scala types of types @ lambda days
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Scala’s Types of Types
Konrad 'ktoso' Malawski Lambda Days 2014 @ Krakówbg = game @ http://www.swordandsworcery.com/
_ @
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
class Robot!class Human ! !val human: Human = new Human!val roman: Human = new Robot!!!!!!!
Types are: !
static
error: type mismatch;! found : Robot! required: Human! val robot: Human = new Robot! ^
Types in Scala
var two = 2!two = "two"!!
Types are: !
static strong error: type mismatch;!
found : String("two")! required: Int! two = "two"! ^
Types in Scala
val n = 2!n.getClass.toString == "int"!!!!!
Types are: !
static strong
inferred !
class Human!val p = new Human!p.getClass.toString == "class Human"
Types in Scala
Types are: !
static strong
inferred annotated after :
!! ! def add(a: Int, b: Int): Int!
! val n: Int = 2
Types with Traits
Types with Traits
Traits are: !
interfaces !
trait HasName { ! def name: String!}!!!
class Human extends HasName {! def name = ""!}
class Human(val name: String) ! extends HasName!
implementation:
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
object X extends Robot ! with Humanoid! with Lasers
trait Robot extends Lasers!trait Humanoid!trait 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
// 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!
trait Robot extends Lasers!trait Humanoid!trait Lasers
object X extends Robot ! with Humanoid! with Lasers
Type linearization
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
reordered slightly
Type linearization
// 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!
trait Robot extends Lasers!trait Humanoid!trait Lasers
object X extends Humanoid! with Lasers! with Robot
Type Refinement
Type Refinement
val human: Human = new Human {}!val roman: Human = new Robot!
trait Human!trait Robot
Type Refinement
val human: Human = new Human {}!val roman: Human = new Robot with Human!
Waaah! It’s a robot with human traits!
plain trait compositiontype refinement
trait Human!trait Robot
Compound Types
Compound Types
are intersections
of types !
trait Openable {! def open()! }! trait Closable {! def close()! }!!!!!
Compound Types
are intersections
!
trait Openable {! def open()! }! trait Closable {! def close()! }!!!!!
open() close()
Compound Types
are intersections
!
trait Openable {! def open()! }! trait Closable {! def close()! }!!!!! def openAndClose(it: Openable with Closable) {! it.open() ! it.close()! }
Compound Types
are intersections
!
trait Openable {! def open()! }! trait Closable {! def close()! }!!!!! def openAndClose(it: Openable with Closable) {! it.open() ! it.close()! }
Compound Types
this.type
def openAndClose(it: Openable with Closable) =! it.open().close()
trait Openable {! def open(): this.type! }! trait Closable {! def close()! }!!!!!
!
Type Parameters
!
Type Parameters [Type Variance]
!
Type Parameters [Type Variance] <: Type Bounds >:
Type Parameters
class C[T]
type parameter
type constructor
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 // parent is “more” general!Bottom <: Parent // bottom is “less” general!Parent =:= Parent // 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 TypesKinda’ like “duck typing”
def send(msg: String, box: {def receive(a: String)}) =! box receive msg
structural type
Structural Types
type MailBoxLike = { ! def receive(a: String)!}
def send(msg: String, box: MailboxLike) =! box receive msg
type alias
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
trait StringList! extends List[String] => trait StringList !
extends List {! type A = String!}
if List was using Type Members
if List was using Type Params
Type Member + Type Bound
Same as + / - variance
trait List {! type A!}
trait IntegerList extends NumbersList {! type A = Integer!}
trait NumbersList extends List {! type A <: Number!}
=>
trait FailList extends NumbersList {! type A = Human // Human is not <: Number!!}
Type Alias
Without Type Alias
object `bytes -> string` ! extends Builder[Array[Byte], String] {! ! def make(in: Array[Byte]): String = new String(in)! }!
“1st” and “2nd” type param ALL HOPE IS LOST!
Without Type Alias
object `bytes -> string` ! extends Builder[Array[Byte], String] {! ! def make(in: Array[Byte]): String = new String(in)! }!
“1st” and “2nd” type param Some meaning is lost!
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
uhm… where are they?
Exactly!
Phantom Types are never actually instanciated.
Phantom Types
sealed trait DoorState!final class Open extends DoorState!final class Closed extends DoorState!
Marker traits:
Phantom Types
sealed trait DoorState!final class Open extends DoorState!final class Closed extends DoorState!
Marker traits:
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
sealed trait DoorState!final class Open extends DoorState!final class Closed extends DoorState!
Marker traits:
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
sealed trait DoorState!final class Open extends DoorState!final class Closed extends DoorState!
Marker traits:
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
sealed trait DoorState!final class Open extends DoorState!final class Closed extends DoorState!
Marker traits:
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
sealed trait DoorState!final class Open extends DoorState!final class Closed extends DoorState!
Marker traits:
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
Int!
scala> :kind -v 42!!scala.Int's kind is A!*!!This is a proper type.
Proper Kind
Kind: x -> x
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.
Type Constructor
Kind: (x -> x) -> x
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 Kind
Higher Kinded Types
import scala.language.higherKinds!!trait Functor [F[_]] {! def map[A,B] (fn: A => B)(fa: F[A]): F[B]!}
takes Type Constructor
Higher Kinded Typesimport 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 Typesimport 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 Typesimport 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 Polymorphismtrait 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 Polymorphismtrait 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 Polymorphismtrait 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 Classtrait Writes[In, Out] { ! def write(in: In): Out!}!!!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]
Separated “what” from “who”Separated “what” from “who”
Type Classtrait Writes[In, Out] { ! def write(in: In): Out!}!!!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]
Implicit parameter
Implicit value
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]()!
val jsonNum = Num(12).writeAs[Json]()(jsonNum)!
compiler does:
Links & Kudos
ktoso/scala-types-of-types @ github
12444 words and growing
Other Types of Types
type annotation unified type system
bottom types type variance
traits type refinements
type alias abstract type member
case class value class type class
universal trait self type annotation
phantom type structural type
path dependent type
type projection self recursive type type constructor specialized type dynamic type
existential type type lambda
algebraic data type
Links and Kudoshttp://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 !!!
K.Malawski @ ebay.com Konrad.Malwski @ geecon.org t: ktosopl / g: ktoso blog: project13.pl Lambda Days 2014 @ Kraków
Dziękuję! Thank you! あろがとう!
!
(guess “type” occurrences)
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