Override Foldable methods

- Override Foldable methods in a lot of instances (including
  NonEmptyReducible)
- Override MonoidK algebra to get kernel Monoid instance
- Add Reducible for Tuple2

I might have gone overboard with the "one element foldables" (Option,
Either, ...).

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

@@ -314,7 +314,6 @@ import simulacrum.typeclass
   def foldK[G[_], A](fga: F[G[A]])(implicit G: MonoidK[G]): G[A] =
     fold(fga)(G.algebra)
 
-
   /**
    * Find the first element matching the predicate, if one exists.
    */

core/src/main/scala/cats/Reducible.scala

@@ -114,7 +114,7 @@ import simulacrum.typeclass
    * Traverse `F[A]` using `Apply[G]`.
    *
    * `A` values will be mapped into `G[B]` and combined using
-   * `Applicative#map2`.
+   * `Apply#map2`.
    *
    * This method is similar to [[Foldable.traverse_]]. There are two
    * main differences:
@@ -176,6 +176,16 @@ import simulacrum.typeclass
       case NonEmptyList(hd, tl) =>
         Reducible[NonEmptyList].reduce(NonEmptyList(hd, a :: intersperseList(tl, a)))
     }
+
+  override def isEmpty[A](fa: F[A]): Boolean = false
+
+  override def nonEmpty[A](fa: F[A]): Boolean = true
+
+  override def minimumOption[A](fa: F[A])(implicit A: Order[A]): Option[A] =
+    Some(minimum(fa))
+
+  override def maximumOption[A](fa: F[A])(implicit A: Order[A]): Option[A] =
+    Some(maximum(fa))
 }
 
 /**
@@ -210,4 +220,55 @@ abstract class NonEmptyReducible[F[_], G[_]](implicit G: Foldable[G]) extends Re
         case None => Later(f(a))
       }
     }
+
+  override def size[A](fa: F[A]): Long = {
+    val (_, tail) = split(fa)
+    1 + G.size(tail)
+  }
+
+  override def fold[A](fa: F[A])(implicit A: Monoid[A]): A = {
+    val (a, ga) = split(fa)
+    A.combine(a, G.fold(ga))
+  }
+
+  override def find[A](fa: F[A])(f: A => Boolean): Option[A] = {
+    val (a, ga) = split(fa)
+    if (f(a)) Some(a) else G.find(ga)(f)
+  }
+
+  override def exists[A](fa: F[A])(p: A => Boolean): Boolean = {
+    val (a, ga) = split(fa)
+    p(a) || G.exists(ga)(p)
+  }
+
+  override def forall[A](fa: F[A])(p: A => Boolean): Boolean = {
+    val (a, ga) = split(fa)
+    p(a) && G.forall(ga)(p)
+  }
+
+  override def toList[A](fa: F[A]): List[A] = {
+    val (a, ga) = split(fa)
+    a :: G.toList(ga)
+  }
+
+  override def toNonEmptyList[A](fa: F[A]): NonEmptyList[A] = {
+    val (a, ga) = split(fa)
+    NonEmptyList(a, G.toList(ga))
+  }
+
+  override def filter_[A](fa: F[A])(p: A => Boolean): List[A] = {
+    val (a, ga) = split(fa)
+    val filteredTail = G.filter_(ga)(p)
+    if (p(a)) a :: filteredTail else filteredTail
+  }
+
+  override def takeWhile_[A](fa: F[A])(p: A => Boolean): List[A] = {
+    val (a, ga) = split(fa)
+    if (p(a)) a :: G.takeWhile_(ga)(p) else Nil
+  }
+
+  override def dropWhile_[A](fa: F[A])(p: A => Boolean): List[A] = {
+    val (a, ga) = split(fa)
+    if (p(a)) G.dropWhile_(ga)(p) else a :: G.toList(ga)
+  }
 }

core/src/main/scala/cats/data/NonEmptyList.scala

@@ -286,6 +286,15 @@ private[data] sealed trait NonEmptyListInstances extends NonEmptyListInstances0
         NonEmptyList.fromListUnsafe(buf.result())
       }
 
+      override def fold[A](fa: NonEmptyList[A])(implicit A: Monoid[A]): A =
+        fa.reduce
+
+      override def foldM[G[_], A, B](fa: NonEmptyList[A], z: B)(f: (B, A) => G[B])(implicit G: Monad[G]): G[B] =
+        Foldable.iteratorFoldM(fa.toList.toIterator, z)(f)
+
+      override def find[A](fa: NonEmptyList[A])(f: A => Boolean): Option[A] =
+        fa find f
+
       override def forall[A](fa: NonEmptyList[A])(p: A => Boolean): Boolean =
         fa forall p
 

core/src/main/scala/cats/data/NonEmptyVector.scala

@@ -229,7 +229,6 @@ private[data] sealed trait NonEmptyVectorInstances {
       def traverse[G[_], A, B](fa: NonEmptyVector[A])(f: (A) => G[B])(implicit G: Applicative[G]): G[NonEmptyVector[B]] =
         G.map2Eval(f(fa.head), Always(Traverse[Vector].traverse(fa.tail)(f)))(NonEmptyVector(_, _)).value
 
-
       override def foldLeft[A, B](fa: NonEmptyVector[A], b: B)(f: (B, A) => B): B =
         fa.foldLeft(b)(f)
 
@@ -251,6 +250,21 @@ private[data] sealed trait NonEmptyVectorInstances {
         NonEmptyVector.fromVectorUnsafe(buf.result())
       }
 
+      override def fold[A](fa: NonEmptyVector[A])(implicit A: Monoid[A]): A =
+        fa.reduce
+
+      override def foldM[G[_], A, B](fa: NonEmptyVector[A], z: B)(f: (B, A) => G[B])(implicit G: Monad[G]): G[B] =
+        Foldable.iteratorFoldM(fa.toVector.toIterator, z)(f)
+
+      override def find[A](fa: NonEmptyVector[A])(f: A => Boolean): Option[A] =
+        fa.find(f)
+
+      override def forall[A](fa: NonEmptyVector[A])(p: A => Boolean): Boolean =
+        fa.forall(p)
+
+      override def exists[A](fa: NonEmptyVector[A])(p: A => Boolean): Boolean =
+        fa.exists(p)
+
       override def toList[A](fa: NonEmptyVector[A]): List[A] = fa.toVector.toList
 
       override def toNonEmptyList[A](fa: NonEmptyVector[A]): NonEmptyList[A] =

core/src/main/scala/cats/data/Validated.scala

@@ -294,6 +294,7 @@ private[data] sealed abstract class ValidatedInstances extends ValidatedInstance
         fab.leftMap(f)
     }
 
+  // scalastyle:off method.length
   implicit def catsDataInstancesForValidated[E](implicit E: Semigroup[E]): Traverse[Validated[E, ?]] with ApplicativeError[Validated[E, ?], E] =
     new Traverse[Validated[E, ?]] with ApplicativeError[Validated[E, ?], E] {
       def traverse[F[_]: Applicative, A, B](fa: Validated[E, A])(f: A => F[B]): F[Validated[E, B]] =
@@ -323,7 +324,40 @@ private[data] sealed abstract class ValidatedInstances extends ValidatedInstance
           case v @ Validated.Valid(_) => v
         }
       def raiseError[A](e: E): Validated[E, A] = Validated.Invalid(e)
+
+      override def reduceLeftToOption[A, B](fa: Validated[E, A])(f: A => B)(g: (B, A) => B): Option[B] =
+        fa.map(f).toOption
+
+      override def reduceRightToOption[A, B](fa: Validated[E, A])(f: A => B)(g: (A, Eval[B]) => Eval[B]): Eval[Option[B]] =
+        Now(fa.map(f).toOption)
+
+      override def reduceLeftOption[A](fa: Validated[E, A])(f: (A, A) => A): Option[A] =
+        fa.toOption
+
+      override def reduceRightOption[A](fa: Validated[E, A])(f: (A, Eval[A]) => Eval[A]): Eval[Option[A]] =
+        Now(fa.toOption)
+
+      override def size[A](fa: Validated[E, A]): Long =
+        fa.fold(_ => 0L, _ => 1L)
+
+      override def foldMap[A, B](fa: Validated[E, A])(f: A => B)(implicit B: Monoid[B]): B =
+        fa.fold(_ => B.empty, f)
+
+      override def find[A](fa: Validated[E, A])(f: A => Boolean): Option[A] =
+        fa.toOption.filter(f)
+
+      override def exists[A](fa: Validated[E, A])(p: A => Boolean): Boolean =
+        fa.exists(p)
+
+      override def forall[A](fa: Validated[E, A])(p: A => Boolean): Boolean =
+        fa.forall(p)
+
+      override def toList[A](fa: Validated[E, A]): List[A] =
+        fa.fold(_ => Nil, _ :: Nil)
+
+      override def isEmpty[A](fa: Validated[E, A]): Boolean = fa.isInvalid
     }
+    // scalastyle:on method.length
 }
 
 private[data] sealed abstract class ValidatedInstances1 extends ValidatedInstances2 {

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

@@ -83,12 +83,48 @@ trait EitherInstances extends cats.kernel.instances.EitherInstances {
 
       override def attempt[B](fab: Either[A, B]): Either[A, Either[A, B]] =
         Right(fab)
+
       override def recover[B](fab: Either[A, B])(pf: PartialFunction[A, B]): Either[A, B] =
         fab recover pf
+
       override def recoverWith[B](fab: Either[A, B])(pf: PartialFunction[A, Either[A, B]]): Either[A, B] =
         fab recoverWith pf
+
       override def ensure[B](fab: Either[A, B])(error: => A)(predicate: B => Boolean): Either[A, B] =
         fab.ensure(error)(predicate)
+
+      override def reduceLeftToOption[B, C](fab: Either[A, B])(f: B => C)(g: (C, B) => C): Option[C] =
+        fab.right.map(f).toOption
+
+      override def reduceRightToOption[B, C](fab: Either[A, B])(f: B => C)(g: (B, Eval[C]) => Eval[C]): Eval[Option[C]] =
+        Now(fab.right.map(f).toOption)
+
+      override def reduceLeftOption[B](fab: Either[A, B])(f: (B, B) => B): Option[B] =
+        fab.right.toOption
+
+      override def reduceRightOption[B](fab: Either[A, B])(f: (B, Eval[B]) => Eval[B]): Eval[Option[B]] =
+        Now(fab.right.toOption)
+
+      override def size[B](fab: Either[A, B]): Long =
+        fab.fold(_ => 0L, _ => 1L)
+
+      override def foldMap[B, C](fab: Either[A, B])(f: B => C)(implicit C: Monoid[C]): C =
+        fab.fold(_ => C.empty, f)
+
+      override def find[B](fab: Either[A, B])(f: B => Boolean): Option[B] =
+        fab.fold(_ => None, r => if (f(r)) Some(r) else None)
+
+      override def exists[B](fab: Either[A, B])(p: B => Boolean): Boolean =
+        fab.right.exists(p)
+
+      override def forall[B](fab: Either[A, B])(p: B => Boolean): Boolean =
+        fab.right.forall(p)
+
+      override def toList[B](fab: Either[A, B]): List[B] =
+        fab.fold(_ => Nil, _ :: Nil)
+
+      override def isEmpty[B](fab: Either[A, B]): Boolean =
+        fab.isLeft
     }
   // scalastyle:on method.length
 

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

@@ -86,6 +86,19 @@ trait ListInstances extends cats.kernel.instances.ListInstances {
       override def fold[A](fa: List[A])(implicit A: Monoid[A]): A = A.combineAll(fa)
 
       override def toList[A](fa: List[A]): List[A] = fa
+
+      override def reduceLeftOption[A](fa: List[A])(f: (A, A) => A): Option[A] =
+        fa.reduceLeftOption(f)
+
+      override def find[A](fa: List[A])(f: A => Boolean): Option[A] = fa.find(f)
+
+      override def filter_[A](fa: List[A])(p: A => Boolean): List[A] = fa.filter(p)
+
+      override def takeWhile_[A](fa: List[A])(p: A => Boolean): List[A] = fa.takeWhile(p)
+
+      override def dropWhile_[A](fa: List[A])(p: A => Boolean): List[A] = fa.dropWhile(p)
+
+      override def algebra[A]: Monoid[List[A]] = new kernel.instances.ListMonoid[A]
     }
 
   implicit def catsStdShowForList[A:Show]: Show[List[A]] =

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

@@ -71,12 +71,46 @@ trait OptionInstances extends cats.kernel.instances.OptionInstances {
       override def filter[A](fa: Option[A])(p: A => Boolean): Option[A] =
         fa.filter(p)
 
+      override def reduceLeftToOption[A, B](fa: Option[A])(f: A => B)(g: (B, A) => B): Option[B] =
+        fa.map(f)
+
+      override def reduceRightToOption[A, B](fa: Option[A])(f: A => B)(g: (A, Eval[B]) => Eval[B]): Eval[Option[B]] =
+        Now(fa.map(f))
+
+      override def reduceLeftOption[A](fa: Option[A])(f: (A, A) => A): Option[A] = fa
+
+      override def reduceRightOption[A](fa: Option[A])(f: (A, Eval[A]) => Eval[A]): Eval[Option[A]] =
+        Now(fa)
+
+      override def minimumOption[A](fa: Option[A])(implicit A: Order[A]): Option[A] = fa
+
+      override def maximumOption[A](fa: Option[A])(implicit A: Order[A]): Option[A] = fa
+
+      override def size[A](fa: Option[A]): Long = fa.fold(0L)(_ => 1L)
+
+      override def foldMap[A, B](fa: Option[A])(f: A => B)(implicit B: Monoid[B]): B =
+        fa.fold(B.empty)(f)
+
+      override def find[A](fa: Option[A])(f: A => Boolean): Option[A] =
+        fa.filter(f)
+
       override def exists[A](fa: Option[A])(p: A => Boolean): Boolean =
         fa.exists(p)
 
       override def forall[A](fa: Option[A])(p: A => Boolean): Boolean =
         fa.forall(p)
 
+      override def toList[A](fa: Option[A]): List[A] = fa.toList
+
+      override def filter_[A](fa: Option[A])(p: A => Boolean): List[A] =
+        fa.filter(p).toList
+
+      override def takeWhile_[A](fa: Option[A])(p: A => Boolean): List[A] =
+        fa.filter(p).toList
+
+      override def dropWhile_[A](fa: Option[A])(p: A => Boolean): List[A] =
+        fa.filterNot(p).toList
+
       override def isEmpty[A](fa: Option[A]): Boolean =
         fa.isEmpty
     }

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

@@ -34,6 +34,11 @@ trait SetInstances extends cats.kernel.instances.SetInstances {
       override def fold[A](fa: Set[A])(implicit A: Monoid[A]): A = A.combineAll(fa)
 
       override def toList[A](fa: Set[A]): List[A] = fa.toList
+
+      override def reduceLeftOption[A](fa: Set[A])(f: (A, A) => A): Option[A] =
+        fa.reduceLeftOption(f)
+
+      override def find[A](fa: Set[A])(f: A => Boolean): Option[A] = fa.find(f)
     }
 
   implicit def catsStdShowForSet[A:Show]: Show[Set[A]] = new Show[Set[A]] {

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

@@ -113,6 +113,13 @@ trait StreamInstances extends cats.kernel.instances.StreamInstances {
       override def fold[A](fa: Stream[A])(implicit A: Monoid[A]): A = A.combineAll(fa)
 
       override def toList[A](fa: Stream[A]): List[A] = fa.toList
+
+      override def reduceLeftOption[A](fa: Stream[A])(f: (A, A) => A): Option[A] =
+        fa.reduceLeftOption(f)
+
+      override def find[A](fa: Stream[A])(f: A => Boolean): Option[A] = fa.find(f)
+
+      override def algebra[A]: Monoid[Stream[A]] = new kernel.instances.StreamMonoid[A]
     }
 
   implicit def catsStdShowForStream[A: Show]: Show[Stream[A]] =

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

@@ -63,6 +63,7 @@ trait TryInstances extends TryInstances1 {
         ta.recoverWith { case t => f(t) }
 
       def raiseError[A](e: Throwable): Try[A] = Failure(e)
+
       override def handleError[A](ta: Try[A])(f: Throwable => A): Try[A] =
         ta.recover { case t => f(t) }
 
@@ -75,6 +76,53 @@ trait TryInstances extends TryInstances1 {
       override def recoverWith[A](ta: Try[A])(pf: PartialFunction[Throwable, Try[A]]): Try[A] = ta.recoverWith(pf)
 
       override def map[A, B](ta: Try[A])(f: A => B): Try[B] = ta.map(f)
+
+      override def reduceLeftToOption[A, B](fa: Try[A])(f: A => B)(g: (B, A) => B): Option[B] =
+        fa.map(f).toOption
+
+      override def reduceRightToOption[A, B](fa: Try[A])(f: A => B)(g: (A, Eval[B]) => Eval[B]): Eval[Option[B]] =
+        Now(fa.map(f).toOption)
+
+      override def reduceLeftOption[A](fa: Try[A])(f: (A, A) => A): Option[A] =
+        fa.toOption
+
+      override def reduceRightOption[A](fa: Try[A])(f: (A, Eval[A]) => Eval[A]): Eval[Option[A]] =
+        Now(fa.toOption)
+
+      override def size[A](fa: Try[A]): Long =
+        fa match {
+          case Failure(_) => 0L
+          case Success(a) => 1L
+        }
+
+      override def find[A](fa: Try[A])(f: A => Boolean): Option[A] =
+        fa.toOption.filter(f)
+
+      override def foldMap[A, B](fa: Try[A])(f: A => B)(implicit B: Monoid[B]): B =
+        fa match {
+          case Failure(_) => B.empty
+          case Success(a) => f(a)
+        }
+
+      override def exists[A](fa: Try[A])(p: A => Boolean): Boolean =
+        fa match {
+          case Failure(_) => false
+          case Success(a) => p(a)
+        }
+
+      override def forall[A](fa: Try[A])(p: A => Boolean): Boolean =
+        fa match {
+          case Failure(_) => true
+          case Success(a) => p(a)
+        }
+
+      override def toList[A](fa: Try[A]): List[A] =
+        fa match {
+          case Failure(_) => Nil
+          case Success(a) => a :: Nil
+        }
+
+      override def isEmpty[A](fa: Try[A]): Boolean = fa.isFailure
     }
   // scalastyle:on method.length