diff --git a/alleycats-core/src/main/scala/alleycats/ReferentialEq.scala b/alleycats-core/src/main/scala/alleycats/ReferentialEq.scala
index 7f1013cbab..e922612207 100644
--- a/alleycats-core/src/main/scala/alleycats/ReferentialEq.scala
+++ b/alleycats-core/src/main/scala/alleycats/ReferentialEq.scala
@@ -6,8 +6,12 @@ import cats.Eq
  * An `Eq[A]` that delegates to referential equality (`eq`).
  * Note that it is not referentially transparent!
  */
+trait ReferentialEq[A <: AnyRef] extends Eq[A] {
+  def eqv(x: A, y: A): Boolean = x eq y
+}
+
 object ReferentialEq {
-  def apply[A <: AnyRef]: Eq[A] = new Eq[A] {
-    def eqv(x: A, y: A) = x eq y
-  }
+  private[this] val referentialEq: Eq[AnyRef] = new ReferentialEq[AnyRef] {}
+
+  def apply[A <: AnyRef]: Eq[A] = referentialEq.asInstanceOf[Eq[A]]
 }
diff --git a/alleycats-core/src/main/scala/alleycats/SystemIdentityHash.scala b/alleycats-core/src/main/scala/alleycats/SystemIdentityHash.scala
new file mode 100644
index 0000000000..170e07f8c8
--- /dev/null
+++ b/alleycats-core/src/main/scala/alleycats/SystemIdentityHash.scala
@@ -0,0 +1,17 @@
+package alleycats
+
+import cats.Hash
+
+/**
+ * A `Hash[A]` that delegates to identity hashcode (`System.identityHashCode`).
+ * It implements `Eq[A]` via referential equality (`eq`) that it is not referentially transparent!
+ */
+trait SystemIdentityHash[A <: AnyRef] extends ReferentialEq[A] with Hash[A] {
+  override def hash(a: A): Int = java.lang.System.identityHashCode(a)
+}
+
+object SystemIdentityHash {
+  private[this] val identityHash: Hash[AnyRef] = new SystemIdentityHash[AnyRef] {}
+
+  def apply[A <: AnyRef]: Hash[A] = identityHash.asInstanceOf[Hash[A]]
+}
diff --git a/alleycats-laws/src/main/scala/alleycats/laws/discipline/ReferentialEqTests.scala b/alleycats-laws/src/main/scala/alleycats/laws/discipline/ReferentialEqTests.scala
new file mode 100644
index 0000000000..5bc5c169fc
--- /dev/null
+++ b/alleycats-laws/src/main/scala/alleycats/laws/discipline/ReferentialEqTests.scala
@@ -0,0 +1,29 @@
+package alleycats.laws.discipline
+
+import cats.kernel.Eq
+import cats.kernel.laws.EqLaws
+import cats.kernel.laws.discipline._
+import org.scalacheck.Arbitrary
+import org.scalacheck.Prop.forAll
+import org.typelevel.discipline.Laws
+
+trait ReferentialEqTests[A] extends Laws {
+  def laws: EqLaws[A]
+
+  def eqv(implicit arbA: Arbitrary[A]): RuleSet = {
+    implicit val eqA: Eq[A] = laws.E
+    new DefaultRuleSet(
+      "referentialEq",
+      None,
+      "reflexivity eq" -> forAll(laws.reflexivityEq _),
+      "symmetry eq" -> forAll(laws.symmetryEq _),
+      "transitivity eq" -> forAll(laws.transitivityEq _)
+    )
+  }
+}
+
+object ReferentialEqTests {
+  def apply[A: Eq]: ReferentialEqTests[A] = new ReferentialEqTests[A] {
+    override def laws: EqLaws[A] = EqLaws[A]
+  }
+}
diff --git a/alleycats-laws/src/main/scala/alleycats/laws/discipline/SystemIdentityHashTests.scala b/alleycats-laws/src/main/scala/alleycats/laws/discipline/SystemIdentityHashTests.scala
new file mode 100644
index 0000000000..1e88a76010
--- /dev/null
+++ b/alleycats-laws/src/main/scala/alleycats/laws/discipline/SystemIdentityHashTests.scala
@@ -0,0 +1,28 @@
+package alleycats.laws.discipline
+
+import cats.kernel.{Eq, Hash}
+import cats.kernel.laws.HashLaws
+import cats.kernel.laws.discipline._
+import org.scalacheck.Arbitrary
+import org.scalacheck.Prop.forAll
+
+import scala.util.hashing.Hashing
+
+trait SystemIdentityHashTests[A] extends ReferentialEqTests[A] {
+  def laws: HashLaws[A]
+
+  def hash(implicit arbA: Arbitrary[A], eqA: Eq[A], hashA: Hashing[A]): RuleSet =
+    new DefaultRuleSet(
+      "systemIdentityHash",
+      Some(eqv),
+      "hash compatibility" -> forAll(laws.hashCompatibility _),
+      "same as universal hash" -> forAll(laws.sameAsUniversalHash _),
+      "same as scala hashing" -> forAll((x: A, y: A) => laws.sameAsScalaHashing(x, y, hashA))
+    )
+}
+
+object SystemIdentityHashTests {
+  def apply[A: Hash]: SystemIdentityHashTests[A] = new SystemIdentityHashTests[A] {
+    override def laws: HashLaws[A] = HashLaws[A]
+  }
+}
diff --git a/alleycats-tests/shared/src/test/scala/alleycats/tests/AlleycatsSuite.scala b/alleycats-tests/shared/src/test/scala/alleycats/tests/AlleycatsSuite.scala
index 621f55de25..72df380181 100644
--- a/alleycats-tests/shared/src/test/scala/alleycats/tests/AlleycatsSuite.scala
+++ b/alleycats-tests/shared/src/test/scala/alleycats/tests/AlleycatsSuite.scala
@@ -4,8 +4,6 @@ import alleycats.std.MapInstances
 import cats._
 import cats.instances.all._
 import org.scalacheck.{Arbitrary, Gen}
-import org.scalacheck.Arbitrary.arbitrary
-import scala.util.{Failure, Success, Try}
 import org.scalacheck.Test.Parameters
 
 /**
@@ -20,7 +18,14 @@ trait AlleycatsSuite extends munit.DisciplineSuite with TestSettings with TestIn
 }
 
 sealed trait TestInstances {
-  // To be replaced by https://github.com/rickynils/scalacheck/pull/170
-  implicit def arbitraryTry[A: Arbitrary]: Arbitrary[Try[A]] =
-    Arbitrary(Gen.oneOf(arbitrary[A].map(Success(_)), arbitrary[Throwable].map(Failure(_))))
+  implicit val arbObject: Arbitrary[Object] =
+    // with some probability we select from a small set of objects
+    // otherwise make a totally new one
+    // courtesy of @johnynek
+    Arbitrary(
+      Gen.oneOf(
+        Gen.oneOf(List.fill(5)(new Object)),
+        Arbitrary.arbUnit.arbitrary.map(_ => new Object)
+      )
+    )
 }
diff --git a/alleycats-tests/shared/src/test/scala/alleycats/tests/ReferentialEqSuite.scala b/alleycats-tests/shared/src/test/scala/alleycats/tests/ReferentialEqSuite.scala
index 0e2810f2d5..c4490301a9 100644
--- a/alleycats-tests/shared/src/test/scala/alleycats/tests/ReferentialEqSuite.scala
+++ b/alleycats-tests/shared/src/test/scala/alleycats/tests/ReferentialEqSuite.scala
@@ -1,44 +1,11 @@
 package alleycats.tests
 
 import alleycats.ReferentialEq
+import alleycats.laws.discipline.ReferentialEqTests
 import cats.kernel.Eq
-import cats.kernel.laws.discipline._
-import cats.kernel.laws.EqLaws
-import org.scalacheck.Arbitrary
-import org.scalacheck.Gen
-import org.scalacheck.Prop.forAll
-import org.typelevel.discipline.Laws
 
 class ReferentialEqSuite extends AlleycatsSuite {
-
-  class ReferentialEqTests[A](eq: Eq[A]) extends Laws {
-    def laws = EqLaws(eq)
-
-    def eqv(implicit arbA: Arbitrary[A]): RuleSet = {
-      implicit val eqA: Eq[A] = laws.E
-      new DefaultRuleSet(
-        "referentialEq",
-        None,
-        "reflexivity eq" -> forAll(laws.reflexivityEq _),
-        "symmetry eq" -> forAll(laws.symmetryEq _),
-        "transitivity eq" -> forAll(laws.transitivityEq _)
-      )
-    }
-  }
-
-  implicit val arbObject: Arbitrary[Object] =
-    // with some probability we select from a small set of objects
-    // otherwise make a totally new one
-    // courtesy of @johnynek
-    Arbitrary(
-      Gen.oneOf(
-        Gen.oneOf(List.fill(5)(new Object)),
-        Arbitrary.arbUnit.arbitrary.map(_ => new Object)
-      )
-    )
-
   implicit val eqObject: Eq[Object] = ReferentialEq[Object]
 
-  checkAll("ReferentialEq[Object]", new ReferentialEqTests(ReferentialEq[Object]).eqv)
-
+  checkAll("ReferentialEq[Object]", ReferentialEqTests[Object].eqv)
 }
diff --git a/alleycats-tests/shared/src/test/scala/alleycats/tests/SystemIdentityHashSuite.scala b/alleycats-tests/shared/src/test/scala/alleycats/tests/SystemIdentityHashSuite.scala
new file mode 100644
index 0000000000..580b7bef38
--- /dev/null
+++ b/alleycats-tests/shared/src/test/scala/alleycats/tests/SystemIdentityHashSuite.scala
@@ -0,0 +1,11 @@
+package alleycats.tests
+
+import alleycats.SystemIdentityHash
+import alleycats.laws.discipline.SystemIdentityHashTests
+import cats.kernel.Hash
+
+class SystemIdentityHashSuite extends AlleycatsSuite {
+  implicit val hashObject: Hash[Object] = SystemIdentityHash[Object]
+
+  checkAll("SystemIdentityHash[Object]", SystemIdentityHashTests[Object].hash)
+}