Add UnorderedFoldable and UnorderedTraverse (#1981)

* Add CommutativeApply and Applicative and an instance for Validated[CommutativeSemigroup, ?]

* Make Future a CommutativeApplicative

* Revert "Make Future a CommutativeApplicative"

This reverts commit 0cd4eb9.

* Add unordered traversal for Sets

* Test commutativeApply instances + Nested + Tuple2K instances

* Add unordered traversal for Map

* Fix priority for Nested instances

* Fix priority for Tuple2K instances

* Move methods to typeclass

* Deduplicate Applicative instance

* Try out new typeclasses

* Add UnorderedFoldable and UnorderedTraverse and move traversal functions there

* Remove Set from Foldable docs

* Add extra ref law

* Revert "Add UnorderedFoldable and UnorderedTraverse and move traversal functions there"

This reverts commit d308cf7.

* Revert "Remove Set from Foldable docs"

This reverts commit 0ffbc55.

* Add Unordered type classes

* Make UnorderedFoldable and Traverse super classes

* Make unorderedFoldMap the main method

* define isEmpty in terms of exists

* Add mention to unorderedFoldable in foldable scaladoc

* Add size to UnorderedFoldable

* Made exists and forall sufficiently lazy

* Add Mima exceptions

* Fix merging mistake

* Remove toSet

* Remove unused imports

build.sbt

@@ -195,6 +195,41 @@ def mimaSettings(moduleName: String) = Seq(
     import com.typesafe.tools.mima.core.ProblemFilters._
     Seq(
       exclude[ReversedMissingMethodProblem]("cats.syntax.FoldableSyntax.catsSyntaxFoldOps"),
+      exclude[ReversedMissingMethodProblem]("cats.Traverse.unorderedTraverse"),
+      exclude[ReversedMissingMethodProblem]("cats.Traverse.unorderedSequence"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedTraverse.unorderedTraverse"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedTraverse.unorderedSequence"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedFoldable.toSet"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedFoldable.unorderedFold"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedFoldable.unorderedFoldMap"),
+      exclude[IncompatibleResultTypeProblem]("cats.implicits.catsStdInstancesForMap"),
+      exclude[IncompatibleResultTypeProblem]("cats.implicits.catsStdInstancesForSet"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedFoldable#Ops.toSet"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedFoldable#Ops.unorderedFold"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedFoldable#Ops.unorderedFoldMap"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedTraverse#Ops.unorderedTraverse"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedTraverse#Ops.unorderedSequence"),
+      exclude[UpdateForwarderBodyProblem]("cats.Foldable.size"),
+      exclude[ReversedMissingMethodProblem]("cats.Foldable.unorderedFold"),
+      exclude[ReversedMissingMethodProblem]("cats.Foldable.unorderedFoldMap"),
+      exclude[DirectMissingMethodProblem]("cats.Foldable#Ops.size"),
+      exclude[DirectMissingMethodProblem]("cats.Foldable#Ops.forall"),
+      exclude[DirectMissingMethodProblem]("cats.Foldable#Ops.isEmpty"),
+      exclude[DirectMissingMethodProblem]("cats.Foldable#Ops.nonEmpty"),
+      exclude[DirectMissingMethodProblem]("cats.Foldable#Ops.exists"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedFoldable#ToUnorderedFoldableOps.toUnorderedFoldableOps"),
+      exclude[InheritedNewAbstractMethodProblem]("cats.UnorderedFoldable#ToUnorderedFoldableOps.toUnorderedFoldableOps"),
+      exclude[IncompatibleResultTypeProblem]("cats.instances.SetInstances.catsStdInstancesForSet"),
+      exclude[ReversedMissingMethodProblem]("cats.instances.SetInstances.cats$instances$SetInstances$_setter_$catsStdInstancesForSet_="),
+      exclude[ReversedMissingMethodProblem]("cats.instances.SetInstances.catsStdInstancesForSet"),
+      exclude[DirectMissingMethodProblem]("cats.instances.MapInstances.catsStdInstancesForMap"),
+      exclude[ReversedMissingMethodProblem]("cats.instances.MapInstances.catsStdInstancesForMap"),
+      exclude[IncompatibleResultTypeProblem]("cats.instances.package#all.catsStdInstancesForMap"),
+      exclude[IncompatibleResultTypeProblem]("cats.instances.package#all.catsStdInstancesForSet"),
+      exclude[IncompatibleResultTypeProblem]("cats.instances.package#map.catsStdInstancesForMap"),
+      exclude[IncompatibleResultTypeProblem]("cats.instances.package#set.catsStdInstancesForSet"),
+      exclude[IncompatibleResultTypeProblem]("cats.instances.MapInstances.catsStdInstancesForMap"),
+      exclude[DirectMissingMethodProblem]("cats.data.EitherTInstances2.catsDataMonadErrorForEitherT"),
       exclude[MissingTypesProblem]("cats.data.OneAndLowPriority3"),
       exclude[MissingTypesProblem]("cats.data.OneAndLowPriority2"),
       exclude[MissingTypesProblem]("cats.data.OneAndLowPriority1"),

core/src/main/scala/cats/Foldable.scala

@@ -2,7 +2,7 @@ package cats
 
 import scala.collection.mutable
 import cats.instances.either._
-import cats.instances.long._
+import cats.kernel.CommutativeMonoid
 import simulacrum.typeclass
 import Foldable.sentinel
 
@@ -16,6 +16,7 @@ import Foldable.sentinel
  * `Foldable[_]` instance.
  *
  * Instances of Foldable should be ordered collections to allow for consistent folding.
+ * Use the `UnorderedFoldable` type class if you want to fold over unordered collections.
  *
  * Foldable[F] is implemented in terms of two basic methods:
  *
@@ -27,7 +28,7 @@ import Foldable.sentinel
  *
  * See: [[http://www.cs.nott.ac.uk/~pszgmh/fold.pdf A tutorial on the universality and expressiveness of fold]]
  */
-@typeclass trait Foldable[F[_]] { self =>
+@typeclass trait Foldable[F[_]] extends UnorderedFoldable[F] { self =>
 
   /**
    * Left associative fold on 'F' using the function 'f'.
@@ -55,6 +56,7 @@ import Foldable.sentinel
    */
   def foldLeft[A, B](fa: F[A], b: B)(f: (B, A) => B): B
 
+
   /**
    * Right associative lazy fold on `F` using the folding function 'f'.
    *
@@ -192,16 +194,6 @@ import Foldable.sentinel
   def maximumOption[A](fa: F[A])(implicit A: Order[A]): Option[A] =
     reduceLeftOption(fa)(A.max)
 
-  /**
-   * The size of this Foldable.
-   *
-   * This is overriden in structures that have more efficient size implementations
-   * (e.g. Vector, Set, Map).
-   *
-   * Note: will not terminate for infinite-sized collections.
-   */
-  def size[A](fa: F[A]): Long = foldMap(fa)(_ => 1)
-
   /**
     * Get the element at the index of the `Foldable`.
     */
@@ -390,7 +382,7 @@ import Foldable.sentinel
    *
    * If there are no elements, the result is `false`.
    */
-  def exists[A](fa: F[A])(p: A => Boolean): Boolean =
+  override def exists[A](fa: F[A])(p: A => Boolean): Boolean =
     foldRight(fa, Eval.False) { (a, lb) =>
       if (p(a)) Eval.True else lb
     }.value
@@ -400,7 +392,7 @@ import Foldable.sentinel
    *
    * If there are no elements, the result is `true`.
    */
-  def forall[A](fa: F[A])(p: A => Boolean): Boolean =
+  override def forall[A](fa: F[A])(p: A => Boolean): Boolean =
     foldRight(fa, Eval.True) { (a, lb) =>
       if (p(a)) lb else Eval.False
     }.value
@@ -539,10 +531,10 @@ import Foldable.sentinel
   /**
    * Returns true if there are no elements. Otherwise false.
    */
-  def isEmpty[A](fa: F[A]): Boolean =
+  override def isEmpty[A](fa: F[A]): Boolean =
     foldRight(fa, Eval.True)((_, _) => Eval.False).value
 
-  def nonEmpty[A](fa: F[A]): Boolean =
+  override def nonEmpty[A](fa: F[A]): Boolean =
     !isEmpty(fa)
 
   /**
@@ -581,6 +573,11 @@ import Foldable.sentinel
       val F = self
       val G = Foldable[G]
     }
+
+  override def unorderedFold[A: CommutativeMonoid](fa: F[A]): A = fold(fa)
+
+  override def unorderedFoldMap[A, B: CommutativeMonoid](fa: F[A])(f: (A) => B): B =
+    foldMap(fa)(f)
 }
 
 object Foldable {

core/src/main/scala/cats/Traverse.scala

@@ -16,7 +16,7 @@ import simulacrum.typeclass
  *
  * See: [[https://www.cs.ox.ac.uk/jeremy.gibbons/publications/iterator.pdf The Essence of the Iterator Pattern]]
  */
-@typeclass trait Traverse[F[_]] extends Functor[F] with Foldable[F] { self =>
+@typeclass trait Traverse[F[_]] extends Functor[F] with Foldable[F] with UnorderedTraverse[F] { self =>
 
   /**
    * Given a function which returns a G effect, thread this effect
@@ -124,4 +124,10 @@ import simulacrum.typeclass
    */
   def zipWithIndex[A](fa: F[A]): F[(A, Int)] =
     mapWithIndex(fa)((a, i) => (a, i))
+
+  override def unorderedTraverse[G[_] : CommutativeApplicative, A, B](sa: F[A])(f: (A) => G[B]): G[F[B]] =
+    traverse(sa)(f)
+
+  override def unorderedSequence[G[_] : CommutativeApplicative, A](fga: F[G[A]]): G[F[A]] =
+    sequence(fga)
 }

core/src/main/scala/cats/UnorderedFoldable.scala

@@ -0,0 +1,71 @@
+package cats
+
+import cats.kernel.CommutativeMonoid
+import simulacrum.typeclass
+import cats.instances.long._
+/**
+  * `UnorderedFoldable` is like a `Foldable` for unordered containers.
+  */
+@typeclass trait UnorderedFoldable[F[_]] {
+
+  def unorderedFoldMap[A, B: CommutativeMonoid](fa: F[A])(f: A => B): B
+
+  def unorderedFold[A: CommutativeMonoid](fa: F[A]): A =
+    unorderedFoldMap(fa)(identity)
+
+
+  /**
+    * Returns true if there are no elements. Otherwise false.
+    */
+  def isEmpty[A](fa: F[A]): Boolean =
+    exists(fa)(Function.const(true))
+
+  def nonEmpty[A](fa: F[A]): Boolean =
+    !isEmpty(fa)
+
+  /**
+    * Check whether at least one element satisfies the predicate.
+    *
+    * If there are no elements, the result is `false`.
+    */
+  def exists[A](fa: F[A])(p: A => Boolean): Boolean =
+    unorderedFoldMap(fa)(a => Eval.later(p(a)))(UnorderedFoldable.commutativeMonoidEval(UnorderedFoldable.orMonoid))
+      .value
+
+  /**
+    * Check whether all elements satisfy the predicate.
+    *
+    * If there are no elements, the result is `true`.
+    */
+  def forall[A](fa: F[A])(p: A => Boolean): Boolean =
+    unorderedFoldMap(fa)(a => Eval.later(p(a)))(UnorderedFoldable.commutativeMonoidEval(UnorderedFoldable.andMonoid))
+      .value
+
+  /**
+    * The size of this UnorderedFoldable.
+    *
+    * This is overriden in structures that have more efficient size implementations
+    * (e.g. Vector, Set, Map).
+    *
+    * Note: will not terminate for infinite-sized collections.
+    */
+  def size[A](fa: F[A]): Long = unorderedFoldMap(fa)(_ => 1L)
+}
+
+object UnorderedFoldable {
+  private val orMonoid: CommutativeMonoid[Boolean] = new CommutativeMonoid[Boolean] {
+    val empty: Boolean = false
+
+    def combine(x: Boolean, y: Boolean): Boolean = x || y
+  }
+
+  private val andMonoid: CommutativeMonoid[Boolean] = new CommutativeMonoid[Boolean] {
+    val empty: Boolean = true
+
+    def combine(x: Boolean, y: Boolean): Boolean = x && y
+  }
+
+  private def commutativeMonoidEval[A: CommutativeMonoid]: CommutativeMonoid[Eval[A]] =
+    new EvalMonoid[A] with CommutativeMonoid[Eval[A]] { val algebra = Monoid[A] }
+
+}

core/src/main/scala/cats/UnorderedTraverse.scala

@@ -0,0 +1,13 @@
+package cats
+
+import simulacrum.typeclass
+
+/**
+  * `UnorderedTraverse` is like a `Traverse` for unordered containers.
+  */
+@typeclass trait UnorderedTraverse[F[_]] extends UnorderedFoldable[F] {
+  def unorderedTraverse[G[_]: CommutativeApplicative, A, B](sa: F[A])(f: A => G[B]): G[F[B]]
+
+  def unorderedSequence[G[_]: CommutativeApplicative, A](fga: F[G[A]]): G[F[A]] =
+    unorderedTraverse(fga)(identity)
+}

core/src/main/scala/cats/instances/map.scala

@@ -1,6 +1,8 @@
 package cats
 package instances
 
+import cats.kernel.CommutativeMonoid
+
 import scala.annotation.tailrec
 
 trait MapInstances extends cats.kernel.instances.MapInstances {
@@ -14,8 +16,16 @@ trait MapInstances extends cats.kernel.instances.MapInstances {
     }
 
   // scalastyle:off method.length
-  implicit def catsStdInstancesForMap[K]: FlatMap[Map[K, ?]] =
-    new FlatMap[Map[K, ?]] {
+  implicit def catsStdInstancesForMap[K]: UnorderedTraverse[Map[K, ?]] with FlatMap[Map[K, ?]] =
+    new UnorderedTraverse[Map[K, ?]] with FlatMap[Map[K, ?]] {
+
+      def unorderedTraverse[G[_], A, B](fa: Map[K, A])(f: A => G[B])(implicit G: CommutativeApplicative[G]): G[Map[K, B]] = {
+        val gba: Eval[G[Map[K, B]]] = Always(G.pure(Map.empty))
+        val gbb = Foldable.iterateRight(fa, gba){ (kv, lbuf) =>
+          G.map2Eval(f(kv._2), lbuf)({ (b, buf) => buf + (kv._1 -> b)})
+        }.value
+        G.map(gbb)(_.toMap)
+      }
 
       override def map[A, B](fa: Map[K, A])(f: A => B): Map[K, B] =
         fa.map { case (k, a) => (k, f(a)) }
@@ -39,6 +49,9 @@ trait MapInstances extends cats.kernel.instances.MapInstances {
       def flatMap[A, B](fa: Map[K, A])(f: (A) => Map[K, B]): Map[K, B] =
         fa.flatMap { case (k, a) => f(a).get(k).map((k, _)) }
 
+      def unorderedFoldMap[A, B: CommutativeMonoid](fa: Map[K, A])(f: (A) => B) =
+        fa.foldLeft(Monoid[B].empty){ case (b, (k, a)) => Monoid[B].combine(b, f(a)) }
+
       def tailRecM[A, B](a: A)(f: A => Map[K, Either[A, B]]): Map[K, B] = {
         val bldr = Map.newBuilder[K, B]
 
@@ -57,6 +70,13 @@ trait MapInstances extends cats.kernel.instances.MapInstances {
         f(a).foreach { case (k, a) => descend(k, a) }
         bldr.result
       }
+
+
+      override def isEmpty[A](fa: Map[K, A]): Boolean = fa.isEmpty
+
+      override def unorderedFold[A](fa: Map[K, A])(implicit A: CommutativeMonoid[A]): A =
+        A.combineAll(fa.values)
+
     }
   // scalastyle:on method.length
 }

core/src/main/scala/cats/instances/set.scala

@@ -1,17 +1,38 @@
 package cats
 package instances
 
+import cats.kernel.CommutativeMonoid
+
 import cats.syntax.show._
 
 trait SetInstances extends cats.kernel.instances.SetInstances {
 
-  implicit val catsStdInstancesForSet: MonoidK[Set] =
-    new MonoidK[Set] {
+  implicit val catsStdInstancesForSet: UnorderedTraverse[Set] with MonoidK[Set] =
+    new UnorderedTraverse[Set] with MonoidK[Set] {
+
+      def unorderedTraverse[G[_]: CommutativeApplicative, A, B](sa: Set[A])(f: A => G[B]): G[Set[B]] =
+        sa.foldLeft(Applicative[G].pure(Set.empty[B])) { (acc, a) =>
+          Apply[G].map2(acc, f(a))(_ + _)
+        }
+
+      override def unorderedSequence[G[_]: CommutativeApplicative, A](sa: Set[G[A]]): G[Set[A]] =
+        sa.foldLeft(Applicative[G].pure(Set.empty[A])) { (acc, a) =>
+          Apply[G].map2(acc, a)(_ + _)
+        }
 
       def empty[A]: Set[A] = Set.empty[A]
 
       def combineK[A](x: Set[A], y: Set[A]): Set[A] = x | y
 
+      def unorderedFoldMap[A, B](fa: Set[A])(f: A => B)(implicit B: CommutativeMonoid[B]): B =
+        fa.foldLeft(B.empty)((b, a) => B.combine(f(a), b))
+
+      override def unorderedFold[A](fa: Set[A])(implicit A: CommutativeMonoid[A]): A = A.combineAll(fa)
+
+      override def forall[A](fa: Set[A])(p: A => Boolean): Boolean =
+        fa.forall(p)
+
+      override def isEmpty[A](fa: Set[A]): Boolean = fa.isEmpty
     }
 
   implicit def catsStdShowForSet[A:Show]: Show[Set[A]] = new Show[Set[A]] {

core/src/main/scala/cats/syntax/foldable.scala

@@ -1,7 +1,7 @@
 package cats
 package syntax
 
-trait FoldableSyntax extends Foldable.ToFoldableOps {
+trait FoldableSyntax extends Foldable.ToFoldableOps with UnorderedFoldable.ToUnorderedFoldableOps {
   implicit final def catsSyntaxNestedFoldable[F[_]: Foldable, G[_], A](fga: F[G[A]]): NestedFoldableOps[F, G, A] =
     new NestedFoldableOps[F, G, A](fga)
 

docs/src/main/tut/typeclasses/foldable.md

@@ -10,7 +10,7 @@ scaladoc: "#cats.Foldable"
 Foldable type class instances can be defined for data structures that can be 
 folded to a summary value.
 
-In the case of a collection (such as `List` or `Set`), these methods will fold 
+In the case of a collection (such as `List` or `Vector`), these methods will fold
 together (combine) the values contained in the collection to produce a single 
 result. Most collection types have `foldLeft` methods, which will usually be 
 used by the associated `Foldable[_]` instance.