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Scala example source code file (Lens.scala)

This example Scala source code file (Lens.scala) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Scala by Example" TM.

Learn more about this Scala project at its project page.

Java - Scala tags/keywords

indexedstate, lensfamily

The Lens.scala Scala example source code

package scalaz

import Id._

/**
 * A Lens Family, offering a purely functional means to access and retrieve
 * a field transitioning from type `B1` to type `B2` in a record simultaneously
 * transitioning from type `A1` to type `A2`.  [[scalaz.Lens]] is a convenient
 * alias for when `A1 =:= A2`, and `B1 =:= B2`.
 *
 * The term ''field'' should not be interpreted restrictively to mean a member of a class. For example, a lens
 * family can address membership of a `Set`.
 *
 * @see [[scalaz.PLens]]
 *
 * @tparam A1 The initial type of the record
 * @tparam A2 The final type of the record
 * @tparam B1 The initial type of the field
 * @tparam B2 The final type of the field
 */
sealed abstract class LensFamily[A1, A2, B1, B2] {
  def run(a: A1): IndexedStore[B1, B2, A2]

  def apply(a: A1): IndexedStore[B1, B2, A2] =
    run(a)

  import LensFamily._
  import BijectionT._

  def xmapA[X1, X2](f: A2 => X2)(g: X1 => A1): LensFamily[X1, X2, B1, B2] =
    lensFamily(x => run(g(x)) map f)

  def xmapbA[X, A >: A2 <: A1](b: Bijection[A, X]): LensFamily[X, X, B1, B2] =
    xmapA(b to _)(b from _)

  def xmapB[X1, X2](f: B1 => X1)(g: X2 => B2): LensFamily[A1, A2, X1, X2] =
    lensFamily(a => run(a).xmap(f)(g))

  def xmapbB[X, B >: B1 <: B2](b: Bijection[B, X]): LensFamily[A1, A2, X, X] =
    xmapB(b to _)(b from _)

  def get(a: A1): B1 =
    run(a).pos

  def set(a: A1, b: B2): A2 =
    run(a).put(b)

  def st: State[A1, B1] =
    State(s => (s, get(s)))

  /** Modify the value viewed through the lens */
  def mod(f: B1 => B2, a: A1): A2 = {
    val (p, q) = run(a).run
    p(f(q))
  }

  def =>=(f: B1 => B2): A1 => A2 =
    mod(f, _)

  /** Modify the value viewed through the lens, returning a functor `X` full of results. */
  def modf[X[_]](f: B1 => X[B2], a: A1)(implicit XF: Functor[X]): X[A2] = {
    val c = run(a)
    XF.map(f(c.pos))(c put _)
  }

  def =>>=[X[_]](f: B1 => X[B2])(implicit XF: Functor[X]): A1 => X[A2] =
    modf(f, _)

  /** Modify the value viewed through the lens, returning a `C` on the side.  */
  def modp[C](f: B1 => (B2, C), a: A1): (A2, C) = {
    val (b, c) = f(get(a))
    (set(a, b), c)
  }

  /** Modify the portion of the state viewed through the lens and return its new value. */
  def mods(f: B1 => B2): IndexedState[A1, A2, B2] =
    IndexedState(a => {
      val c = run(a)
      val b = f(c.pos)
      (c put b, b)
    })

  /** Modify the portion of the state viewed through the lens and return its new value. */
  def %=(f: B1 => B2): IndexedState[A1, A2, B2] =
    mods(f)

  /** Modify the portion of the state viewed through the lens and return its old value.
   * @since 7.0.2
   */
  def modo(f: B1 => B2): IndexedState[A1, A2, B1] =
    IndexedState(a => {
      val c = run(a)
      val o = c.pos
      (c put f(o), o)
    })

  /** Modify the portion of the state viewed through the lens and return its old value. alias for `modo`
   * @since 7.0.2
   */
  def <%=(f: B1 => B2): IndexedState[A1, A2, B1] =
    modo(f)

  /** Set the portion of the state viewed through the lens and return its new value. */
  def assign(b: => B2): IndexedState[A1, A2, B2] =
    mods(_ => b)

  /** Set the portion of the state viewed through the lens and return its new value. */
  def :=(b: => B2): IndexedState[A1, A2, B2] =
    assign(b)

  /** Set the portion of the state viewed through the lens and return its old value.
   * @since 7.0.2
   */
  def assigno(b: => B2): IndexedState[A1, A2, B1] =
    modo(_ => b)

  /** Set the portion of the state viewed through the lens and return its old value. alias for `assigno`
   * @since 7.0.2
   */
  def <:=(b: => B2): IndexedState[A1, A2, B1] =
    assigno(b)

  /** Modify the portion of the state viewed through the lens, but do not return its new value. */
  def mods_(f: B1 => B2): IndexedState[A1, A2, Unit] =
    IndexedState(a =>
      (mod(f, a), ()))

  /** Modify the portion of the state viewed through the lens, but do not return its new value. */
  def %==(f: B1 => B2): IndexedState[A1, A2, Unit] =
    mods_(f)

  /** Contravariantly map a state action through a lens. */
  def lifts[C](s: IndexedState[B1, B2, C]): IndexedState[A1, A2, C] =
    IndexedState(a => modp(s(_), a))

  def %%=[C](s: IndexedState[B1, B2, C]): IndexedState[A1, A2, C] =
    lifts(s)

  /** Map the function `f` over the lens as a state action. */
  def map[C](f: B1 => C): State[A1, C] =
    State(a => (a, f(get(a))))

  /** Map the function `f` over the value under the lens, as a state action. */
  def >-[C](f: B1 => C): State[A1, C] = map(f)

  /** Bind the function `f` over the value under the lens, as a state action. */
  def flatMap[C](f: B1 => IndexedState[A1, A2, C]): IndexedState[A1, A2, C] =
    IndexedState(a => f(get(a))(a))

  /** Bind the function `f` over the value under the lens, as a state action. */
  def >>-[C](f: B1 => IndexedState[A1, A2, C]): IndexedState[A1, A2, C] =
    flatMap[C](f)

  /** Sequence the monadic action of looking through the lens to occur before the state action `f`. */
  def ->>-[C](f: => IndexedState[A1, A2, C]): IndexedState[A1, A2, C] =
    flatMap(_ => f)

  /** Contravariantly mapping the state of a state monad through a lens is a natural transformation */
  def liftsNT: IndexedState[B1, B2, ?] ~> IndexedState[A1, A2, ?] =
    new (IndexedState[B1, B2, ?] ~> IndexedState[A1, A2, ?]) {
      def apply[C](s : IndexedState[B1, B2, C]): IndexedState[A1, A2, C] =
        IndexedState[A1, A2, C](a => modp(s(_), a))
    }

  /** Lenses can be composed */
  def compose[C1, C2](that: LensFamily[C1, C2, A1, A2]): LensFamily[C1, C2, B1, B2] =
    lensFamily(c => {
      val (ac, a) = that.run(c).run
      val (ba, b) = run(a).run
      IndexedStore(ac compose ba, b)
    })

  /** alias for `compose` */
  def <=<[C1, C2](that: LensFamily[C1, C2, A1, A2]): LensFamily[C1, C2, B1, B2] = compose(that)

  def andThen[C1, C2](that: LensFamily[B1, B2, C1, C2]): LensFamily[A1, A2, C1, C2] =
    that compose this

  /** alias for `andThen` */
  def >=>[C1, C2](that: LensFamily[B1, B2, C1, C2]): LensFamily[A1, A2, C1, C2] = andThen(that)

  /** Two lenses that view a value of the same type can be joined */
  def sum[C1, C2](that: => LensFamily[C1, C2, B1, B2]): LensFamily[A1 \/ C1, A2 \/ C2, B1, B2] =
    lensFamily{
      case -\/(a) =>
        run(a) map  (\/.left)
      case \/-(c) =>
        that run c map (\/.right)
    }

  /** Alias for `sum` */
  def |||[C1, C2](that: => LensFamily[C1, C2, B1, B2]): LensFamily[A1 \/ C1, A2 \/ C2, B1, B2] = sum(that)

  /** Two disjoint lenses can be paired */
  def product[C1, C2, D1, D2](that: LensFamily[C1, C2, D1, D2]): LensFamily[(A1, C1), (A2, C2), (B1, D1), (B2, D2)] =
    lensFamily {
      case (a, c) => run(a) *** that.run(c)
    }

  /** alias for `product` */
  def ***[C1, C2, D1, D2](that: LensFamily[ C1, C2, D1, D2]): LensFamily[(A1, C1), (A2, C2), (B1, D1), (B2, D2)] = product(that)

  trait LensLaw {
    def identity[A >: A2 <: A1, B >: B1 <: B2](a: A)(implicit A: Equal[A]): Boolean = {
      val c = run(a)
      A.equal(c.put(c.pos: B), a)
    }
    def retention[A >: A2 <: A1, B >: B1 <: B2](a: A, b: B)(implicit B: Equal[B]): Boolean =
      B.equal(run(run(a).put(b): A).pos, b)
    def doubleSet[A >: A2 <: A1, B >: B1 <: B2](a: A, b1: B, b2: B)(implicit A: Equal[A]): Boolean = {
      val r = run(a)
      A.equal(run(r.put(b1): A) put b2, r put b2)
    }
  }

  def lensLaw = new LensLaw {}

  /** A homomorphism of lens categories */
  def partial: PLensFamily[A1, A2, B1, B2] =
    PLensFamily.plensFamily(a => Some(run(a)):Option[IndexedStore[B1, B2, A2]])

  /** alias for `partial` */
  def unary_~ : PLensFamily[A1, A2, B1, B2] =
    partial

}

object LensFamily extends LensInstances with LensFunctions {
  def apply[A1, A2, B1, B2](r: A1 => IndexedStore[B1, B2, A2]): LensFamily[A1, A2, B1, B2] =
    lensFamily(r)
}

trait LensFamilyFunctions {

  def lensFamily[A1, A2, B1, B2](r: A1 => IndexedStore[B1, B2, A2]): LensFamily[A1, A2, B1, B2] = new LensFamily[A1, A2, B1, B2] {
    def run(a: A1): IndexedStore[B1, B2, A2] = r(a)
  }

  def lensFamilyg[A1, A2, B1, B2](set: A1 => B2 => A2, get: A1 => B1): LensFamily[A1, A2, B1, B2] =
    lensFamily(a => IndexedStore(set(a), get(a)))

  def lensFamilyu[A1, A2, B1, B2](set: (A1, B2) => A2, get: A1 => B1): LensFamily[A1, A2, B1, B2] =
    lensFamilyg(set.curried, get)

  /** The identity lens family for a given pair of objects */
  def lensFamilyId[A1, A2]: LensFamily[A1, A2, A1, A2] =
    lensFamily(IndexedStore(identity, _))

  /** A lens family that discards the choice of right or left from disjunction */
  def codiagLensFamily[A1, A2]: LensFamily[A1 \/ A1, A2 \/ A2, A1, A2] =
    lensFamilyId[A1, A2] ||| lensFamilyId[A1, A2]

  /** Polymorphically access the first field of a tuple */
  def firstLensFamily[A1, A2, B]: LensFamily[(A1, B), (A2, B), A1, A2] =
    lensFamily {
      case (a, b) => IndexedStore(x => (x, b), a)
    }

  /** Polymorphically access the second field of a tuple */
  def secondLensFamily[A, B1, B2]: LensFamily[(A, B1), (A, B2), B1, B2] =
    lensFamily {
      case (a, b) => IndexedStore(x => (a, x), b)
    }

  /** Polymorphically access the first field of a tuple */
  def lazyFirstLensFamily[A1, A2, B]: LensFamily[LazyTuple2[A1, B], LazyTuple2[A2, B], A1, A2] =
    lensFamily(z => IndexedStore(x => LazyTuple2(x, z._2), z._1))

  /** Polymorphically access the second field of a tuple */
  def lazySecondLensFamily[A, B1, B2]: LensFamily[LazyTuple2[A, B1], LazyTuple2[A, B2], B1, B2] =
    lensFamily(z => IndexedStore(x => LazyTuple2(z._1, x), z._2))

  def predicateLensFamily[A1, A2]: LensFamily[Store[A1, Boolean], Store[A2, Boolean], (A1 \/ A1), (A2 \/ A2)] =
    lensFamily(q => IndexedStore(_ match {
      case -\/(l) => Store(_ => true, l)
      case \/-(r) => Store(_ => false, r)
    }, {
      val x = q.pos
      if(q put x) -\/(x) else \/-(x)
    }))

  def factorLensFamily[A1, A2, B1, B2, C1, C2]: LensFamily[((A1, B1) \/ (A1, C1)), ((A2, B2) \/ (A2, C2)), (A1, B1 \/ C1), (A2, B2 \/ C2)] =
    lensFamily(e => IndexedStore({
      case (a, -\/(b)) => -\/(a, b)
      case (a, \/-(c)) => \/-(a, c)
    }, e match {
      case -\/((a, b)) => (a, -\/(b))
      case \/-((a, c)) => (a, \/-(c))
    }))

  def distributeLensFamily[A1, A2, B1, B2, C1, C2]: LensFamily[(A1, B1 \/ C1), (A2, B2 \/ C2), ((A1, B1) \/ (A1, C1)), ((A2, B2) \/ (A2, C2))] =
    lensFamily {
      case (a, e) => IndexedStore({
        case -\/((aa, bb)) => (aa, -\/(bb))
        case \/-((aa, cc)) => (aa, \/-(cc))
      }, e match {
        case -\/(b) => -\/(a, b)
        case \/-(c) => \/-(a, c)

      })
    }

}

trait LensFunctions extends LensFamilyFunctions {

  def lens[A, B](r: A => Store[B, A]): Lens[A, B] = new Lens[A, B] {
    def run(a: A): Store[B, A] = r(a)
  }

  def lensg[A, B](set: A => B => A, get: A => B): Lens[A, B] =
    lens(a => Store(set(a), get(a)))

  def lensu[A, B](set: (A, B) => A, get: A => B): Lens[A, B] =
    lensg(set.curried, get)

  /** The identity lens for a given object */
  def lensId[A]: Lens[A, A] =
    lens(Store(identity, _))

  /** The trivial lens that can retrieve Unit from anything */
  def trivialLens[A]: Lens[A, Unit] =
    lens[A, Unit](a => Store(_ => a, ()))

  /** A lens that discards the choice of right or left from disjunction */
  def codiagLens[A]: Lens[A \/ A, A] =
    lensId[A] ||| lensId[A]

  /** Access the first field of a tuple */
  def firstLens[A, B]: (A, B) @> A =
    lens {
      case (a, b) => Store(x => (x, b), a)
    }

  /** Access the second field of a tuple */
  def secondLens[A, B]: (A, B) @> B =
    lens {
      case (a, b) => Store(x => (a, x), b)
    }

  /** Access the first field of a tuple */
  def lazyFirstLens[A, B]: LazyTuple2[A, B] @> A =
    lens(z => Store(x => LazyTuple2(x, z._2), z._1))

  /** Access the second field of a tuple */
  def lazySecondLens[A, B]: LazyTuple2[A, B] @> B =
    lens(z => Store(x => LazyTuple2(z._1, x), z._2))

  def nelHeadLens[A]: NonEmptyList[A] @> A =
    lens(l => Store(NonEmptyList.nel(_, l.tail), l.head))

  def nelTailLens[A]: NonEmptyList[A] @> List[A] =
    lens(l => Store(ll => NonEmptyList.nel(l.head, IList.fromList(ll)), l.tail.toList))

  /** Access the value at a particular key of a Map **/
  def mapVLens[K, V](k: K): Map[K, V] @> Option[V] =
    lensg(m => ({
      case None => m - k
      case Some(v) => m.updated(k, v)
    }: Option[V] => Map[K, V]), _ get k)

  /** Access the value at a particular key of a Map.WithDefault */
  def mapWithDefaultLens[K,V](k: K): Map.WithDefault[K,V] @> V =
    lensg(m => v => m.updated(k,v), m => m(k))

  /** Specify whether a value is in a Set */
  def setMembershipLens[A](a: A): Set[A] @> Boolean =
    lensg(s => b => if (b) s + a else s - a, _.contains(a))

  def applyLens[A, B](k: B => A)(implicit e: Equal[A]): Store[A, B] @> B =
    lens(q => {
      val x = Need(q.pos)
      val y = Need(q put x.value)
      Store(b =>
        Store(w => if(e equal (x.value, w)) b else y.value, x.value), y.value)
    })

  def predicateLens[A]: Store[A, Boolean] @> (A \/ A) =
    lens(q => Store(_ match {
      case -\/(l) => Store(_ => true, l)
      case \/-(r) => Store(_ => false, r)
    }, {
      val x = q.pos
      if(q put x) -\/(x) else \/-(x)
    }))

  def factorLens[A, B, C]: ((A, B) \/ (A, C)) @> (A, B \/ C) =
    lens(e => Store({
      case (a, -\/(b)) => -\/(a, b)
      case (a, \/-(c)) => \/-(a, c)
    }, e match {
      case -\/((a, b)) => (a, -\/(b))
      case \/-((a, c)) => (a, \/-(c))
    }))

  def distributeLens[A, B, C]: (A, B \/ C) @> ((A, B) \/ (A, C)) =
    lens {
      case (a, e) => Store({
        case -\/((aa, bb)) => (aa, -\/(bb))
        case \/-((aa, cc)) => (aa, \/-(cc))
      }, e match {
        case -\/(b) => -\/(a, b)
        case \/-(c) => \/-(a, c)

      })
    }
}

sealed abstract class LensInstances0 { this: LensInstances =>
  import scala.collection.SeqLike

  implicit def seqLikeLensFamily[S1, S2, A, Repr <: SeqLike[A, Repr]](lens: LensFamily[S1, S2, Repr, Repr]) =
    SeqLikeLens[S1, S2, A, Repr](lens)

}

abstract class LensInstances extends LensInstances0 {
  import LensFamily._
  import BijectionT._
  import collection.SeqLike
  import collection.immutable.Queue

  implicit val lensCategory: LensCategory = new LensCategory {
  }

  /** Lenses may be used implicitly as State monadic actions that get the viewed portion of the state */
  implicit def LensFamilyState[A, B](lens: LensFamily[A, _, B, _]): State[A, B] =
    lens.st

  implicit def LensFamilyUnzip[S, R]: Unzip[λ[α => LensFamily[S, R, α, α]]] =
    new Unzip[λ[α => LensFamily[S, R, α, α]]] {
      def unzip[A, B](a: LensFamily[S, R, (A, B), (A, B)]) =
        (
          lensFamily(x => {
            val c = a run x
            val (p, q) = c.pos
            IndexedStore(a => c.put((a, q)): R, p)
          })
        , lensFamily(x => {
          val c = a run x
          val (p, q) = c.pos
          IndexedStore(a => c.put((p, a)): R, q)
        })
        )
    }

  type SetLens[S, K] = SetLensFamily[S, S, K]
  val SetLens: SetLensFamily.type = SetLensFamily
  case class SetLensFamily[S1, S2, K](lens: LensFamily[S1, S2, Set[K], Set[K]]) {
    /** Setting the value of this lens will change whether or not it is present in the set */
    def contains(key: K) = lensFamilyg[S1, S2, Boolean, Boolean](
      s => b => lens.mod(m => if (b) m + key else m - key, s): Id[S2]
    , s => lens.get(s).contains(key)
    )

    def &=(that: Set[K]): IndexedState[S1, S2, Set[K]] =
      lens %= (_ & that)

    def &~=(that: Set[K]): IndexedState[S1, S2, Set[K]] =
      lens %= (_ &~ that)

    def |=(that: Set[K]): IndexedState[S1, S2, Set[K]] =
      lens %= (_ | that)

    def +=(elem: K): IndexedState[S1, S2, Set[K]] =
      lens %= (_ + elem)

    def +=(elem1: K, elem2: K, elems: K*): IndexedState[S1, S2, Set[K]] =
      lens %= (_ + elem1 + elem2 ++ elems)

    def ++=(xs: TraversableOnce[K]): IndexedState[S1, S2, Set[K]] =
      lens %= (_ ++ xs)

    def -=(elem: K): IndexedState[S1, S2, Set[K]] =
      lens %= (_ - elem)

    def -=(elem1: K, elem2: K, elems: K*): IndexedState[S1, S2, Set[K]] =
      lens %= (_ - elem1 - elem2 -- elems)

    def --=(xs: TraversableOnce[K]): IndexedState[S1, S2, Set[K]] =
      lens %= (_ -- xs)
  }

  /** A lens that views a Set can provide the appearance of in place mutation */
  implicit def setLensFamily[S1, S2, K](lens: LensFamily[S1, S2, Set[K], Set[K]]) =
    SetLensFamily[S1, S2, K](lens)

  type MapLens[S, K, V] = MapLensFamily[S, S, K, V]
  val MapLens: MapLensFamily.type = MapLensFamily
  /** A lens that views an immutable Map type can provide a mutable.Map-like API via State */
  case class MapLensFamily[S1, S2, K, V](lens: LensFamily[S1, S2, Map[K, V], Map[K, V]]) {
    /** Allows both viewing and setting the value of a member of the map */
    def member(k: K): LensFamily[S1, S2, Option[V], Option[V]] = lensFamilyg[S1, S2, Option[V], Option[V]](
      s => opt => lens.mod((m: Map[K, V]) => (opt match {
        case Some(v) => m + (k -> v)
        case None    => m - k
      }): Map[K, V], s): Id[S2]
      , s => lens.get(s).get(k))

    /** This lens has undefined behavior when accessing an element not present in the map! */
    def at(k: K): LensFamily[S1, S2, V, V] =
      lensFamilyg[S1, S2, V, V](s => v => lens.mod(_ + (k -> v), s): Id[S2], lens.get(_) apply k)

    def +=(elem1: (K, V), elem2: (K, V), elems: (K, V)*): IndexedState[S1, S2, Map[K, V]] =
      lens %= (_ + elem1 + elem2 ++ elems)

    def +=(elem: (K, V)): IndexedState[S1, S2, Map[K, V]] =
      lens %= (_ + elem)

    def ++=(xs: TraversableOnce[(K, V)]): IndexedState[S1, S2, Map[K, V]] =
      lens %= (_ ++ xs)

    def update(key: K, value: V): IndexedState[S1, S2, Unit] =
      lens %== (_.updated(key, value))

    def -=(elem: K): IndexedState[S1, S2, Map[K, V]] =
      lens %= (_ - elem)

    def -=(elem1: K, elem2: K, elems: K*): IndexedState[S1, S2, Map[K, V]] =
      lens %= (_ - elem1 - elem2 -- elems)

    def --=(xs: TraversableOnce[K]): IndexedState[S1, S2, Map[K, V]] =
      lens %= (_ -- xs)
  }

  implicit def mapLensFamily[S1, S2, K, V](lens: LensFamily[S1, S2, Map[K, V], Map[K, V]]) =
    MapLensFamily[S1, S2, K, V](lens)

  type SeqLikeLens[S, A, Repr <: SeqLike[A, Repr]] = SeqLikeLensFamily[S, S, A, Repr]
  val SeqLikeLens: SeqLikeLensFamily.type = SeqLikeLensFamily
  /** Provide the appearance of a mutable-like API for sorting sequences through a lens */
  case class SeqLikeLensFamily[S1, S2, A, Repr <: SeqLike[A, Repr]](lens: LensFamily[S1, S2, Repr, Repr]) {
    def sortWith(lt: (A, A) => Boolean): IndexedState[S1, S2, Unit] =
      lens %== (_ sortWith lt)

    def sortBy[B: math.Ordering](f: A => B): IndexedState[S1, S2, Unit] =
      lens %== (_ sortBy f)

    def sort[B >: A](implicit ord: math.Ordering[B]): IndexedState[S1, S2, Unit] =
      lens %== (_.sorted[B])
  }

  implicit def seqLensFamily[S1, S2, A](lens: LensFamily[S1, S2, scala.collection.immutable.Seq[A], scala.collection.immutable.Seq[A]]) =
    seqLikeLensFamily[S1, S2, A, scala.collection.immutable.Seq[A]](lens)

  type QueueLens[S, A] = QueueLensFamily[S, S, A]
  val QueueLens: QueueLensFamily.type = QueueLensFamily
  /** Provide an imperative-seeming API for queues viewed through a lens */
  case class QueueLensFamily[S1, S2, A](lens: LensFamily[S1, S2, Queue[A], Queue[A]]) {
    def enqueue(elem: A): IndexedState[S1, S2, Unit] =
      lens %== (_ enqueue elem)

    def dequeue: IndexedState[S1, S2, A] =
      lens %%= State[Queue[A], A](_.dequeue.swap)

    def length: State[S1, Int] =
      lens >- (_.length)
  }

  implicit def queueLensFamily[S1, S2, A](lens: LensFamily[S1, S2, Queue[A], Queue[A]]) =
    QueueLensFamily[S1, S2, A](lens)

  type ArrayLens[S, A] = ArrayLensFamily[S, S, A]
  val ArrayLens: ArrayLensFamily.type = ArrayLensFamily
  /** Provide an imperative-seeming API for arrays viewed through a lens */
  case class ArrayLensFamily[S1, S2, A](lens: LensFamily[S1, S2, Array[A], Array[A]]) {
    def at(n: Int): LensFamily[S1, S2, A, A] =
      lensFamilyg[S1, S2, A, A](
        s => v => lens.mod(array => {
          val copy = array.clone()
          copy.update(n, v)
          copy
        }, s): Id[S2]
        , s => lens.get(s) apply n
      )

    def length: State[S1, Int] =
      lens >- (_.length)
  }

  implicit def arrayLensFamily[S1, S2, A](lens: LensFamily[S1, S2, Array[A], Array[A]]) =
    ArrayLensFamily[S1, S2, A](lens)

  type NumericLens[S, N] = NumericLensFamily[S, S, N]
  val NumericLens: NumericLensFamily.type = NumericLensFamily
  /** Allow the illusion of imperative updates to numbers viewed through a lens */
  case class NumericLensFamily[S1, S2, N](lens: LensFamily[S1, S2, N, N], num: Numeric[N]) {
    def +=(that: N): IndexedState[S1, S2, N] =
      lens %= (num.plus(_, that))

    def -=(that: N): IndexedState[S1, S2, N] =
      lens %= (num.minus(_, that))

    def *=(that: N): IndexedState[S1, S2, N] =
      lens %= (num.times(_, that))
  }

  implicit def numericLensFamily[S1, S2, N: Numeric](lens: LensFamily[S1, S2, N, N]) =
    NumericLens[S1, S2, N](lens, implicitly[Numeric[N]])

  type FractionalLens[S, F] = FractionalLensFamily[S, S, F]
  val FractionalLens: FractionalLensFamily.type = FractionalLensFamily
  /** Allow the illusion of imperative updates to numbers viewed through a lens */
  case class FractionalLensFamily[S1, S2, F](lens: LensFamily[S1, S2, F, F], frac: Fractional[F]) {
    def /=(that: F): IndexedState[S1, S2, F] =
      lens %= (frac.div(_, that))
  }

  implicit def fractionalLensFamily[S1, S2, F: Fractional](lens: LensFamily[S1, S2, F, F]) =
    FractionalLensFamily[S1, S2, F](lens, implicitly[Fractional[F]])

  type IntegralLens[S, I] = IntegralLensFamily[S, S, I]
  val IntegralLens: IntegralLensFamily.type = IntegralLensFamily
  /** Allow the illusion of imperative updates to numbers viewed through a lens */
  case class IntegralLensFamily[S1, S2, I](lens: LensFamily[S1, S2, I, I], ig: Integral[I]) {
    def %=(that: I): IndexedState[S1, S2, I] =
      lens %= (ig.quot(_, that))
  }

  implicit def integralLensFamily[S1, S2, I: Integral](lens: LensFamily[S1, S2, I, I]) =
    IntegralLensFamily[S1, S2, I](lens, implicitly[Integral[I]])

  implicit def tuple2LensFamily[S1, S2, A, B](lens: LensFamily[S1, S2, (A, B), (A, B)]):
  (LensFamily[S1, S2, A, A], LensFamily[S1, S2, B, B]) =
    LensFamilyUnzip[S1, S2].unzip(lens)

  implicit def tuple3LensFamily[S1, S2, A, B, C](lens: LensFamily[S1, S2, (A, B, C), (A, B, C)]):
  (LensFamily[S1, S2, A, A], LensFamily[S1, S2, B, B], LensFamily[S1, S2, C, C]) =
    LensFamilyUnzip[S1, S2].unzip3(lens.xmapbB(tuple3B))

  implicit def tuple4LensFamily[S1, S2, A, B, C, D](lens: LensFamily[S1, S2, (A, B, C, D), (A, B, C, D)]):
  (LensFamily[S1, S2, A, A], LensFamily[S1, S2, B, B], LensFamily[S1, S2, C, C], LensFamily[S1, S2, D, D]) =
    LensFamilyUnzip[S1, S2].unzip4(lens.xmapbB(tuple4B))

  implicit def tuple5LensFamily[S1, S2, A, B, C, D, E](lens: LensFamily[S1, S2, (A, B, C, D, E), (A, B, C, D, E)]):
  (LensFamily[S1, S2, A, A], LensFamily[S1, S2, B, B], LensFamily[S1, S2, C, C], LensFamily[S1, S2, D, D], LensFamily[S1, S2, E, E]) =
    LensFamilyUnzip[S1, S2].unzip5(lens.xmapbB(tuple5B))

  implicit def tuple6LensFamily[S1, S2, A, B, C, D, E, H](lens: LensFamily[S1, S2, (A, B, C, D, E, H), (A, B, C, D, E, H)]):
  (LensFamily[S1, S2, A, A], LensFamily[S1, S2, B, B], LensFamily[S1, S2, C, C], LensFamily[S1, S2, D, D], LensFamily[S1, S2, E, E], LensFamily[S1, S2, H, H]) =
    LensFamilyUnzip[S1, S2].unzip6(lens.xmapbB(tuple6B))

  implicit def tuple7LensFamily[S1, S2, A, B, C, D, E, H, I](lens: LensFamily[S1, S2, (A, B, C, D, E, H, I), (A, B, C, D, E, H, I)]):
  (LensFamily[S1, S2, A, A], LensFamily[S1, S2, B, B], LensFamily[S1, S2, C, C], LensFamily[S1, S2, D, D], LensFamily[S1, S2, E, E], LensFamily[S1, S2, H, H], LensFamily[S1, S2, I, I]) =
    LensFamilyUnzip[S1, S2].unzip7(lens.xmapbB(tuple7B))
}

private[scalaz] trait LensCategory
  extends Choice[Lens]
  with Split[Lens] {

  def compose[A, B, C](bc: Lens[B, C], ab: Lens[A, B]): Lens[A, C] = ab >=> bc

  def id[A] = LensFamily.lensId

  def choice[A, B, C](f: => Lens[A, C], g: => Lens[B, C]): Lens[A \/ B, C] =
    LensFamily.lens {
      case -\/(a) =>
        f run a map (\/.left)
      case \/-(b) =>
        g run b map (\/.right)
    }

  def split[A, B, C, D](f: Lens[A, B], g: Lens[C, D]): Lens[(A,  C), (B, D)] =
    f *** g

}

Other Scala examples (source code examples)

Here is a short list of links related to this Scala Lens.scala source code file:



my book on functional programming

 

new blog posts

 

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