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Scalaz There’s an applicative in my functor! Photo Credit: http://www.flickr.com/photos/yannconz/2796312310

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Agenda • Option • Monoid • Applicative • Validation • Lens

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Options • Option functions & typeclass instances • Option syntax extensions • Using Option with other parts of Scalaz

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Constructing Options Some(42) Some[Int] None None

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Constructing Options Some(42) Some[Int] None None import scalaz.std.option._ some(42) Option[Int] none[Int] Option[Int]

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Constructing Options Some(42) Some[Int] None None import scalaz.std.option._ some(42) Option[Int] none[Int] Option[Int] Imports functions & typeclass instances for option

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Constructing Options val os = List(Some(42), None, Some(20)) os.foldLeft(None) { (acc, o) => acc orElse o }

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Constructing Options val os = List(Some(42), None, Some(20)) os.foldLeft(None) { (acc, o) => acc orElse o } error: type mismatch; found : Option[Int] required: None.type os.foldLeft(None) { (acc, o) => acc orElse o } ^

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Constructing Options val os = List(Some(42), None, Some(20)) os.foldLeft(None) { (acc, o) => acc orElse o } os.foldLeft(None: Option[Int]) { (acc, o) => acc orElse o } error: type mismatch; found : Option[Int] required: None.type os.foldLeft(None) { (acc, o) => acc orElse o } ^ Some(42)

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Constructing Options val os = List(Some(42), None, Some(20)) os.foldLeft(None) { (acc, o) => acc orElse o } os.foldLeft(None: Option[Int]) { (acc, o) => acc orElse o } error: type mismatch; found : Option[Int] required: None.type os.foldLeft(None) { (acc, o) => acc orElse o } ^ os.foldLeft(none[Int]) { (acc, o) => acc orElse o } Some(42) Some(42)

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Option conditional import scalaz.syntax.std.option._ def xget(opt: Option[Int]) = opt | Int.MaxValue xget(Some(42)) xget(None)

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Option conditional import scalaz.syntax.std.option._ def xget(opt: Option[Int]) = opt | Int.MaxValue xget(Some(42)) xget(None) Imports syntax extensions for option

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Option conditional import scalaz.syntax.std.option._ def xget(opt: Option[Int]) = opt | Int.MaxValue xget(Some(42)) xget(None) Alias for getOrElse

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Option conditional import scalaz.syntax.std.option._ def xget(opt: Option[Int]) = opt | Int.MaxValue xget(Some(42)) xget(None) 42 2147483647

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Option unary ~ import scalaz.std.anyVal._ import scalaz.std.option._ import scalaz.syntax.std.option._ def zget(opt: Option[Int]) = ~opt zget(Some(42)) zget(None)

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Option unary ~ import scalaz.std.anyVal._ import scalaz.std.option._ import scalaz.syntax.std.option._ def zget(opt: Option[Int]) = ~opt zget(Some(42)) zget(None) Imports functions & typeclass instances for int, float, etc.

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Option unary ~ import scalaz.std.anyVal._ import scalaz.std.option._ import scalaz.syntax.std.option._ def zget(opt: Option[Int]) = ~opt zget(Some(42)) zget(None) Alias for getOrElse(zero)

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Option unary ~ import scalaz.std.anyVal._ import scalaz.std.option._ import scalaz.syntax.std.option._ def zget(opt: Option[Int]) = ~opt zget(Some(42)) zget(None) Alias for getOrElse(zero) 0 42

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Option unary ~ import scalaz.std.anyVal._ import scalaz.std.option._ import scalaz.syntax.std.option._ def zget(opt: Option[Int]) = ~opt zget(Some(42)) zget(None) Alias for getOrElse(zero) 0 42 Where does zero come from?

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Option unary ~ import scalaz.Monoid import scalaz.std.string._ import scalaz.std.list._ def mzget[A : Monoid](opt: Option[A]) = ~opt mzget(none[Int]) mzget(none[String]) mzget(none[List[Int]]) 0 “” List()

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Aside: Context Bounds def mzget[A : Monoid](opt: Option[A]) = ~opt

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Aside: Context Bounds def mzget[A : Monoid](opt: Option[A]) = ~opt • Monoid is a context bound for type A

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Aside: Context Bounds def mzget[A : Monoid](opt: Option[A]) = ~opt • Monoid is a context bound for type A • Means there must be an implicit value of type Monoid[A] in implicit scope

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Aside: Context Bounds def mzget[A : Monoid](opt: Option[A]) = ~opt • Monoid is a context bound for type A • Means there must be an implicit value of type Monoid[A] in implicit scope • Equivalent to: def mzget[A](opt: Option[A])( implicit m: Monoid[A]) = ~opt

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Aside: Context Bounds def mzget[A : Monoid](opt: Option[A]) = ~opt • Monoid is a context bound for type A • Means there must be an implicit value of type Monoid[A] in implicit scope • Equivalent to: def mzget[A](opt: Option[A])( implicit m: Monoid[A]) = ~opt • Even supports multiple bounds: def other[A : Monoid : Functor] = ...

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Option err def knowBetter[A](opt: Option[A]) = opt err "You promised!" knowBetter(some(42)) knowBetter(none)

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Option err def knowBetter[A](opt: Option[A]) = opt err "You promised!" knowBetter(some(42)) knowBetter(none) Alias for getOrElse(sys.err(msg)) 42 throws RuntimException(“You promised!”) Good alternative to opt.get when you know it’s defined!

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Option fold/cata import java.net.InetAddress def ipAddress(opt: Option[InetAddress]) = opt.fold(_.getHostAddress, "0.0.0.0") ipAddress(Some(InetAddress.getLocalHost)) ipAddress(None)

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Option fold/cata import java.net.InetAddress def ipAddress(opt: Option[InetAddress]) = opt.fold(_.getHostAddress, "0.0.0.0") ipAddress(Some(InetAddress.getLocalHost)) ipAddress(None) 10.0.1.12 0.0.0.0 Replacement for matching on Some/None

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Option ifNone var cnt = 0 some(42) ifNone { cnt += 1 } none ifNone { cnt += 1 } println(cnt)

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Concatenate Given a list of options, how do you sum them? List(some(42), none, some(51)).sum error: could not find implicit value for parameter num: Numeric[Option[Int]]

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Concatenate Given a list of options, how do you sum them? List(some(42), none, some(51)).sum error: could not find implicit value for parameter num: Numeric[Option[Int]] import scalaz.syntax.traverse._ List(some(42), none, some(51)).concatenate 93

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Sequence Given a list of options, how do you get option of list? List(some(42), none, some(51)).sequence List(some(42), some(51)).sequence None Some(List(42, 51))

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Semigroup & Monoid Review • Semigroup append: A 㱺 A 㱺 A • Monoid extends Semigroup zero: A Not Scala syntax!

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import scalaz.std.anyVal._ import scalaz.syntax.monoid._ 1 |+| 2 import scalaz.std.list._ List(1, 2) |+| List(3, 4) Syntax 3 List(1, 2, 3, 4)

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import scalaz.std.map._ import scalaz.std.set._ val low = Map( 'odd -> Set(1, 3), 'even -> Set(2, 4)) val hi = Map( 'odd -> Set(5, 7), 'even -> Set(6, 8)) low |+| hi Syntax

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import scalaz.std.map._ import scalaz.std.set._ val low = Map( 'odd -> Set(1, 3), 'even -> Set(2, 4)) val hi = Map( 'odd -> Set(5, 7), 'even -> Set(6, 8)) low |+| hi Syntax Map(‘odd -> Set(1, 3, 5, 7), ‘even -> Set(2, 4, 6, 8))

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Option is Monoid • There’s a monoid of Option[A] if A is a Semigroup • zero = None • append = ???

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Option is Monoid implicit def optionMonoid[A: Semigroup]: Monoid[Option[A]] = new Monoid[Option[A]] { 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, Some(a2)) => f2 case (None, None) => None } def zero: Option[A] = None } From Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/std/Option.scala

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Option is Monoid import scalaz.syntax.monoid._ some(20) |+| none |+| some(22) Some(42)

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Option alternative monoids • Can we find other monoids for Option? • Must implement zero and append • But remember the monoid laws: • Closure • Associativity • Identity See: http://en.wikipedia.org/wiki/Monoid

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Option alternative monoids • Keep everything the same as semigroup based monoid but focus on: case (Some(a1), Some(a2)) => • Left case (Some(a1), Some(a2)) => f1 • Right case (Some(a1), Some(a2)) => f2

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some(20).first |+| none.first |+| some(22).first some(20).last |+| none.last |+| some(22).last Option alternative monoids Some(20) Some(22)

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Functor & Monad Review • Functor map: F[A] 㱺 (A 㱺 B) 㱺 F[B] • Monad extends Functor point: A 㱺 M[A] flatMap: M[A] 㱺 (A 㱺 M[B]) 㱺 M[B] Not Scala syntax!

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Functor & Monad Review • Functor map: F[A] 㱺 (A 㱺 B) 㱺 F[B] • Monad extends Functor point: A 㱺 M[A] flatMap: M[A] 㱺 (A 㱺 M[B]) 㱺 M[B] Not Scala syntax! Option[Int] 㱺 (Int 㱺 String) 㱺 Option[String]

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Functor & Monad Review • Functor map: F[A] 㱺 (A 㱺 B) 㱺 F[B] • Monad extends Functor point: A 㱺 M[A] flatMap: M[A] 㱺 (A 㱺 M[B]) 㱺 M[B] Not Scala syntax! Option[Int] 㱺 (Int 㱺 String) 㱺 Option[String]

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Functor & Monad Review • Functor map: F[A] 㱺 (A 㱺 B) 㱺 F[B] • Monad extends Functor point: A 㱺 M[A] flatMap: M[A] 㱺 (A 㱺 M[B]) 㱺 M[B] Not Scala syntax! Option[Int] 㱺 (Int 㱺 String) 㱺 Option[String] Option[String] 㱺 (String 㱺 Option[Int]) 㱺 Option[Int] String 㱺 Option[String]

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What’s this? • ??? extends Functor point: A 㱺 F[A] ???: F[A] 㱺 F[A 㱺 B] 㱺 F[B]

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What’s this? • ??? extends Functor point: A 㱺 F[A] ???: F[A] 㱺 F[A 㱺 B] 㱺 F[B] • Read as... Given a function from A to B in a context F and a value of A in a context F, produce a value of B in context F.

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What’s this? • ??? extends Functor point: A 㱺 F[A] ???: F[A] 㱺 F[A 㱺 B] 㱺 F[B] • Read as... Given a function from A to B in a context F and a value of A in a context F, produce a value of B in context F. • Represents function application in a context

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What’s this? • ??? extends Functor point: A 㱺 F[A] ???: F[A] 㱺 F[A 㱺 B] 㱺 F[B] • Read as... Given a function from A to B in a context F and a value of A in a context F, produce a value of B in context F. • Represents function application in a context • Defined in http://www.soi.city.ac.uk/~ross/papers/Applicative.html

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Applicative • Applicative extends Functor point: A 㱺 F[A] ap: F[A] 㱺 F[A 㱺 B] 㱺 F[B] Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Pointed.scala https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Applicative.scala

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Applicative • Applicative extends Functor point: A 㱺 F[A] ap: F[A] 㱺 F[A 㱺 B] 㱺 F[B] • Or in proper Scala: trait Pointed[F[_]] extends Functor[F] { def point[A](a: => A): F[A] } trait Applicative[F[_]] extends Functor[F] with Pointed[F] { def ap[A,B](fa: => F[A])(f: => F[A => B]): F[B] } Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Pointed.scala https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Applicative.scala

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implicit val optionInstance = new Applicative[Option] { override def point[A](a: => A) = ??? override def ap[A, B]( fa: => Option[A])(f: => Option[A => B]) = ??? } Option Is Applicative Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Option.scala Let’s define an applicative instance for Option

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implicit val optionInstance = new Applicative[Option] { override def point[A](a: => A) = ??? override def ap[A, B]( fa: => Option[A])(f: => Option[A => B]) = ??? } Option Is Applicative Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Option.scala How can we lift a value of A to Option[A]?

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implicit val optionInstance = new Applicative[Option] { override def point[A](a: => A) = Some(a) override def ap[A, B]( fa: => Option[A])(f: => Option[A => B]) = ??? } Option Is Applicative Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Option.scala

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implicit val optionInstance = new Applicative[Option] { override def point[A](a: => A) = Some(a) override def ap[A, B]( fa: => Option[A])(f: => Option[A => B]) = ??? } Option Is Applicative Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Option.scala How can we apply the function in Option[A=>B] to Option[A]?

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implicit val optionInstance = new Applicative[Option] { override def point[A](a: => A) = Some(a) override def ap[A, B]( fa: => Option[A])(f: => Option[A => B]) = f match { case Some(f) => fa match { case Some(x) => Some(f(x)) case None => None } case None => None } } Option Is Applicative Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Option.scala

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implicit val optionInstance = new Applicative[Option] { override def point[A](a: => A) = Some(a) override def ap[A, B]( fa: => Option[A])(f: => Option[A => B]) = f match { case Some(f) => fa match { case Some(x) => Some(f(x)) case None => None } case None => None } } Option Is Applicative Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Option.scala What about map[A](f: A => B): Option[B]?

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trait Applicative[F[_]] extends Functor[F] with Pointed[F] { def ap[A,B](fa: => F[A])(f: => F[A => B]): F[B] override def map[A, B](fa: F[A])(f: A => B): F[B] = ??? } Functor.map on Applicative Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Option.scala Can we define map in terms of pointed and ap?

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trait Applicative[F[_]] extends Functor[F] with Pointed[F] { def ap[A,B](fa: => F[A])(f: => F[A => B]): F[B] override def map[A, B](fa: F[A])(f: A => B): F[B] = ap(fa)(point(f)) } Functor.map on Applicative Summarized from Scalaz Seven source https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/Option.scala

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import scalaz.std.option._ import scalaz.syntax.applicative._ val oa5: Option[Int => Int] = Some((_: Int) + 5) some(15) <*> oa5 Applicative Usage

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import scalaz.std.option._ import scalaz.syntax.applicative._ val oa5: Option[Int => Int] = Some((_: Int) + 5) some(15) <*> oa5 Applicative Usage Alias for ap

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import scalaz.std.option._ import scalaz.syntax.applicative._ val oa5: Option[Int => Int] = Some((_: Int) + 5) some(15) <*> oa5 Applicative Usage Alias for ap Some(20)

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import scalaz.std.option._ import scalaz.syntax.applicative._ some(15).<**>(some(5)) { _ + _ } some(15).<***>(some(5), some(6)) { _ + _ + _ } some(15).<****>(some(5), some(6), some(7)) { _ + _ + _ + _ } Applicative Usage

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import scalaz.std.option._ import scalaz.syntax.applicative._ some(15).<**>(some(5)) { _ + _ } some(15).<***>(some(5), some(6)) { _ + _ + _ } some(15).<****>(some(5), some(6), some(7)) { _ + _ + _ + _ } Applicative Usage Some(20) Some(26) Some(33)

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import scalaz.std.option._ import scalaz.syntax.applicative._ (some(15) |@| some(5)) apply { _ + _ } (some(15) |@| some(5) |@| some(6)) apply { _ + _ + _ } (some(15) |@| some(5)).tupled Applicative Builder Most common and convenient usage

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import scalaz.std.option._ import scalaz.syntax.applicative._ (some(15) |@| some(5)) apply { _ + _ } (some(15) |@| some(5) |@| some(6)) apply { _ + _ + _ } (some(15) |@| some(5)).tupled Applicative Builder Some(20) Some(26) Some((15, 5)) Most common and convenient usage

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import scalaz.std.option._ import scalaz.syntax.applicative._ (some(15) |@| some(5)) apply { _ + _ } (some(15) |@| some(5) |@| some(6)) apply { _ + _ + _ } (some(15) |@| some(5)).tupled Applicative Builder Supports up to 12 arguments Some(20) Some(26) Some((15, 5)) Most common and convenient usage

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import scalaz.std.option._ import scalaz.syntax.applicative._ case class Album(name: String, artist: String) (some("Wilco") ⊛ some("Sky Blue Sky")) apply Album.apply Applicative Builder

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import scalaz.std.option._ import scalaz.syntax.applicative._ case class Album(name: String, artist: String) (some("Wilco") ⊛ some("Sky Blue Sky")) apply Album.apply Applicative Builder Companion has an apply method automatically created

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import scalaz.std.option._ import scalaz.syntax.applicative._ case class Album(name: String, artist: String) (some("Wilco") ⊛ some("Sky Blue Sky")) apply Album.apply Applicative Builder Companion has an apply method automatically created Alias for |@|

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import scalaz.std.option._ import scalaz.syntax.applicative._ case class Album(name: String, artist: String) (some("Wilco") ⊛ some("Sky Blue Sky")) apply Album.apply Applicative Builder Some(Album(Wilco, Sky Blue Sky)) Companion has an apply method automatically created Alias for |@|

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Why Applicatives? • Less restrictive than Monads, and thus, more general (powerful) • Composable http://blog.tmorris.net/monads-do-not-compose/ • Support parallel computation More on this point later...

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A word on typeclasses • So far we’ve seen Semigroup, Monoid, Functor, Pointed, Applicative, Monad

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A word on typeclasses • So far we’ve seen Semigroup, Monoid, Functor, Pointed, Applicative, Monad • There are many others -- ApplicativePlus, MonadPlus, Comonad, Category, Arrow, ArrowPlus, Foldable, Traversable, Monad Transformers, Reader, Writer, State, Identity, and more

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A word on typeclasses • So far we’ve seen Semigroup, Monoid, Functor, Pointed, Applicative, Monad • There are many others -- ApplicativePlus, MonadPlus, Comonad, Category, Arrow, ArrowPlus, Foldable, Traversable, Monad Transformers, Reader, Writer, State, Identity, and more • These are functional design patterns • Simpler than most OO design patterns

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Some Haskell Typeclasses Credit: Typeclassopedia http://www.haskell.org/haskellwiki/Typeclassopedia#Introduction

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Typeclass References • Haskell Typeclassopedia is a great reference for learning these http://www.haskell.org/haskellwiki/Typeclassopedia • Scala Typeclassopedia describes the big 3 (Functor, Applicative, Monad) http://typeclassopedia.bitbucket.org/

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sealed trait Validation[+E, +A] { ... } final case class Success[E, A](a: A) extends Validation[E, A] final case class Failure[E, A](e: E) extends Validation[E, A] Validation

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Validation • Represents either success or failure • On success, provides the successful value • On failure, provides the failure value • Sound familiar?

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Isomorphic to Either ≅

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Isomorphic to Either Validation Either Success Right Failure Left ≅

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Isomorphic to Either Validation Either Success Right Failure Left ≅ Q: So why not just use Either?

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Isomorphic to Either Validation Either Success Right Failure Left ≅ Q: So why not just use Either? A: When Validation is constructed with an error type that has a Semigroup, there exists an Applicative Functor for Validation that accumulates errors

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import scalaz.{Success, Failure} Success(42) Failure("boom") Constructing Validations Success[Nothing, Int] Failure[String, Nothing]

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import scalaz.{Success, Failure} Success(42) Failure("boom") Constructing Validations Success[Nothing, Int] Failure[String, Nothing] import scalaz.Validation Validation.success(42) Validation.failure("boom") Validation[Nothing, Int] Validation[String, Nothing]

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import scalaz.{Success, Failure} Success(42) Failure("boom") Constructing Validations Success[Nothing, Int] Failure[String, Nothing] import scalaz.Validation Validation.success(42) Validation.failure("boom") Validation[Nothing, Int] Validation[String, Nothing] import scalaz.syntax.validation._ 42.success "boom".fail Validation[Nothing, Int] Validation[String, Nothing]

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import scalaz.{Success, Failure} Success(42) Failure("boom") Constructing Validations Success[Nothing, Int] Failure[String, Nothing] import scalaz.Validation Validation.success(42) Validation.failure("boom") Validation[Nothing, Int] Validation[String, Nothing] import scalaz.syntax.validation._ 42.success "boom".fail Validation[Nothing, Int] Validation[String, Nothing] 42.success[String] "boom".fail[Int] Validation[String, Int] Validation[String, Int]

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import scalaz.std.option._ import scalaz.syntax.std.option._ some(42).toSuccess("boom") none[Int].toSuccess("boom") some(42).toFailure("boom") none[Int].toFailure("boom") Option to Validation

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import scalaz.std.option._ import scalaz.syntax.std.option._ some(42).toSuccess("boom") none[Int].toSuccess("boom") some(42).toFailure("boom") none[Int].toFailure("boom") Option to Validation Success(42) Failure(“boom”)

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import scalaz.std.option._ import scalaz.syntax.std.option._ some(42).toSuccess("boom") none[Int].toSuccess("boom") some(42).toFailure("boom") none[Int].toFailure("boom") Option to Validation Success(42) Failure(“boom”) Failure(42) Success(“boom”)

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import scalaz.syntax.id._ import scalaz.Validation.fromEither fromEither(42.right) fromEither("boom".left) Either to Validation

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import scalaz.syntax.id._ import scalaz.Validation.fromEither fromEither(42.right) fromEither("boom".left) Either to Validation Success(42) Failure(“boom”)

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import scalaz.Validation.fromTryCatch fromTryCatch("42".toInt) fromTryCatch("notAnInt".toInt) Throwing to Validation

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import scalaz.Validation.fromTryCatch fromTryCatch("42".toInt) fromTryCatch("notAnInt".toInt) Throwing to Validation Success(42) Failure(java.lang.NumberFormatException: For input string: "notAnInt")

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import scalaz.Validation.fromTryCatch fromTryCatch("42".toInt) fromTryCatch("notAnInt".toInt) Throwing to Validation Success(42) Failure(java.lang.NumberFormatException: For input string: "notAnInt") fromTryCatch("notAnInt".toInt) .fail.map { _.getMessage }.validation

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import scalaz.Validation.fromTryCatch fromTryCatch("42".toInt) fromTryCatch("notAnInt".toInt) Throwing to Validation Success(42) Failure(java.lang.NumberFormatException: For input string: "notAnInt") fromTryCatch("notAnInt".toInt) .fail.map { _.getMessage }.validation Failure(For input string: "notAnInt")

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import scalaz.syntax.bifunctor._ fromTryCatch("notAnInt".toInt). <-: { _.getMessage } Mapping via Bifunctor Bifunctor = functor of 2 arguments <-: = Map left value

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import scalaz.syntax.bifunctor._ fromTryCatch("notAnInt".toInt). <-: { _.getMessage } Mapping via Bifunctor Failure(For input string: "notAnInt") Bifunctor = functor of 2 arguments <-: = Map left value

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import scalaz.syntax.bifunctor._ fromTryCatch("notAnInt".toInt). <-: { _.getMessage } Mapping via Bifunctor fromTryCatch("notAnInt".toInt). bimap(_.getMessage, identity) Failure(For input string: "notAnInt") Bifunctor = functor of 2 arguments <-: = Map left value

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import scalaz.syntax.bifunctor._ fromTryCatch("notAnInt".toInt). <-: { _.getMessage } Mapping via Bifunctor fromTryCatch("notAnInt".toInt). bimap(_.getMessage, identity) Failure(For input string: "notAnInt") Failure(For input string: "notAnInt") Bifunctor = functor of 2 arguments <-: = Map left value

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Validation is Monad def justMessage[S]( v: Validation[Throwable, S]): Validation[String, S] = v.<-: { _.getMessage } def extractId( metadata: Map[String, String]): Validation[String, UUID] = for { str <- metadata.get("id").toSuccess("No id property") id <- justMessage(fromTryCatch(UUID.fromString(str))) } yield id extractId(Map.empty) extractId(Map("id" -> "notUuid")) extractId(Map("id" -> UUID.randomUUID.toString))

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Validation is Monad def justMessage[S]( v: Validation[Throwable, S]): Validation[String, S] = v.<-: { _.getMessage } def extractId( metadata: Map[String, String]): Validation[String, UUID] = for { str <- metadata.get("id").toSuccess("No id property") id <- justMessage(fromTryCatch(UUID.fromString(str))) } yield id extractId(Map.empty) extractId(Map("id" -> "notUuid")) extractId(Map("id" -> UUID.randomUUID.toString)) Failure(No id property) Failure(Invalid UUID string: notUuid) Success(f6af15db-feeb-4895-8c67-a70a6f947db9)

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Aside: Monadic DSL def justMessage[S]( v: Validation[Throwable, S]): Validation[String, S] = v.<-: { _.getMessage } def extractId( metadata: Map[String, String]): Validation[String, UUID] = for { str <- metadata.get("id").toSuccess("No id property") id <- justMessage(fromTryCatch(UUID.fromString(str))) } yield id extractId(Map.empty) extractId(Map("id" -> "notUuid")) extractId(Map("id" -> UUID.randomUUID.toString)) This reads pretty naturally!

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Aside: Monadic DSL def justMessage[S]( v: Validation[Throwable, S]): Validation[String, S] = v.<-: { _.getMessage } def extractId( metadata: Map[String, String]): Validation[String, UUID] = for { str <- metadata.get("id").toSuccess("No id property") id <- justMessage(fromTryCatch(UUID.fromString(str))) } yield id extractId(Map.empty) extractId(Map("id" -> "notUuid")) extractId(Map("id" -> UUID.randomUUID.toString)) This doesn’t! Notation is inside-out!

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Aside: Monadic DSL import scalaz.syntax.id._ def justMessage[S]( v: Validation[Throwable, S]): Validation[String, S] = v.<-: { _.getMessage } def parseUUID(s: String): Validation[Throwable, UUID] = fromTryCatch(UUID.fromString(s)) def extractId( metadata: Map[String, String]): Validation[String, UUID] = for { str <- metadata.get("id").toSuccess("No id property") id <- str |> parseUUID |> justMessage } yield id Pipe-forward operator reverses order of function application (from F#) For more info on pipe-forward, see: http://stackoverflow.com/questions/1457140/haskell-composition-vs-fs-pipe-forward-operator

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Validation • Monadic usage of Validation is incredibly useful • As useful as monadic option but provides why failures have occurred • Can it get better?

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Validation is Applicative... ... if the error type is Semigroup

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Validation is Applicative... ... if the error type is Semigroup Validation[Int, Any] Validation[Any, Int] Validation[List[String], String] Validation[String, Int] Which of these are applicative?

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Validation is Applicative... ... if the error type is Semigroup Validation[Int, Any] Validation[Any, Int] Validation[List[String], String] Validation[String, Int] Which of these are applicative? ✔

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Validation is Applicative... ... if the error type is Semigroup Validation[Int, Any] Validation[Any, Int] Validation[List[String], String] Validation[String, Int] Which of these are applicative? ✔ ✘

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Validation is Applicative... ... if the error type is Semigroup Validation[Int, Any] Validation[Any, Int] Validation[List[String], String] Validation[String, Int] Which of these are applicative? ✔ ✘ ✔

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Validation is Applicative... ... if the error type is Semigroup Validation[Int, Any] Validation[Any, Int] Validation[List[String], String] Validation[String, Int] Which of these are applicative? ✔ ✘ ✔ ✔

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Validation[List[_], _] Validation[List[String], Int]

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Success(42) Validation[List[_], _] Validation[List[String], Int]

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Success(42) Failure(List(“Tigers”, “Lions”, “Bears”)) Validation[List[_], _] Validation[List[String], Int]

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Success(42) Failure(List(“Tigers”, “Lions”, “Bears”)) Failure(List()) Validation[List[_], _] Validation[List[String], Int]

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Success(42) Failure(List(“Tigers”, “Lions”, “Bears”)) Failure(List()) Validation[List[_], _] Validation[List[String], Int] Failure of no errors? Can we do better? Use the type system?

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Success(42) Failure(NonEmptyList( “Tigers”, “Lions”, “Bears”)) ValidationNEL Validation[NonEmptyList[String], Int]

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Success(42) Failure(NonEmptyList( “Tigers”, “Lions”, “Bears”)) ValidationNEL Validation[NonEmptyList[String], Int] ValidationNEL[String, Int] This is so common, there’s an alias for it:

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Success(42) Failure(NonEmptyList( “Tigers”, “Lions”, “Bears”)) ValidationNEL Validation[NonEmptyList[String], Int] ValidationNEL[String, Int] This is so common, there’s an alias for it: And any Validation[E, S] can be converted to ValidationNEL[E, S]: v.toValidationNEL

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Putting together the pieces • Given a map of string to string containing keys name, level, manager, representing the name of an employee, their numeric level, and true if they are an manager and false otherwise, create an Employee containing those values if: • Name is non-empty • Level is 1 to 15 • Otherwise, report all errors in the map

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case class Employee( name: String, level: Int, manager: Boolean) type Metadata = Map[String, String] Putting together the pieces

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def justMessage[S]( v: Validation[Throwable, S]): Validation[String, S] = v.<-: { _.getMessage } def extractString( metadata: Metadata, key: String): Validation[String, String] = metadata. get(key). toSuccess("Missing required property %s".format(key)) Putting together the pieces

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def extractName( metadata: Metadata): Validation[String, String] = extractString(metadata, "name") flatMap { name => if (name.isEmpty) "Must have a non-empty name!".fail else name.success } Putting together the pieces

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def extractLevel( metadata: Metadata): Validation[String, Int] = extractString(metadata, "level"). flatMap { _.parseInt |> justMessage }. flatMap { level => if (level < 1) "Level must be at least 1".fail else if (level > 15) "Really?".fail else level.success } Putting together the pieces

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def extractManager( metadata: Metadata): Validation[String, Boolean] = extractString(metadata, "manager"). flatMap { _.parseBoolean |> justMessage } Putting together the pieces

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def extractEmployee( metadata: Metadata): ValidationNEL[String, Employee] = { extractName(metadata).toValidationNel |@| extractLevel(metadata).toValidationNel |@| extractManager(metadata).toValidationNel } apply Employee.apply Putting together the pieces

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extractEmployee(Map( "name" -> "Turing", "level" -> "15", "manager" -> "false")) extractEmployee(Map( "name" -> "Turing", "level" -> "0", "manager" -> "true")) extractEmployee(Map( "name" -> "Turing", "level" -> "17", "manager" -> "true")) Putting together the pieces

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extractEmployee(Map( "name" -> "Turing", "level" -> "15", "manager" -> "false")) extractEmployee(Map( "name" -> "Turing", "level" -> "0", "manager" -> "true")) extractEmployee(Map( "name" -> "Turing", "level" -> "17", "manager" -> "true")) Putting together the pieces Success(Employee(Turing,15,false))

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extractEmployee(Map( "name" -> "Turing", "level" -> "15", "manager" -> "false")) extractEmployee(Map( "name" -> "Turing", "level" -> "0", "manager" -> "true")) extractEmployee(Map( "name" -> "Turing", "level" -> "17", "manager" -> "true")) Putting together the pieces Success(Employee(Turing,15,false)) Failure(NonEmptyList(Level must be at least 1))

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extractEmployee(Map( "name" -> "Turing", "level" -> "15", "manager" -> "false")) extractEmployee(Map( "name" -> "Turing", "level" -> "0", "manager" -> "true")) extractEmployee(Map( "name" -> "Turing", "level" -> "17", "manager" -> "true")) Putting together the pieces Success(Employee(Turing,15,false)) Failure(NonEmptyList(Level must be at least 1)) Failure(NonEmptyList(Really?))

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extractEmployee(Map( "name" -> "Turing")) extractEmployee(Map( "name" -> "", "level" -> "17", "manager" -> "notBool")) Putting together the pieces

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extractEmployee(Map( "name" -> "Turing")) extractEmployee(Map( "name" -> "", "level" -> "17", "manager" -> "notBool")) Putting together the pieces Failure(NonEmptyList( Missing required property level, Missing required property manager))

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extractEmployee(Map( "name" -> "Turing")) extractEmployee(Map( "name" -> "", "level" -> "17", "manager" -> "notBool")) Putting together the pieces Failure(NonEmptyList( Missing required property level, Missing required property manager)) Failure(NonEmptyList( Must have a non-empty name!, Really?, For input string: "notBool"))

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Putting together the pieces • Building upon previous example, given a list of metadata, produce a list of employees or a list of errors

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Putting together the pieces def extractEmployees( metadata: List[Metadata] ): ValidationNEL[String, List[Employee]] = ???

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Putting together the pieces def extractEmployees( metadata: List[Metadata] ): ValidationNEL[String, List[Employee]] = { val vEmps: List[ValidationNEL[String, Employee]] = metadata map extractEmployee ??? }

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Putting together the pieces def extractEmployees( metadata: List[Metadata] ): ValidationNEL[String, List[Employee]] = { val vEmps: List[ValidationNEL[String, Employee]] = metadata map extractEmployee ??? } How can we swap order of ValidationNEL and List?

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Putting together the pieces def extractEmployees( metadata: List[Metadata] ): ValidationNEL[String, List[Employee]] = { val vEmps: List[ValidationNEL[String, Employee]] = metadata map extractEmployee vEmps.sequence[ ({type λ[a] = ValidationNEL[String, a]})#λ, Employee] } Type annotation necessary due to limitations in Scala type inferencing

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Type Lambdas sequence[({type λ[a] = ValidationNEL[String, a]})#λ, Employee]

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Type Lambdas sequence[({type λ[a] = ValidationNEL[String, a]})#λ, Employee] Defines an anonymous structural type with one member, λ[a]

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Type Lambdas Defines type λ[a] as an alias for ValidationNEL[String, a] sequence[({type λ[a] = ValidationNEL[String, a]})#λ, Employee]

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Type Lambdas sequence[({type λ[a] = ValidationNEL[String, a]})#λ, Employee] References the λ member of the structural type

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Type Lambdas Not valid Scala syntax, but IntelliJ will render type lambdas this way sequence[λ[a] = ValidationNEL[String, a], Employee]

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Type Lambdas Can be thought of this way (sort of) sequence[ValidationNEL[String, _], Employee]

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Using sequenceU def extractEmployees( metadata: List[Metadata] ): ValidationNEL[String, List[Employee]] = { val vEmps: List[ValidationNEL[String, Employee]] = metadata map extractEmployee vEmps.sequenceU } In this case, type params can be inferred via sequenceU

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case class Contact( name: Name, phone: Phone) case class Name( salutation: String, first: String, last: String) case class Phone( digits: String) val seth = Contact( Name("Mr.", "Seth", "Avett"), Phone("555-5555")) Lens: Problem Statement

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case class Contact( name: Name, phone: Phone) case class Name( salutation: String, first: String, last: String) case class Phone( digits: String) val seth = Contact( Name("Mr.", "Seth", "Avett"), Phone("555-5555")) Lens: Problem Statement We need a copy of seth with first name set to “Scott”

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val seth = Contact( Name("Mr.", "Seth", "Avett"), Phone("555-5555")) val scott = seth.copy( name = seth.name.copy(first = "Scott")) Lens: Problem Statement

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val seth = Contact( Name("Mr.", "Seth", "Avett"), Phone("555-5555")) val scott = seth.copy( name = seth.name.copy(first = "Scott")) Lens: Problem Statement Doesn’t scale - each layer in record structure results in another layer of copies and duplication

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Lens • Given a record type and a field, a lens provides the ability to focus on the specified field, which allows accessing the field value and setting the field value (immutably)

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Lens • Given a record type and a field, a lens provides the ability to focus on the specified field, which allows accessing the field value and setting the field value (immutably) • Translation: Lens = immutable getter/setter

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case class Contact( name: Name, phone: Phone) val contactNameLens = Lens.lensu[Contact, Name]( (c, n) => c.copy(name = n), _.name) val contactPhoneLens = Lens.lensu[Contact, Phone]( (c, p) => c.copy(phone = p), _.phone) Lens Setter Getter Setter Getter Record Type Field Type

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case class Contact( name: Name, phone: Phone) val contactNameLens = Lens.lensu[Contact, Name]( (c, n) => c.copy(name = n), _.name) val contactPhoneLens = Lens.lensu[Contact, Phone]( (c, p) => c.copy(phone = p), _.phone) Lens Setter Getter Setter Getter •Case class lenses usually use copy in setter

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case class Contact( name: Name, phone: Phone) val contactNameLens = Lens.lensu[Contact, Name]( (c, n) => c.copy(name = n), _.name) val contactPhoneLens = Lens.lensu[Contact, Phone]( (c, p) => c.copy(phone = p), _.phone) Lens Setter Getter Setter Getter •Case class lenses usually use copy in setter •Case class lenses are purely mechanical to author (there’s even a compiler plugin that does it!)

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case class Name( salutation: String, first: String, last: String) val nameSalutationLens = Lens.lensu[Name, String]( (n, s) => n.copy(salutation = s), _.salutation) val nameFirstLens = Lens.lensu[Name, String]( (n, f) => n.copy(first = f), _.first) val nameLastLens = Lens.lensu[Name, String]( (n, l) => n.copy(last = l), _.last) Lens

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case class Phone( digits: String) val phoneDigitsLens = Lens.lensu[Phone, String]( (p, d) => p.copy(digits = d), _.digits) Lens

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val contactFirstNameLens = contactNameLens >=> nameFirstLens Lens Lenses compose!! Composes 2 lenses in to a Contact to First Name lens via andThen

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val seth = Contact( Name("Mr.", "Seth", "Avett"), Phone("555-5555")) val contactFirstNameLens = contactNameLens >=> nameFirstLens Lens Lenses compose!! Composes 2 lenses in to a Contact to First Name lens via andThen

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val seth = Contact( Name("Mr.", "Seth", "Avett"), Phone("555-5555")) val contactFirstNameLens = contactNameLens >=> nameFirstLens Lens Lenses compose!! Composes 2 lenses in to a Contact to First Name lens via andThen contactFirstNameLens.get(seth) “Seth”

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val seth = Contact( Name("Mr.", "Seth", "Avett"), Phone("555-5555")) val contactFirstNameLens = contactNameLens >=> nameFirstLens Lens Lenses compose!! Composes 2 lenses in to a Contact to First Name lens via andThen contactFirstNameLens.get(seth) “Seth” contactFirstNameLens.set(seth, "Scott") Contact(Name(Mr.,Scott,Avett),Phone(555-5555))

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Future Topics • Zipper • Reader • Writer • State • Monad Transformers • Arrow • Kleisli • Category • Iteratees ...and much more!

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Questions? Photo Credit: http://www.flickr.com/photos/yannconz/2795462449