Fix many cats-kernel instances.

This commit does a bunch of things:

 1. Move relevant either/function instnaces into kernel
 2. Add missing Eq/PartialOrder instances for Either
 3. Add many missing instances for Function0/Function1
 4. Add instances for BitSet
 5. Remove code duplication between collection monoids
 6. Improve test coverage of function instances
 7. Add some missing package objects in kernel
 8. A few stylistic changes

This is a relatively large commit but I think almost all of this is
stuff we'd like to get done before we freeze cats-kernel.

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

@@ -1,7 +1,7 @@
 package cats
 package instances
 
-trait BigDecimalInstances {
+trait BigDecimalInstances extends cats.kernel.instances.BigDecimalInstances {
   implicit val catsStdShowForBigDecimal: Show[BigDecimal] =
     Show.fromToString[BigDecimal]
 }

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

@@ -5,7 +5,7 @@ import cats.syntax.EitherUtil
 import cats.syntax.either._
 import scala.annotation.tailrec
 
-trait EitherInstances extends EitherInstances1 {
+trait EitherInstances extends cats.kernel.instances.EitherInstances {
   implicit val catsStdBitraverseForEither: Bitraverse[Either] =
     new Bitraverse[Either] {
       def bitraverse[G[_], A, B, C, D](fab: Either[A, B])(f: A => G[C], g: B => G[D])(implicit G: Applicative[G]): G[Either[C, D]] =
@@ -81,51 +81,19 @@ trait EitherInstances extends EitherInstances1 {
     }
   // scalastyle:on method.length
 
-  implicit def catsStdOrderForEither[A, B](implicit A: Order[A], B: Order[B]): Order[Either[A, B]] = new Order[Either[A, B]] {
-    def compare(x: Either[A, B], y: Either[A, B]): Int = x.fold(
-      a => y.fold(A.compare(a, _), _ => -1),
-      b => y.fold(_ => 1, B.compare(b, _))
-    )
-  }
-
-  implicit def catsStdShowForEither[A, B](implicit A: Show[A], B: Show[B]): Show[Either[A, B]] =
-    new Show[Either[A, B]] {
-      def show(f: Either[A, B]): String = f.fold(
-        a => s"Left(${A.show(a)})",
-        b => s"Right(${B.show(b)})"
-      )
-    }
-
-  implicit def catsDataMonoidForEither[A, B](implicit B: Monoid[B]): Monoid[Either[A, B]] =
-    new Monoid[Either[A, B]] {
-      def empty: Either[A, B] = Right(B.empty)
-      def combine(x: Either[A, B], y: Either[A, B]): Either[A, B] = x combine y
-    }
-
   implicit def catsDataSemigroupKForEither[L]: SemigroupK[Either[L, ?]] =
     new SemigroupK[Either[L, ?]] {
       def combineK[A](x: Either[L, A], y: Either[L, A]): Either[L, A] = x match {
         case Left(_) => y
         case Right(_) => x
       }
     }
-}
 
-private[instances] sealed trait EitherInstances1 extends EitherInstances2 {
-  implicit def catsStdPartialOrderForEither[A, B](implicit A: PartialOrder[A], B: PartialOrder[B]): PartialOrder[Either[A, B]] =
-    new PartialOrder[Either[A, B]] {
-      def partialCompare(x: Either[A, B], y: Either[A, B]): Double = x.fold(
-        a => y.fold(A.partialCompare(a, _), _ => -1),
-        b => y.fold(_ => 1, B.partialCompare(b, _))
+  implicit def catsStdShowForEither[A, B](implicit A: Show[A], B: Show[B]): Show[Either[A, B]] =
+    new Show[Either[A, B]] {
+      def show(f: Either[A, B]): String = f.fold(
+        a => s"Left(${A.show(a)})",
+        b => s"Right(${B.show(b)})"
       )
     }
 }
-
-private[instances] sealed trait EitherInstances2 {
-  implicit def catsStdEqForEither[A, B](implicit A: Eq[A], B: Eq[B]): Eq[Either[A, B]] = new Eq[Either[A, B]] {
-    def eqv(x: Either[A, B], y: Either[A, B]): Boolean = x.fold(
-      a => y.fold(A.eqv(a, _), _ => false),
-      b => y.fold(_ => false, B.eqv(b, _))
-    )
-  }
-}

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

@@ -5,6 +5,10 @@ import cats.arrow.{Arrow, Choice}
 import cats.functor.Contravariant
 import annotation.tailrec
 
+
+trait FunctionInstances extends cats.kernel.instances.FunctionInstances
+    with Function0Instances with Function1Instances
+
 private[instances] sealed trait Function0Instances {
 
   implicit val catsStdBimonadForFunction0: Bimonad[Function0] with RecursiveTailRecM[Function0] =
@@ -29,14 +33,9 @@ private[instances] sealed trait Function0Instances {
           loop(a)
         }
     }
-
-  implicit def catsStdEqForFunction0[A](implicit A: Eq[A]): Eq[() => A] =
-    new Eq[() => A] {
-      def eqv(x: () => A, y: () => A): Boolean = A.eqv(x(), y())
-    }
 }
 
-private[instances] sealed trait Function1Instances extends Function1Instances0 {
+private[instances] sealed trait Function1Instances {
   implicit def catsStdContravariantForFunction1[R]: Contravariant[? => R] =
     new Contravariant[? => R] {
       def contramap[T1, T0](fa: T1 => R)(f: T0 => T1): T0 => R =
@@ -91,43 +90,9 @@ private[instances] sealed trait Function1Instances extends Function1Instances0 {
       def compose[A, B, C](f: B => C, g: A => B): A => C = f.compose(g)
     }
 
-  implicit def catsStdMonoidForFunction1[A, B](implicit M: Monoid[B]): Monoid[A => B] =
-    new Function1Monoid[A, B] { def B: Monoid[B] = M }
-
-  implicit val catsStdMonoidKForFunction1: MonoidK[λ[α => α => α]] =
-    new Function1MonoidK {}
-}
-
-private[instances] sealed trait Function1Instances0 {
-  implicit def catsStdSemigroupForFunction1[A, B](implicit S: Semigroup[B]): Semigroup[A => B] =
-    new Function1Semigroup[A, B] { def B: Semigroup[B] = S }
-
-  implicit val catsStdSemigroupKForFunction1: SemigroupK[λ[α => α => α]] =
-    new Function1SemigroupK {}
-}
-
-private[instances] sealed trait Function1Semigroup[A, B] extends Semigroup[A => B] {
-  implicit def B: Semigroup[B]
-
-  override def combine(x: A => B, y: A => B): A => B = { a =>
-    B.combine(x(a), y(a))
-  }
-}
-
-private[instances] sealed trait Function1Monoid[A, B] extends Monoid[A => B] with Function1Semigroup[A, B] {
-  implicit def B: Monoid[B]
-
-  override def empty: A => B = _ => B.empty
-}
-
-private[instances] sealed trait Function1SemigroupK extends SemigroupK[λ[α => α => α]] {
-  override def combineK[A](x: A => A, y: A => A): A => A = x compose y
-}
-
-private[instances] sealed trait Function1MonoidK extends MonoidK[λ[α => α => α]] with Function1SemigroupK {
-  override def empty[A]: A => A = identity[A]
+  implicit val catsStdMonoidKForFunction1: MonoidK[λ[α => Function1[α, α]]] =
+    new MonoidK[λ[α => Function1[α, α]]] {
+      def empty[A]: A => A = identity[A]
+      def combineK[A](x: A => A, y: A => A): A => A = x compose y
+    }
 }
-
-trait FunctionInstances
-  extends Function0Instances
-  with Function1Instances

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

@@ -84,6 +84,7 @@ trait ListInstances extends cats.kernel.instances.ListInstances {
 
   implicit def catsStdShowForList[A:Show]: Show[List[A]] =
     new Show[List[A]] {
-      def show(fa: List[A]): String = fa.map(_.show).mkString("List(", ", ", ")")
+      def show(fa: List[A]): String =
+        fa.iterator.map(_.show).mkString("List(", ", ", ")")
     }
 }

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

@@ -6,11 +6,11 @@ import scala.annotation.tailrec
 trait MapInstances extends cats.kernel.instances.MapInstances {
 
   implicit def catsStdShowForMap[A, B](implicit showA: Show[A], showB: Show[B]): Show[Map[A, B]] =
-    Show.show[Map[A, B]] { m =>
-      val body = m.map { case (a, b) =>
-        s"${showA.show(a)} -> ${showB.show(b)})"
-      }.mkString(",")
-      s"Map($body)"
+    new Show[Map[A, B]] {
+      def show(m: Map[A, B]): String =
+        m.iterator
+          .map { case (a, b) => showA.show(a) + " -> " + showB.show(b) }
+          .mkString("Map(", ", ", ")")
     }
 
   // scalastyle:off method.length

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

@@ -90,6 +90,7 @@ trait VectorInstances extends cats.kernel.instances.VectorInstances {
 
   implicit def catsStdShowForVector[A:Show]: Show[Vector[A]] =
     new Show[Vector[A]] {
-      def show(fa: Vector[A]): String = fa.map(_.show).mkString("Vector(", ", ", ")")
+      def show(fa: Vector[A]): String =
+        fa.iterator.map(_.show).mkString("Vector(", ", ", ")")
     }
 }

kernel/src/main/scala/cats/kernel/instances/StaticMethods.scala

@@ -68,4 +68,15 @@ object StaticMethods {
     true
   }
   // scalastyle:on return
+
+  def combineNIterable[A, R](b: mutable.Builder[A, R], x: Iterable[A], n: Int): R = {
+    var i = n
+    while (i > 0) { b ++= x; i -= 1 }
+    b.result
+  }
+
+  def combineAllIterable[A, R](b: mutable.Builder[A, R], xs: TraversableOnce[Iterable[A]]): R = {
+    xs.foreach(b ++= _)
+    b.result
+  }
 }

kernel/src/main/scala/cats/kernel/instances/all.scala

@@ -6,11 +6,13 @@ package object all extends AllInstances
 trait AllInstances
     extends BigDecimalInstances
     with BigIntInstances
+    with BitSetInstances
     with BooleanInstances
     with ByteInstances
     with CharInstances
     with DoubleInstances
     with FloatInstances
+    with FunctionInstances
     with IntInstances
     with ListInstances
     with LongInstances

kernel/src/main/scala/cats/kernel/instances/bitSet.scala

@@ -0,0 +1,31 @@
+package cats.kernel
+package instances
+
+import scala.collection.immutable.BitSet
+
+package object bitSet extends BitSetInstances
+
+trait BitSetInstances {
+  implicit val catsKernelStdPartialOrderForBitSet: PartialOrder[BitSet] =
+    new BitSetPartialOrder
+
+  implicit val catsKernelStdSemilatticeForBitSet: BoundedSemilattice[BitSet] =
+    new BitSetSemilattice
+}
+
+class BitSetPartialOrder extends PartialOrder[BitSet] {
+  def partialCompare(x: BitSet, y: BitSet): Double =
+    if (x eq y) 0.0
+    else if (x.size < y.size) if (x.subsetOf(y)) -1.0 else Double.NaN
+    else if (y.size < x.size) if (y.subsetOf(x)) 1.0 else Double.NaN
+    else if (x == y) 0.0
+    else Double.NaN
+
+  override def eqv(x: BitSet, y: BitSet): Boolean =
+    x == y
+}
+
+class BitSetSemilattice extends BoundedSemilattice[BitSet] {
+  def empty: BitSet = BitSet.empty
+  def combine(x: BitSet, y: BitSet): BitSet = x | y
+}

kernel/src/main/scala/cats/kernel/instances/double.scala

@@ -3,6 +3,8 @@ package instances
 
 import java.lang.Math
 
+package object double extends DoubleInstances
+
 trait DoubleInstances {
   implicit val catsKernelStdOrderForDouble: Order[Double] = new DoubleOrder
   implicit val catsKernelStdGroupForDouble: CommutativeGroup[Double] = new DoubleGroup

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

@@ -0,0 +1,71 @@
+package cats.kernel
+package instances
+
+package object either extends EitherInstances
+
+trait EitherInstances extends EitherInstances0 {
+
+  implicit def catsStdOrderForEither[A, B](implicit A: Order[A], B: Order[B]): Order[Either[A, B]] =
+    new Order[Either[A, B]] {
+      def compare(x: Either[A, B], y: Either[A, B]): Int =
+        x match {
+          case Left(xx) => y match {
+            case Left(yy) => A.compare(xx, yy)
+            case Right(_) => -1
+          }
+          case Right(xx) => y match {
+            case Left(_) => 1
+            case Right(yy) => B.compare(xx, yy)
+          }
+        }
+    }
+
+  implicit def catsDataMonoidForEither[A, B](implicit B: Monoid[B]): Monoid[Either[A, B]] =
+    new Monoid[Either[A, B]] {
+      def empty: Either[A, B] =
+        Right(B.empty)
+      def combine(x: Either[A, B], y: Either[A, B]): Either[A, B] =
+        x match {
+          case left @ Left(_) => left
+          case Right(xx) => y match {
+            case left @ Left(_) => left
+            case Right(yy) => Right(B.combine(xx, yy))
+          }
+        }
+    }
+}
+
+trait EitherInstances0 extends EitherInstances1 {
+
+  implicit def catsStdPartialOrderForEither[A, B](implicit A: PartialOrder[A], B: PartialOrder[B]): PartialOrder[Either[A, B]] =
+    new PartialOrder[Either[A, B]] {
+      def partialCompare(x: Either[A, B], y: Either[A, B]): Double =
+        x match {
+          case Left(xx) => y match {
+            case Left(yy) => A.partialCompare(xx, yy)
+            case Right(_) => -1.0
+          }
+          case Right(xx) => y match {
+            case Left(_) => 1.0
+            case Right(yy) => B.partialCompare(xx, yy)
+          }
+        }
+    }
+}
+
+trait EitherInstances1 {
+  implicit def catsStdEqForEither[A, B](implicit A: Eq[A], B: Eq[B]): Eq[Either[A, B]] =
+    new Eq[Either[A, B]] {
+      def eqv(x: Either[A, B], y: Either[A, B]): Boolean =
+        x match {
+          case Left(xx) => y match {
+            case Left(yy) => A.eqv(xx, yy)
+            case Right(_) => false
+          }
+          case Right(xx) => y match {
+            case Left(_) => false
+            case Right(yy) => B.eqv(xx, yy)
+          }
+        }
+    }
+}

kernel/src/main/scala/cats/kernel/instances/float.scala

@@ -1,6 +1,8 @@
 package cats.kernel
 package instances
 
+package object float extends FloatInstances
+
 trait FloatInstances {
   implicit val catsKernelStdOrderForFloat: Order[Float] = new FloatOrder
   implicit val catsKernelStdGroupForFloat: CommutativeGroup[Float] = new FloatGroup