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Scala Types of Types @ Lambda Days

Konrad Malawski
Konrad Malawski

The document discusses various types and constructs in Scala, including static and trait types, type parameters, compound and structural types, and phantom types. It illustrates type variance, type bounds, and higher-kinded types, explaining concepts through numerous code examples. The presentation focuses on type linearization, ad-hoc polymorphism, and type classes, providing a comprehensive overview of Scala's type system.

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Scala’s Types of Types bg = game @ http://www.swordandsworcery.com/ Konrad 'ktoso' Malawski Lambda Days 2014 @ Kraków
_@ Konrad `@ktosopl` Malawski geecon.org Java.pl / KrakowScala.pl sckrk.com / meetup.com/Paper-Cup @ London GDGKrakow.pl meetup.com/Lambda-Lounge-Krakow
Types
Types “Implementation is an implementation detail.” ~ ktoso
Types in Scala
Types in Scala
Types in Scala Types are: ! static class Robot! class Human ! ! val human: Human = new Human! val roman: Human = new Robot! ! ! error: type mismatch;! ! found : Robot! ! required: Human! ! val robot: Human = new Robot! ! ^
Types in Scala Types are: ! static strong var two = 2! two = "two"! ! error: type mismatch;! found : String("two")! required: Int! two = "two"! ^
Types in Scala Types are: ! static strong inferred ! val n = 2! n.getClass.toString == "int"! ! ! !class Human! !val p = new Human! p.getClass.toString == "class Human"
Types in Scala Types are: ! val n: Int = 2 ! static strong inferred annotated after : ! ! ! def add(a: Int, b: Int): Int!
Types with Traits
Types with Traits Traits are: ! interfaces ! implementation: trait HasName { ! def name: String! }! ! ! class Human extends HasName {! def name = ""! } class Human(val name: String) ! extends HasName!
Types with Traits Traits are: ! interfaces with implementation ! trait HasName { def name = "name" }! ! object Human extends HasName! ! Human.name == "name"!
Types with Traits Traits are: ! interfaces with implementation can be “mixed in” trait Robot! trait Humanoid! trait Lasers! ! object X extends Robot ! with Humanoid! with Lasers! ! Multiple inheritance panic?!
Type linearization trait Robot extends Lasers! trait Humanoid! trait Lasers object X extends Robot ! with Humanoid! with Lasers // type linearization:! X Robot Humanoid Lasers // reverse! X Lasers Humanoid Robot! ! ! // expand! X Lasers Humanoid Robot Lasers // right-keep-unique! X Lasers Humanoid Robot Lasers! X Humanoid Robot Lasers // add common! X Humanoid Robot Lasers Object Any
Type linearization trait Robot extends Lasers! trait Humanoid! trait Lasers object X extends Robot ! with Humanoid! with Lasers // don’t trust me, trust the compiler:! import scala.reflect.runtime.universe._! typeOf[X.type].baseClasses.map(_.name).mkString(“ extends ")! ! // output:! X extends Humanoid ! extends Robot extends Lasers ! extends Object extends Any!
Type linearization reordered slightly trait Robot extends Lasers! trait Humanoid! trait Lasers object X extends Humanoid! with Lasers! with Robot // type linearization:! X Humanoid Lasers Robot // reverse! X Robot Lasers Humanoid! ! ! // expand! X Robot Lasers Lasers Humanoid // right-keep-unique! X Robot Lasers Lasers Humanoid! X Robot Lasers Humanoid // add common! X Robot Lasers Humanoid Object Any
Type linearization trait Robot extends Lasers! trait Humanoid! trait Lasers object X extends Humanoid! with Lasers! with Robot // don’t trust me, trust the compiler:! import scala.reflect.runtime.universe._! typeOf[X.type].baseClasses.map(_.name).mkString(“ extends ")! ! // output:! X extends Robot ! extends Lasers extends Humanoid! extends Object extends Any!
Type Refinement
Type Refinement trait Human! trait Robot val human: Human = new Human {}! val roman: Human = new Robot!
Type Refinement trait Human! trait Robot val human: Human = new Human {}! val roman: Human = new Robot with Human! plain trait composition type refinement Waaah! It’s a robot with human traits!
Compound Types
Compound Types are intersections of types ! ! ! ! ! trait def }! trait def }! Openable {! open()! Closable {! close()!
Compound Types are intersections ! ! ! ! ! open() trait def }! trait def }! Openable {! open()! Closable {! close()! close()
Compound Types are intersections ! trait def }! trait def }! Openable {! open()! Closable {! close()! ! ! ! def openAndClose(it: Openable with Closable) {! it.open() ! ! it.close()! }
Compound Types are intersections ! trait def }! trait def }! Openable {! open()! Closable {! close()! ! ! ! def openAndClose(it: Openable with Closable) {! it.open() ! ! it.close()! }
Compound Types this.type trait def }! trait def }! Openable {! open(): this.type! Closable {! close()! ! ! ! def openAndClose(it: Openable with Closable) =! ! it.open().close()
! Type Parameters
! Type Parameters [Type Variance]
! Type Parameters [Type Variance] <: Type Bounds >:
Type Parameters type constructor class C[T] type parameter
Type Variance class C[T] // in-variant! class C[+T] // co-variant! class C[-T] // contra-variant!
Type Bounds (still variance) class Parent! class Bottom extends Parent! ! Type Bounds ! Parent >: Bottom Bottom <: Parent Parent =:= Parent // parent is “more” general! // bottom is “less” general! // parent is “equal” parent
Type Variance class C[T] // in-variant val x: C[Parent] = new C[Parent]! ! val x: C[Parent] = new C[Bottom]! error: type mismatch; found: C[Bottom] required: C[Parent]! Note: Bottom <: Parent, but class C is invariant in type A.! You may wish to define A as +A instead. (SLS 4.5)! ! val x: C[Bottom] = new C[Parent]! error: type mismatch; found: C[Parent] required: C[Bottom]! Note: Parent >: Bottom, but class C is invariant in type A.! You may wish to define A as -A instead. (SLS 4.5)!
Type Variance class C[+T] // co-variant val x: C[Parent] = new C[Parent]! ! val x: C[Parent] = new C[Bottom]! ! val x: C[Bottom] = new C[Parent]! error: type mismatch; found: C[Parent] required: C[Bottom]! ! !
Type Variance class C[-T] // contra-variant val x: C[Parent] = new C[Parent]! ! val x: C[Parent] = new C[Bottom]! error: type mismatch; found: C[Bottom] required: C[Parent]! ! val x: C[Bottom] = new C[Parent]! ! !
Structural Type
Structural Types // a type! class Closeable {! def close()! } => // structural type! type Closeable = {! def close()! }
Structural Types Kinda’ like “duck typing” def send(msg: String, box: {def receive(a: String)}) =! box receive msg structural type
Structural Types type alias type MailBoxLike = { ! def receive(a: String)! } def send(msg: String, box: MailboxLike) =! box receive msg
Structural Types type MailBoxLike = { ! def receive(a: String)! } def send(msg: String, box: MailboxLike) =! box receive msg object Home { def receive(a: String) = ??? }! object Work { def receive(a: String) = ??? } send("hello at home", Home)! send("hello at work", Work)
Type Member
Type Member Same goal as Type Parameter if List was using Type Params trait StringList! extends List[String] => trait StringList ! extends List {! type A = String! } if List was using Type Members
Type Member + Type Bound Same as + / - variance trait List {! type A! } => trait NumbersList extends List {! type A <: Number! } trait IntegerList extends NumbersList {! type A = Integer! } trait FailList extends NumbersList {! type A = Human // Human is not <: Number!! }
Type Alias
Without Type Alias “1st” and “2nd” type param ALL HOPE IS LOST! object `bytes -> string` ! extends Builder[Array[Byte], String] {! ! def make(in: Array[Byte]): String = new String(in)! }!
Without Type Alias “1st” and “2nd” type param Some meaning is lost! object `bytes -> string` ! extends Builder[Array[Byte], String] {! ! def make(in: Array[Byte]): String = new String(in)! }!
Type Alias From Type Parameter to Type Members trait Builder[From, To] => trait Builder {! type From! type To! def make(in: From): To! }
Type Alias trait Builder { type From; type To; def make(in: From): To }! trait StringBuilder extends Builder {! type To = String! } trait FromBytesBuilder extends Builder {! type From = Array[Byte]! } object `bytes -> string` extends Builder! with FromBytesBuilder! with StringBuilder {! ! def make(in: From): To = new String(in)! }!
Type Alias trait Builder { type From; type To; def make(in: From): To }! object `bytes -> string` extends Builder {! type From = Array[Bytes]! type To = String! ! def make(in: From): To = new String(in)! }!
Phantom Types
Phantom Types Phantom Types are never actually instanciated. Exactly! uhm… where are they?
Phantom Types Marker traits: sealed trait DoorState! final class Open extends DoorState! final class Closed extends DoorState!
Phantom Types Marker traits: sealed trait DoorState! final class Open extends DoorState! final class Closed extends DoorState! trait Door[State <: DoorState] {! ! def open[T >: State <: Closed](): Door[Open] ! ! ! def close[T >: State <: Open](): Door[Closed]! ! }! !
Phantom Types Only slide in this talk with implementation! class Door[State <: DoorState] private () {! ! def open[T >: State <: Closed]() = ! this.asInstanceOf[Door[Open]]! ! def close[T >: State <: Open]() = this.asInstanceOf[Door[Closed]]! ! }! ! object Door { def apply() = new Door[Closed] }
Phantom Types Marker traits: sealed trait DoorState! final class Open extends DoorState! final class Closed extends DoorState! class Door[State <: DoorState] private () {! ! def open[T >: State <: Closed]() = ! this.asInstanceOf[Door[Open]]! ! def stop[T >: State <: Open]() = ! this.asInstanceOf[Door[Closed]]! }! ! object Door { def apply() = new Door[Closed] }
Phantom Types Marker traits: sealed trait DoorState! final class Open extends DoorState! final class Closed extends DoorState! class Door[State <: DoorState] private () {! ! def open[T >: State <: Closed]() = ! this.asInstanceOf[Door[Open]]! ! def stop[T >: State <: Open]() = ! this.asInstanceOf[Door[Closed]]! }! ! object Door { def apply() = new Door[Closed] }
Phantom Types Marker traits: sealed trait DoorState! final class Open extends DoorState! final class Closed extends DoorState! class Door[State <: DoorState] private () {! ! def open[T >: State <: Closed]() = ! this.asInstanceOf[Door[Open]]! ! def stop[T >: State <: Open]() = ! this.asInstanceOf[Door[Closed]]! }! ! object Door { def apply() = new Door[Closed] }
Phantom Types Marker traits: sealed trait DoorState! final class Open extends DoorState! final class Closed extends DoorState! class Door[State <: DoorState] private () {! ! def open[T >: State <: Closed]() = ! this.asInstanceOf[Door[Open]]! ! def stop[T >: State <: Open]() = ! this.asInstanceOf[Door[Closed]]! }! ! object Door { def apply() = new Door[Closed] }
Phantom Types val closed = Door()! // closed: Door[Closed]
Phantom Types val closed = Door()! // closed: Door[Closed]! ! val opened = closed.open()! // opened: Door[Open]
Phantom Types val closed = Door()! // closed: Door[Closed]! ! val opened = closed.open()! // opened: Door[Open]! ! val closedAgain = opened.close()! // closedAgain: Door[Closed]!
Phantom Types val closed = Door()! // closed: Door[Closed]! ! val opened = closed.open()! // opened: Door[Open]! ! val closedAgain = opened.close()! // closedAgain: Door[Closed]! ! closed.close()! error: type arguments [Closed] do not conform to method close's type parameter bounds [T >: Closed <: Open]
Phantom Types val closed = Door()! // closed: Door[Closed]! ! val opened = closed.open()! // opened: Door[Open]! ! val closedAgain = opened.close()! // closedAgain: Door[Closed]! ! closed.close()! error: type arguments [Closed] do not conform to method close's type parameter bounds [T >: Closed <: Open]! ! opened.open()! error: type arguments [Open] do not conform to method ! open's type parameter bounds [T >: Open <: Closed]
Higher Kinded Types
Kind: x Proper Kind Int! scala> :kind -v 42! ! scala.Int's kind is A! *! ! This is a proper type.
Kind: x -> x Type Constructor List[+A]! scala> :kind -v List! ! scala.collection.immutable.List's kind is F[+A]! * -(+)-> *! ! This is a type constructor: ! a 1st-order-kinded type.
Kind: (x -> x) -> x Higher Kind import language.higherKinds! ! class Functor[M[_]]! scala> :kind -v Functor[List]! ! Functor's kind is X[F[A]]! (* -> *) -> *! ! This is a type constructor that takes type constructor(s): ! a higher-kinded type
Higher Kinded Types import scala.language.higherKinds! ! takes Type Constructor trait Functor [F[_]] {! def map[A,B] (fn: A => B)(fa: F[A]): F[B]! }
Higher Kinded Types import scala.language.higherKinds! ! trait Functor [F[_]] {! def map[A,B] (fn: A => B)(fa: F[A]): F[B]! } trait Functor [List] {! def map[Int,String] (fn: Int => String)! (fa: List[Int]): List[String]! }
Higher Kinded Types import scala.language.higherKinds! ! trait Functor [F[_]] {! def map[A,B] (fn: A => B)(fa: F[A]): F[B]! } val funct = new Functor[List] {! def map[String, Int] ! (f: String => Int)! (fa: List[String])! : List[Int] = fa map f // cheating ;-)! }
Higher Kinded Types import scala.language.higherKinds! ! trait Functor [F[_]] {! def map[A,B] (fn: A => B)(fa: F[A]): F[B]! } val funct = new Functor[List] {! def map[String, Int] ! (f: String => Int)! (fa: List[String]): List[Int] = ! ! ! !!! fa map f // cheating ;-)! } val f: Int => String = _.toString! funct.map(f)(List(1, 2)) == List("1", "2")!
Power up: Ad-Hoc Polymorphism trait Container[M[_]] { ! def put[A](x: A): M[A]; def get[A](m: M[A]): A ! }! implicit val listContainer = new Container[List] { ! def put[A](x: A) = List(x)! def get[A](m: List[A]) = m.head ! }! ! implicit val optionContainer = new Container[Some] {! def put[A](x: A) = Some(x);! def get[A](m: Some[A]) = m.get ! }!
Power up: Ad-Hoc Polymorphism trait Container[M[_]] { ! def put[A](x: A): M[A]; def get[A](m: M[A]): A ! }! def tupleize[M[_]: Container, A, B]! (fst: M[A], snd: M[B]) ! (implicit c: Container[M]): M[(A, B)] = c.put(c.get(fst), c.get(snd)) tupleize(Some(1), Some(2))! Some((1,2)): Some[(Int, Int)]! ! tupleize(List(1), List(“2”))! List((1,2)): List[(Int, String)]!
Power up: Ad-Hoc Polymorphism trait Container[M[_]] { ! def put[A](x: A): M[A]; def get[A](m: M[A]): A ! }! def tupleize[M[_]: Container, A, B]! (fst: M[A], snd: M[B]) ! (implicit c: Container[M]): M[(A, B)] = c.put(c.get(fst), c.get(snd)) tupleize(Some(1), Some(2))! Some((1,2)): Some[(Int, Int)]! ! tupleize(List(1), List(“2”))! List((1,2)): List[(Int, String)]!
Type Class
Type Class A.K.A. “ad-hoc polymorphism”
Type Class A.K.A. “More pattern, than type”
Type Class A.K.A. “Stay in this room”
Type Class A.K.A. “Stay in this room” Jerzy has an entire talk about them
Type Class // no type classes yet! trait Writeable[Out] {! def write: Out! }! ! case class Num(a: Int, b: Int) extends Writeable[Json] {! def write = Json.toJson(this)! }!
Type Class trait Writes[In, Out] { def write(in: In): Out! }! ! ! Separated “what” from “who” trait Writeable[Self] { def writeAs[Out]()! (implicit writes: Writes[Self, Out]): Out =! ! ! ! ! writes write this! }! ! ! ! implicit val jsonNum = Writes[Num, Json] {! ! def write(n: Num) = Json.toJson(n)! ! }! ! case class Num(a: Int) extends Writeable[Num]
Type Class trait Writes[In, Out] { def write(in: In): Out! }! ! ! trait Writeable[Self] { def writeAs[Out]()! (implicit writes: Writes[Self, Out]): Out =! ! ! ! ! writes write this! }! Implicit parameter ! ! ! implicit val jsonNum = Writes[Num, Json] {! ! def write(n: Num) = Json.toJson(n)! ! }! ! Implicit value case class Num(a: Int) extends Writeable[Num]
Type Class implicit val jsonNum = Writes[Num, Json] { def (n1: Num, n2: Num) = n1.a < n1.! }! ! case class Num(a: Int) extends Writeable[Num]
Type Class implicit val jsonNum = Writes[Num, Json] { def (n1: Num, n2: Num) = n1.a < n1.! }! ! case class Num(a: Int) extends Writeable[Num] you write: val jsonNum = Num(12).writeAs[Json]()!
Type Class implicit val jsonNum = Writes[Num, Json] { def (n1: Num, n2: Num) = n1.a < n1.! }! ! case class Num(a: Int) extends Writeable[Num] you write: val jsonNum = Num(12).writeAs[Json]()! compiler does: val jsonNum = Num(12).writeAs[Json]()(jsonNum)!
Links & Kudos
ktoso/scala-types-of-types @ github 12444 words and growing
Other Types of Types type annotation case class type projection unified type system value class self recursive type bottom types type class type constructor type variance universal trait specialized type traits self type annotation dynamic type type refinements phantom type existential type type alias structural type type lambda abstract type member path dependent type algebraic data type
Links and Kudos http://docs.scala-lang.org/ ! http://ktoso.github.io/scala-types-of-types/ ! ! http://blog.echo.sh/post/68636331334/experimenting-with-peano-numbers-on-scalas-type-system-1 ! http://stackoverflow.com/questions/6246719/what-is-a-higher-kinded-type-in-scala ! http://twitter.github.io/scala_school/advanced-types.html ! https://github.com/earldouglas/scala-scratchpad/tree/master/type-lambdas ! http://www.scala-lang.org/old/node/136 ! http://eed3si9n.com/learning-scalaz/polymorphism.html ! ! !
Dziękuję! Thank you! あろがとう！ (guess “type” occurrences) K.Malawski @ ebay.com Konrad.Malwski @ geecon.org t: ktosopl / g: ktoso blog: project13.pl Lambda Days 2014 @ Kraków

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