /: mb) { case (result, (k, v)) => result + (k -> result.get(k).cata(_ ++ v, v)) } mb foreach { case (k, v) => result += (k -> result.get(k).cata(_ ++ v, v)) }
(ma /: mb) { case (result, (k, v)) => result + (k -> result.get(k).cata(_ ++ v, v)) } mb foreach { case (k, v) => result += (k -> result.get(k).cata(_ ++ v, v)) }
E se volessimo unire due mappe con type diversi?
Map[String, Set[Int]] Map[String, Map[Int, Set[Int]]]
Map[String, Set[Int]] Map[String, Map[Int, Set[Int]]] def blend(ma: Map[String, Set[Int]], mb: Map[String, Set[Int]]) : Map[String, Set[Int]] = ??? def blend(ma: Map[String, Map[Int, Set[Int]]], mb: Map[String, Map[Int, Set[Int]]]) : Map[String, Map[Int, Set[Int]]] = ???
Map[String, Set[Int]] Map[String, Map[Int, Set[Int]]] (ma /: mb) { case (result, (k, v)) => result + (k -> result.get(k).cata(_ ++ v, v)) } (ma /: mb) { case (result, (k, v)) => result + ??? // { ??? => { ??? } } }
Map[String, Set[Int]] Map[String, Map[Int, Set[Int]]] trait Blendable[A] { def blend(ma: A, mb: A): A }
Map[String, Set[Int]] Map[String, Map[Int, Set[Int]]] trait Blendable[A] { def blend(ma: A, mb: A): A } new Blendable[...] { def blend(ma: ..., mb: ...): ... = ??? }
Map[String, Set[Int]] Map[String, Map[Int, Set[Int]]] trait Blendable[A] { def blend(ma: A, mb: A): A } new Blendable[...] { def blend(ma: ..., mb: ...): ... = ??? } x10 Developer
Cosa intendiamo veramente per “blend”
List utilizzando l’operatore binario ++ Set utilizzando l’operatore binario ++ 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)
(List, ++) (Set, ++) (1 blend 2) == ???
(List, ++) (Set, ++) (Int, +) (1 blend 2) == 1 + 2 == 3
(List, ++) (Set, ++) (Int, +) (String, +)("ab" blend "cd") == ("ab" + "cd") == "abcd"
(List, ++) (Set, ++) (Int, +) (String, +) (Map[...], Blendable[...].blend) Blendable[Map[String, Set[Int]]].blend(ma, mb)
Cosa potrebbe consigliarci un Matematico?
WARNING Algebra ahead ☣
https://it.wikipedia.org/wiki/Semigruppo “Un semigruppo è un insieme S munito di una operazione binaria associativa m: S × S → S”
https://it.wikipedia.org/wiki/Propriet%C3%A0_di_chiusura Proprietà di chiusura ≝ ∀a, b ∈ T : a∙b ∈ T Per ogni a, b in T, il risultato dell’operazione a⋅b è in T: trait Semigroup[T] { def op(a: T, b: T): T } def op(a: Boolean, b: Boolean): Boolean def op(a: Int, b: Int): Boolean ✓ ✘
https://it.wikipedia.org/wiki/Associativit%C3%A0 Legge Associativa ≝ ∀a, b, c ∈ T : (a∙b)∙c = a∙(b∙c) Ogni a, b e c in T soddisfano (a∙b)∙c = a∙(b∙c) trait Semigroup[T] { def op(a: T, b: T): T } ((a op b) op c) == (a op (b op c))
https://it.wikipedia.org/wiki/Semigruppo “Un semigruppo è un insieme S munito di una operazione binaria associativa m: S × S → S”
Scalaz e Semigruppi
import scalaz.std.set._ implicit def setSemigroup[A]:Semigroup[Set[A]] = new Semigroup[Set[A]] { def append(f1: Set[A], f2: => Set[A]) = f1 ++ f2 }
implicit def setSemigroup[A]:Semigroup[Set[A]] = new Semigroup[Set[A]] { def append(f1: Set[A], f2: => Set[A]) = f1 ++ f2 } op
import scalaz.syntax.semigroup._ import scalaz.std.list._ List(1, 2) |+| List(3, 4) res: List[Int] = List(1, 2, 3, 4) import scalaz.syntax.semigroup._ import scalaz.std.set._ Set(1, 2) |+| Set(2, 3) res: Set[Int] = Set(1, 2, 3)
import scalaz.syntax.semigroup._ import scalaz.std.anyVal._ 1 |+| 2 |+| 3 res: Int = 6 import scalaz.syntax.semigroup._ import scalaz.std.string._ "a" |+| "b" |+| "c" res: String = "abc"
/** * 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)) }
import scalaz.scalacheck.ScalazProperties._ import scalaz.std.anyVal._ semigroup.laws[Int].check + semigroup.associative: OK, passed 100 tests.
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.
La nostra Map[_, Set[Int]] è un semigruppo?
Map("a" -> 1, "b" -> 4) |+| Map("a" -> 2) res: Map[…] = Map(a -> 3, b -> 4) “Some data structures form interesting semigroups as long as the types of the elements they contain also form semigroups.”
import scalaz.scalacheck.ScalazProperties._ semigroup.laws[Map[String, Set[Int]]].check + semigroup.associative: OK, passed 100 tests. ✓
Map("a" -> Set(1, 2)) |+| Map("a" -> Set(2, 3)) res: Map[…] = Map(a -> Set(1, 2, 3)) “adattato” da: Functional Programming in Scala - Part 3 - Chapter 10 Monoids ✓
Ma nel mio codebase non ho Map così semplici…
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)))))
Benchmarking
“Experience indicates that nearly everybody has the wrong idea about the real bottlenecks in his programs” – Donald Knuth Computer programming as an art (1974) – http://dl.acm.org/citation.cfm?id=361612
Map[String, Set[Int]]
Settembre 2015 @filippovitale $ tail -f domande

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