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# Scala example source code file (Traverse.scala)

This example Scala source code file (Traverse.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.

## Java - Scala tags/keywords

applicative, state

## The Traverse.scala Scala example source code

```package scalaz

////
import scalaz.Id.Id

/**
* Idiomatic traversal of a structure, as described in
* [[http://www.cs.ox.ac.uk/jeremy.gibbons/publications/iterator.pdf The Essence of the Iterator Pattern]].
*
* @see [[scalaz.Traverse.TraverseLaw]]
*/
////
trait Traverse[F[_]] extends Functor[F] with Foldable[F] { self =>
////

/** Transform `fa` using `f`, collecting all the `G`s with `ap`. */
def traverseImpl[G[_]:Applicative,A,B](fa: F[A])(f: A => G[B]): G[F[B]]

// derived functions

/**The composition of Traverses `F` and `G`, `[x]F[G[x]]`, is a Traverse */
def compose[G[_]](implicit G0: Traverse[G]): Traverse[λ[α => F[G[α]]]] =
new CompositionTraverse[F, G] {
implicit def F = self
implicit def G = G0
}

/** The composition of Traverse `F` and Bitraverse `G`, `[x, y]F[G[x, y]]`, is a Bitraverse */
def bicompose[G[_, _]: Bitraverse]: Bitraverse[λ[(α, β) => F[G[α, β]]]] =
new CompositionTraverseBitraverse[F, G] {
def F = self
def G = implicitly
}

/**The product of Traverses `F` and `G`, `[x](F[x], G[x]])`, is a Traverse */
def product[G[_]](implicit G0: Traverse[G]): Traverse[λ[α => (F[α], G[α])]] =
new ProductTraverse[F, G] {
implicit def F = self
implicit def G = G0
}

/**The product of Traverse `F` and Traverse1 `G`, `[x](F[x], G[x]])`, is a Traverse1 */
def product0[G[_]](implicit G0: Traverse1[G]): Traverse1[λ[α => (F[α], G[α])]] =
new ProductTraverse1R[F, G] {
def F = self
def G = G0
}

class Traversal[G[_]](implicit G: Applicative[G]) {
def run[A,B](fa: F[A])(f: A => G[B]): G[F[B]] = traverseImpl[G,A,B](fa)(f)
}

// reduce - given monoid
def traversal[G[_]:Applicative]: Traversal[G] =
new Traversal[G]
def traversalS[S]: Traversal[State[S, ?]] =
override def run[A, B](fa: F[A])(f: A => State[S, B]) = traverseS(fa)(f)
}

def traverse[G[_]:Applicative,A,B](fa: F[A])(f: A => G[B]): G[F[B]] =
traversal[G].run(fa)(f)

/** A version of `traverse` that infers the type constructor `G`. */
final def traverseU[A, GB](fa: F[A])(f: A => GB)(implicit G: Unapply[Applicative, GB]): G.M[F[G.A]] /*G[F[B]]*/ =
G.TC.traverse(fa)(G.leibniz.onF(f))(this)

/** A version of `traverse` where a subsequent monadic join is applied to the inner result. */
final def traverseM[A, G[_], B](fa: F[A])(f: A => G[F[B]])(implicit G: Applicative[G], F: Bind[F]): G[F[B]] =
G.map(G.traverse(fa)(f)(this))(F.join)

/** Traverse with `State`. */
def traverseS[S,A,B](fa: F[A])(f: A => State[S,B]): State[S,F[B]] =
traverseSTrampoline[S, Id.Id, A, B](fa)(f)

def runTraverseS[S,A,B](fa: F[A], s: S)(f: A => State[S,B]): (S, F[B]) =
traverseS(fa)(f)(s)

/** Traverse `fa` with a `State[S, G[B]]`, internally using a `Trampoline` to avoid stack overflow. */
def traverseSTrampoline[S, G[_] : Applicative, A, B](fa: F[A])(f: A => State[S, G[B]]): State[S, G[F[B]]] = {
import Free._
implicit val A = StateT.stateTMonadState[S, Trampoline].compose(Applicative[G])
State[S, G[F[B]]](s => {
val st = traverse[λ[α => StateT[Trampoline, S, G[α]]], A, B](fa)(f(_: A).lift[Trampoline])
st.run(s).run
})
}

/** Traverse `fa` with a `Kleisli[G, S, B]`, internally using a `Trampoline` to avoid stack overflow. */
def traverseKTrampoline[S, G[_] : Applicative, A, B](fa: F[A])(f: A => Kleisli[G, S, B]): Kleisli[G, S, F[B]] = {
import Free._
Kleisli[G, S, F[B]](s => {
val kl = traverse[λ[α => Kleisli[Trampoline, S, G[α]]], A, B](fa)(z => Kleisli[Id, S, G[B]](i => f(z)(i)).lift[Trampoline]).run(s)
kl.run
})
}

/** Traverse with the identity function. */
def sequence[G[_]:Applicative,A](fga: F[G[A]]): G[F[A]] =
traversal[G].run[G[A], A](fga)(ga => ga)

/** Traverse with `State`. */
def sequenceS[S,A](fga: F[State[S,A]]): State[S,F[A]] =
traverseS(fga)(x => x)

/** A version of `sequence` that infers the nested type constructor. */
final def sequenceU[A](self: F[A])(implicit G: Unapply[Applicative, A]): G.M[F[G.A]] /*G[F[A]] */ =
G.TC.traverse(self)(x => G.apply(x))(this)

override def map[A,B](fa: F[A])(f: A => B): F[B] =
traversal[Id](Id.id).run(fa)(f)

def foldLShape[A,B](fa: F[A], z: B)(f: (B,A) => B): (B, F[Unit]) =
runTraverseS(fa, z)(a => State.modify(f(_, a)))

override def foldLeft[A,B](fa: F[A], z: B)(f: (B,A) => B): B = foldLShape(fa, z)(f)._1

def foldMap[A,B](fa: F[A])(f: A => B)(implicit F: Monoid[B]): B = foldLShape(fa, F.zero)((b, a) => F.append(b, f(a)))._1

override def foldRight[A, B](fa: F[A], z: => B)(f: (A, => B) => B) =
foldMap(fa)((a: A) => (Endo.endo(f(a, _: B)))) apply z

def reverse[A](fa: F[A]): F[A] = {
val (as, shape) = mapAccumL(fa, scala.List[A]())((t,h) => (h :: t,h))
runTraverseS(shape, as)(_ => for {
e <- State.get
_ <- State.put(e.tail)
}

def zipWith[A,B,C](fa: F[A], fb: F[B])(f: (A, Option[B]) => C): (List[B], F[C]) =
runTraverseS(fa, toList(fb))(a => for {
bs <- State.get
_ <- State.put(if (bs.isEmpty) bs else bs.tail)

def zipWithL[A,B,C](fa: F[A], fb: F[B])(f: (A,Option[B]) => C): F[C] = zipWith(fa, fb)(f)._2
def zipWithR[A,B,C](fa: F[A], fb: F[B])(f: (Option[A],B) => C): F[C] = zipWith(fb, fa)((b,oa) => f(oa,b))._2

def indexed[A](fa: F[A]): F[(Int, A)] = mapAccumL(fa, 0) { case (s, a) => (s + 1, (s, a)) }._2

def zipL[A,B](fa: F[A], fb: F[B]): F[(A, Option[B])] = zipWithL(fa, fb)((_,_))
def zipR[A,B](fa: F[A], fb: F[B]): F[(Option[A], B)] = zipWithR(fa, fb)((_,_))

def mapAccumL[S,A,B](fa: F[A], z: S)(f: (S,A) => (S,B)): (S, F[B]) =
runTraverseS(fa, z)(a => for {
s1 <- State.init[S]
(s2,b) = f(s1,a)
_ <- State.put(s2)
} yield b)

def mapAccumR[S,A,B](fa: F[A], z: S)(f: (S,A) => (S,B)): (S, F[B]) =
mapAccumL(reverse(fa), z)(f) match { case (s, fb) => (s, reverse(fb)) }

trait TraverseLaw extends FunctorLaw {
/** Traversal through the [[scalaz.Id]] effect is equivalent to `Functor#map` */
def identityTraverse[A, B](fa: F[A], f: A => B)(implicit FB: Equal[F[B]]) = {
FB.equal(traverse[Id, A, B](fa)(f), map(fa)(f))
}

/** Two sequentially dependent effects can be fused into one, their composition */
def sequentialFusion[N[_], M[_], A, B, C](fa: F[A], amb: A => M[B], bnc: B => N[C])
(implicit N: Applicative[N], M: Applicative[M], MN: Equal[M[N[F[C]]]]): Boolean = {
type MN[A] = M[N[A]]
val t1: MN[F[C]] = M.map(traverse[M, A, B](fa)(amb))(fb => traverse[N, B, C](fb)(bnc))
val t2: MN[F[C]] = traverse[MN, A, C](fa)(a => M.map(amb(a))(bnc))(M compose N)
MN.equal(t1, t2)
}

/** Traversal with the `point` function is the same as applying the `point` function directly */
def purity[G[_], A](fa: F[A])(implicit G: Applicative[G], GFA: Equal[G[F[A]]]): Boolean =
GFA.equal(traverse[G, A, A](fa)(G.point[A](_)), G.point(fa))

/**
* @param nat A natural transformation from `M` to `N` for which these properties hold:
*            `(a: A) => nat(Applicative[M].point[A](a)) === Applicative[N].point[A](a)`
*            `(f: M[A => B], ma: M[A]) => nat(Applicative[M].ap(ma)(f)) === Applicative[N].ap(nat(ma))(nat(f))`
*/
def naturality[N[_], M[_], A](nat: (M ~> N))
(fma: F[M[A]])
(implicit N: Applicative[N], M: Applicative[M], NFA: Equal[N[F[A]]]): Boolean = {
val n1: N[F[A]] = nat[F[A]](sequence[M, A](fma))
val n2: N[F[A]] = sequence[N, A](map(fma)(ma => nat(ma)))
NFA.equal(n1, n2)
}

/** Two independent effects can be fused into a single effect, their product. */
def parallelFusion[N[_], M[_], A, B](fa: F[A], amb: A => M[B], anb: A => N[B])
(implicit N: Applicative[N], M: Applicative[M], MN: Equal[(M[F[B]], N[F[B]])]): Boolean = {
type MN[A] = (M[A], N[A])
val t1: MN[F[B]] = (traverse[M, A, B](fa)(amb), traverse[N, A, B](fa)(anb))
val t2: MN[F[B]] = traverse[MN, A, B](fa)(a => (amb(a), anb(a)))(M product N)
MN.equal(t1, t2)
}
}
def traverseLaw = new TraverseLaw {}

////
val traverseSyntax = new scalaz.syntax.TraverseSyntax[F] { def F = Traverse.this }
}

object Traverse {
@inline def apply[F[_]](implicit F: Traverse[F]): Traverse[F] = F

////

////
}
```

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