Make kernel laws consistent with core laws

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

@@ -111,10 +111,8 @@ And voila, you've successfully proven that your data type upholds the Functor la
 ### Testing cats.kernel instances
 
 For most of the type classes included in cats, the above will work great.
-However, the law tests for the type classes inside `cats.kernel` are structured a bit differently.
-These include `Semigroup`, `Monoid`, `Group` and `Semilattice`.
-Instead of importing the laws from `cats.laws.discipline.*`, we have to import `cats.kernel.laws.GroupLaws`
-and then call the corresponding method, e.g. `GroupLaws[Foo].monoid`, or `GroupLaws[Foo].semigroup`.
+However, the law tests for the type classes inside `cats.kernel` are located in `cats.kernel.laws.discipline.*` instead.
+So we have to import from there to test type classes like `Semigroup`, `Monoid`, `Group` or `Semilattice`.
 
 Let's test it out, by defining a `Semigroup` instance for our `Tree` type.
 
@@ -135,10 +133,10 @@ Then we can again test the instance inside our class extending `CatsSuite`:
 
 ```tut:book
 import cats.laws.discipline.FunctorTests
-import cats.kernel.laws.GroupLaws
+import cats.kernel.laws.discipline.SemigroupLawTests
 
 class TreeLawTests extends CatsSuite {
-  checkAll("Tree[Int].MonoidLaws", GroupLaws[Tree[Int]].semigroup)
+  checkAll("Tree[Int].SemigroupLaws", SemigroupLawTests[Tree[Int]].semigroup)
   checkAll("Tree.FunctorLaws", FunctorTests[Tree].functor[Int, Int, String])
 }
 ```

js/src/test/scala/cats/tests/FutureTests.scala

@@ -2,7 +2,7 @@ package cats
 package js
 package tests
 
-import cats.kernel.laws.GroupLaws
+import cats.kernel.laws.discipline.{MonoidLawTests, SemigroupLawTests}
 import cats.laws.discipline._
 import cats.js.instances.Await
 import cats.js.instances.future.futureComonad
@@ -58,8 +58,8 @@ class FutureTests extends CatsSuite {
 
   {
     implicit val F = ListWrapper.semigroup[Int]
-    checkAll("Future[ListWrapper[Int]]", GroupLaws[Future[ListWrapper[Int]]].semigroup)
+    checkAll("Future[ListWrapper[Int]]", SemigroupLawTests[Future[ListWrapper[Int]]].semigroup)
   }
 
-  checkAll("Future[Int]", GroupLaws[Future[Int]].monoid)
+  checkAll("Future[Int]", MonoidLawTests[Future[Int]].monoid)
 }

jvm/src/test/scala/cats/tests/FutureTests.scala

@@ -2,7 +2,7 @@ package cats
 package jvm
 package tests
 
-import cats.kernel.laws.GroupLaws
+import cats.kernel.laws.discipline.{MonoidLawTests, SemigroupLawTests}
 import cats.laws.discipline._
 import cats.laws.discipline.arbitrary._
 import cats.tests.{CatsSuite, ListWrapper}
@@ -44,8 +44,8 @@ class FutureTests extends CatsSuite {
 
   {
     implicit val F = ListWrapper.semigroup[Int]
-    checkAll("Future[ListWrapper[Int]]", GroupLaws[Future[ListWrapper[Int]]].semigroup)
+    checkAll("Future[ListWrapper[Int]]", SemigroupLawTests[Future[ListWrapper[Int]]].semigroup)
   }
 
-  checkAll("Future[Int]", GroupLaws[Future[Int]].monoid)
+  checkAll("Future[Int]", MonoidLawTests[Future[Int]].monoid)
 }

kernel-laws/src/main/scala/cats/kernel/laws/BandLaws.scala

@@ -0,0 +1,16 @@
+package cats.kernel.laws
+
+import cats.kernel.Band
+
+trait BandLaws[A] extends SemigroupLaws[A] {
+  override implicit def S: Band[A]
+
+  def idempotence(x: A): IsEq[A] =
+    S.combine(x, x) <-> x
+
+}
+
+object BandLaws {
+  def apply[A](implicit ev: Band[A]): BandLaws[A] =
+    new BandLaws[A] { def S: Band[A] = ev }
+}

kernel-laws/src/main/scala/cats/kernel/laws/BoundedSemilatticeLaws.scala

@@ -0,0 +1,13 @@
+package cats.kernel.laws
+
+import cats.kernel.BoundedSemilattice
+
+trait BoundedSemilatticeLaws[A] extends CommutativeMonoidLaws[A] with SemilatticeLaws[A] {
+  override implicit def S: BoundedSemilattice[A]
+
+}
+
+object BoundedSemilatticeLaws {
+  def apply[A](implicit ev: BoundedSemilattice[A]): BoundedSemilatticeLaws[A] =
+    new BoundedSemilatticeLaws[A] { def S: BoundedSemilattice[A] = ev }
+}

kernel-laws/src/main/scala/cats/kernel/laws/CommutativeGroupLaws.scala

@@ -0,0 +1,13 @@
+package cats
+package kernel
+package laws
+
+
+trait CommutativeGroupLaws[A] extends GroupLaws[A] with CommutativeMonoidLaws[A] {
+  override implicit def S: CommutativeGroup[A]
+}
+
+object CommutativeGroupLaws {
+  def apply[A](implicit ev: CommutativeGroup[A]): CommutativeGroupLaws[A] =
+    new CommutativeGroupLaws[A] { def S: CommutativeGroup[A] = ev }
+}

kernel-laws/src/main/scala/cats/kernel/laws/CommutativeMonoidLaws.scala

@@ -0,0 +1,13 @@
+package cats.kernel.laws
+
+import cats.kernel.CommutativeMonoid
+
+trait CommutativeMonoidLaws[A] extends MonoidLaws[A] with CommutativeSemigroupLaws[A] {
+  override implicit def S: CommutativeMonoid[A]
+
+}
+
+object CommutativeMonoidLaws {
+  def apply[A](implicit ev: CommutativeMonoid[A]): CommutativeMonoidLaws[A] =
+    new CommutativeMonoidLaws[A] { def S: CommutativeMonoid[A] = ev }
+}

kernel-laws/src/main/scala/cats/kernel/laws/CommutativeSemigroupLaws.scala

@@ -0,0 +1,16 @@
+package cats.kernel.laws
+
+import cats.kernel.CommutativeSemigroup
+
+trait CommutativeSemigroupLaws[A] extends SemigroupLaws[A] {
+  override implicit def S: CommutativeSemigroup[A]
+
+  def commutative(x: A, y: A): IsEq[A] =
+    S.combine(x, y) <-> S.combine(y, x)
+
+}
+
+object CommutativeSemigroupLaws {
+  def apply[A](implicit ev: CommutativeSemigroup[A]): CommutativeSemigroupLaws[A] =
+    new CommutativeSemigroupLaws[A] { def S: CommutativeSemigroup[A] = ev }
+}

kernel-laws/src/main/scala/cats/kernel/laws/EqLaws.scala

@@ -0,0 +1,26 @@
+package cats.kernel.laws
+
+import cats.kernel.Eq
+
+trait EqLaws[A] {
+
+  implicit def E: Eq[A]
+
+  def reflexitivityEq(x: A): IsEq[A] =
+    x <-> x
+
+  def symmetryEq(x: A, y: A): IsEq[Boolean] =
+    E.eqv(x, y) <-> E.eqv(y, x)
+
+  def antiSymmetryEq(x: A, y: A, f: A => A): IsEq[Boolean] =
+    (!E.eqv(x, y) || E.eqv(f(x), f(y))) <-> true
+
+  def transitivityEq(x: A, y: A, z: A): IsEq[Boolean] =
+    (!(E.eqv(x, y) && E.eqv(y, z)) || E.eqv(x, z)) <-> true
+
+}
+
+object EqLaws {
+  def apply[A](implicit ev: Eq[A]): EqLaws[A] =
+    new EqLaws[A] { def E: Eq[A] = ev }
+}

kernel-laws/src/main/scala/cats/kernel/laws/GroupLaws.scala

@@ -1,101 +1,23 @@
 package cats.kernel
 package laws
 
-import cats.kernel._
-import cats.kernel.instances.option._
 
-import org.typelevel.discipline.Laws
+trait GroupLaws[A] extends MonoidLaws[A] {
+  override implicit def S: Group[A]
 
-import org.scalacheck.{Arbitrary, Prop}
-import org.scalacheck.Prop._
+  def leftInverse(x: A): IsEq[A] =
+    S.empty <-> S.combine(S.inverse(x), x)
 
-object GroupLaws {
-  def apply[A : Eq : Arbitrary]: GroupLaws[A] = new GroupLaws[A] {
-    def Equ = Eq[A]
-    def Arb = implicitly[Arbitrary[A]]
-  }
-}
-
-trait GroupLaws[A] extends Laws {
-
-  implicit def Equ: Eq[A]
-  implicit def Arb: Arbitrary[A]
-
-  // groups
-
-  def semigroup(implicit A: Semigroup[A]): GroupProperties = new GroupProperties(
-    name = "semigroup",
-    parents = Nil,
-    Rules.serializable(A),
-    Rules.associativity(A.combine),
-    Rules.repeat1("combineN")(A.combineN),
-    Rules.repeat2("combineN", "|+|")(A.combineN)(A.combine),
-    "combineAllOption" -> forAll { (xs: Vector[A]) =>
-      A.combineAllOption(xs) ?== xs.reduceOption(A.combine)
-    }
-  )
-
-  def band(implicit A: Band[A]): GroupProperties = new GroupProperties(
-    name = "band",
-    parents = List(semigroup),
-    Rules.idempotence(A.combine),
-    "isIdempotent" -> Semigroup.isIdempotent[A]
-  )
-
-  def commutativeSemigroup(implicit A: CommutativeSemigroup[A]): GroupProperties = new GroupProperties(
-    name = "commutative semigroup",
-    parents = List(semigroup),
-    Rules.commutative(A.combine)
-  )
+  def rightInverse(x: A): IsEq[A] =
+    S.empty <-> S.combine(x, S.inverse(x))
 
-  def semilattice(implicit A: Semilattice[A]): GroupProperties = new GroupProperties(
-    name = "semilattice",
-    parents = List(band, commutativeSemigroup)
-  )
-
-  def monoid(implicit A: Monoid[A]): GroupProperties = new GroupProperties(
-    name = "monoid",
-    parents = List(semigroup),
-    Rules.leftIdentity(A.empty)(A.combine),
-    Rules.rightIdentity(A.empty)(A.combine),
-    Rules.repeat0("combineN", "id", A.empty)(A.combineN),
-    Rules.collect0("combineAll", "id", A.empty)(A.combineAll),
-    Rules.isId("isEmpty", A.empty)(A.isEmpty),
-    "combineAll" -> forAll { (xs: Vector[A]) =>
-      A.combineAll(xs) ?== (A.empty +: xs).reduce(A.combine)
-    }
-  )
-
-  def commutativeMonoid(implicit A: CommutativeMonoid[A]): GroupProperties = new GroupProperties(
-    name = "commutative monoid",
-    parents = List(monoid, commutativeSemigroup)
-  )
-
-  def boundedSemilattice(implicit A: BoundedSemilattice[A]): GroupProperties = new GroupProperties(
-    name = "boundedSemilattice",
-    parents = List(commutativeMonoid, semilattice)
-  )
-
-  def group(implicit A: Group[A]): GroupProperties = new GroupProperties(
-    name = "group",
-    parents = List(monoid),
-    Rules.leftInverse(A.empty)(A.combine)(A.inverse),
-    Rules.rightInverse(A.empty)(A.combine)(A.inverse),
-    Rules.consistentInverse("remove")(A.remove)(A.combine)(A.inverse)
-  )
+  def consistentInverse(x: A, y: A): IsEq[A] =
+    S.remove(x, y) <-> S.combine(x, S.inverse(y))
+}
 
-  def commutativeGroup(implicit A: CommutativeGroup[A]): GroupProperties = new GroupProperties(
-    name = "commutative group",
-    parents = List(group, commutativeMonoid)
-  )
+object GroupLaws {
+  def apply[A](implicit ev: Group[A]): GroupLaws[A] =
+    new GroupLaws[A] { def S: Group[A] = ev }
+}
 
-  // property classes
 
-  class GroupProperties(
-    val name: String,
-    val parents: Seq[GroupProperties],
-    val props: (String, Prop)*
-  ) extends RuleSet {
-    val bases = Nil
-  }
-}

kernel-laws/src/main/scala/cats/kernel/laws/HashLaws.scala

@@ -26,16 +26,14 @@ trait HashLaws[A] extends Laws {
   def hash(implicit A: Hash[A]): HashProperties = new HashProperties(
     name = "hash",
     parent = None,
-    Rules.serializable(Equ),
     "compatibility-hash" -> forAll { (x: A, y: A) =>
-      !(A.eqv(x, y)) ?|| (Hash.hash(x) == Hash.hash(y))
+      !(A.eqv(x, y)) || (Hash.hash(x) == Hash.hash(y))
     }
   )
 
   def sameAsUniversalHash(implicit A: Hash[A]): HashProperties = new HashProperties(
     name = "sameAsUniversalHash",
     parent = None,
-    Rules.serializable(Equ),
     "same-as-universal-hash" -> forAll { (x: A, y: A) =>
       (A.hash(x) == x.hashCode) && (Hash.fromUniversalHashCode[A].hash(x) == x.hashCode()) &&
         (A.eqv(x, y) == Hash.fromUniversalHashCode[A].eqv(x, y))
@@ -45,7 +43,6 @@ trait HashLaws[A] extends Laws {
   def sameAsScalaHashing(implicit catsHash: Hash[A], scalaHashing: Hashing[A]): HashProperties = new HashProperties(
     name = "sameAsScalaHashing",
     parent = None,
-    Rules.serializable(Equ),
     "same-as-scala-hashing" -> forAll { (x: A, y: A) =>
       (catsHash.hash(x) == Hash.fromHashing(scalaHashing).hash(x)) &&
         (catsHash.eqv(x, y) == Hash.fromHashing(scalaHashing).eqv(x, y))

laws/src/main/scala/cats/laws/IsEq.scala → kernel-laws/src/main/scala/cats/kernel/laws/IsEq.scala

@@ -1,5 +1,5 @@
-package cats
+package cats.kernel
 package laws
 
 /** Represents two values of the same type that are expected to be equal. */
-final case class IsEq[A](lhs: A, rhs: A)
+final case class IsEq[A](lhs: A, rhs: A)