diff --git a/test/shared/src/main/scala/zio/test/laws/GenF.scala b/test/shared/src/main/scala/zio/test/laws/GenF.scala
index b26233663add..989f935ab41d 100644
--- a/test/shared/src/main/scala/zio/test/laws/GenF.scala
+++ b/test/shared/src/main/scala/zio/test/laws/GenF.scala
@@ -26,7 +26,6 @@ import zio.test.{ Gen, Sized }
  * knows how to generate lists with elements given a generator of elements of
  * that type. You can think of `GenF` as a "recipe" for building generators
  * for parameterized types.
- * `
  */
 trait GenF[-R, F[_]] {
 
diff --git a/test/shared/src/main/scala/zio/test/laws/GenF2.scala b/test/shared/src/main/scala/zio/test/laws/GenF2.scala
new file mode 100644
index 000000000000..c98376429237
--- /dev/null
+++ b/test/shared/src/main/scala/zio/test/laws/GenF2.scala
@@ -0,0 +1,31 @@
+package zio.test.laws
+
+import zio.random.Random
+import zio.test.{ FunctionVariants, Gen }
+
+/**
+ * A `GenF` knows how to construct a generator of `F[A,B]` values given a
+ * generator of `A` and generator of `B` values. For example, a `GenF2` of `Function1` values
+ * knows how to generate functions A => B with elements given a generator of elements of
+ * that type `B`.
+ */
+trait GenF2[-R, F[_, _]] {
+
+  /**
+   * Construct a generator of `F[A,B]` values given a generator of `B` values.
+   */
+  def apply[R1 <: R, A, B](gen: Gen[R1, B]): Gen[R1, F[A, B]]
+}
+
+object GenF2 extends FunctionVariants {
+
+  /**
+   * A generator of `Function1` A => B values.
+   */
+  val function1: GenF2[Random, Function1] =
+    new GenF2[Random, Function1] {
+
+      override def apply[R1 <: Random, A, B](gen: Gen[R1, B]): Gen[R1, Function1[A, B]] =
+        function[R1, A, B](gen)
+    }
+}
diff --git a/test/shared/src/main/scala/zio/test/laws/ZLawful.scala b/test/shared/src/main/scala/zio/test/laws/ZLawful.scala
index 1af55fa63fb8..19c4794ab02a 100644
--- a/test/shared/src/main/scala/zio/test/laws/ZLawful.scala
+++ b/test/shared/src/main/scala/zio/test/laws/ZLawful.scala
@@ -34,6 +34,7 @@ package zio.test.laws
  */
 trait ZLawful[-Caps[_], -R] { self =>
   def laws: ZLaws[Caps, R]
+
   def +[Caps1[x] <: Caps[x], R1 <: R](that: ZLawful[Caps1, R1]): ZLawful[Caps1, R1] =
     new ZLawful[Caps1, R1] {
       val laws = self.laws + that.laws
diff --git a/test/shared/src/main/scala/zio/test/laws/ZLawfulF.scala b/test/shared/src/main/scala/zio/test/laws/ZLawfulF.scala
index a9268c85468b..8a868cd64d57 100644
--- a/test/shared/src/main/scala/zio/test/laws/ZLawfulF.scala
+++ b/test/shared/src/main/scala/zio/test/laws/ZLawfulF.scala
@@ -17,7 +17,7 @@
 package zio.test.laws
 
 /**
- * `ZLawful[CapsF, Caps, R]` describes a set of laws that a parameterized type
+ * `ZLawfulF[CapsF, Caps, R]` describes a set of laws that a parameterized type
  * `F[A]` with capabilities `CapsF` is expected to satisfy with respect to all
  * types `A` that have capabilities `Caps`. Lawful instances can be combined
  * using `+` to describe a set of capabilities and all of the laws that those
diff --git a/test/shared/src/main/scala/zio/test/laws/ZLawfulF2.scala b/test/shared/src/main/scala/zio/test/laws/ZLawfulF2.scala
new file mode 100644
index 000000000000..ebc00d9f7153
--- /dev/null
+++ b/test/shared/src/main/scala/zio/test/laws/ZLawfulF2.scala
@@ -0,0 +1,15 @@
+package zio.test.laws
+
+object ZLawfulF2 {
+
+  trait Divariant[-CapsBoth[_[-_, +_]], -CapsLeft[_], -CapsRight[_], -R] { self =>
+    def laws: ZLawsF2.Divariant[CapsBoth, CapsLeft, CapsRight, R]
+
+    def +[CapsBoth1[x[-_, +_]] <: CapsBoth[x], CapsLeft1[x] <: CapsLeft[x], CapsRight1[x] <: CapsRight[x], R1 <: R](
+      that: Divariant[CapsBoth1, CapsLeft1, CapsRight1, R1]
+    ): Divariant[CapsBoth1, CapsLeft1, CapsRight1, R1] =
+      new Divariant[CapsBoth1, CapsLeft1, CapsRight1, R1] {
+        val laws = self.laws + that.laws
+      }
+  }
+}
diff --git a/test/shared/src/main/scala/zio/test/laws/ZLawsF2.scala b/test/shared/src/main/scala/zio/test/laws/ZLawsF2.scala
new file mode 100644
index 000000000000..62c6d54ca61a
--- /dev/null
+++ b/test/shared/src/main/scala/zio/test/laws/ZLawsF2.scala
@@ -0,0 +1,90 @@
+package zio.test.laws
+
+import zio.{ URIO, ZIO }
+import zio.test.{ check, Gen, TestConfig, TestResult }
+
+object ZLawsF2 {
+
+  /**
+   * `ZLawsF2` for Divariant type constructors.
+   */
+  abstract class Divariant[-CapsF[_[-_, +_]], -CapsLeft[_], -CapsRight[_], -R] { self =>
+
+    /**
+     * Test that values of type `F[+_,-_]` satisfy the laws using the specified
+     * function to construct a generator of `F[A,B]` values given a generator of
+     * `B` values.
+     */
+    def run[R1 <: R with TestConfig, F[-_, +_]: CapsF, A: CapsLeft, B: CapsRight](
+      genF: GenF2[R1, F],
+      gen: Gen[R1, B]
+    ): ZIO[R1, Nothing, TestResult]
+
+    /**
+     * Combine these laws with the specified laws to produce a set of laws that
+     * require both sets of laws to be satisfied.
+     */
+    def +[CapsF1[x[-_, +_]] <: CapsF[x], CapsLeft1[x] <: CapsLeft[x], CapsRight1[x] <: CapsRight[x], R1 <: R](
+      that: Divariant[CapsF1, CapsLeft1, CapsRight1, R1]
+    ): Divariant[CapsF1, CapsLeft1, CapsRight1, R1] =
+      Divariant.Both(self, that)
+  }
+
+  object Divariant {
+
+    private final case class Both[-CapsBothF[_[-_, +_]], -CapsLeft[_], -CapsRight[_], -R](
+      left: Divariant[CapsBothF, CapsLeft, CapsRight, R],
+      right: Divariant[CapsBothF, CapsLeft, CapsRight, R]
+    ) extends Divariant[CapsBothF, CapsLeft, CapsRight, R] {
+
+      override final def run[R1 <: R with TestConfig, F[-_, +_]: CapsBothF, A: CapsLeft, B: CapsRight](
+        genF: GenF2[R1, F],
+        gen: Gen[R1, B]
+      ): ZIO[R1, Nothing, TestResult] = {
+        val lhs: ZIO[R1, Nothing, TestResult] = left.run(genF, gen)
+        val rhs: ZIO[R1, Nothing, TestResult] = right.run(genF, gen)
+        lhs.zipWith(rhs)(_ && _)
+      }
+    }
+
+    /**
+     * Constructs a law from a pure function taking one parameterized value and
+     * two functions that can be composed.
+     */
+    abstract class ComposeLaw[-CapsBothF[_[-_, +_]], -Caps[_]](label: String)
+        extends Divariant[CapsBothF, Caps, Caps, Any] {
+      self =>
+      def apply[F[-_, +_]: CapsBothF, A: Caps, B: Caps, A1: Caps, A2: Caps](
+        fa: F[A, B],
+        f: A => A1,
+        g: A1 => A2
+      ): TestResult
+
+      final def run[R <: TestConfig, F[-_, +_]: CapsBothF, A: Caps, B: Caps, A1: Caps, A2: Caps](
+        genF: GenF2[R, F],
+        genB: Gen[R, B],
+        genA1: Gen[R, A1],
+        genA2: Gen[R, A2]
+      ): URIO[R, TestResult] =
+        check(
+          genF[R, A, B](genB),
+          Gen.function[R, A, A1](genA1),
+          Gen.function[R, A1, A2](genA2)
+        )(apply(_, _, _).map(_.label(label)))
+    }
+
+    /**
+     * Constructs a law from a pure function taking a single parameter.
+     */
+    abstract class Law1[-CapsBothF[_[-_, +_]], -CapsLeft[_], -CapsRight[_]](label: String)
+        extends Divariant[CapsBothF, CapsLeft, CapsRight, Any] { self =>
+      def apply[F[-_, +_]: CapsBothF, A: CapsLeft, B: CapsRight](fa: F[A, B]): TestResult
+
+      final def run[R <: TestConfig, F[-_, +_]: CapsBothF, A: CapsLeft, B: CapsRight](
+        genF: GenF2[R, F],
+        gen: Gen[R, B]
+      ): URIO[R, TestResult] =
+        check(genF[R, A, B](gen))(apply(_).map(_.label(label)))
+    }
+  }
+}
diff --git a/test/shared/src/main/scala/zio/test/laws/package.scala b/test/shared/src/main/scala/zio/test/laws/package.scala
index 60ffb3a97ce6..2b14a869a27f 100644
--- a/test/shared/src/main/scala/zio/test/laws/package.scala
+++ b/test/shared/src/main/scala/zio/test/laws/package.scala
@@ -78,6 +78,11 @@ package object laws {
     type Invariant[-CapsF[_[_]], -Caps[_]]      = ZLawfulF.Invariant[CapsF, Caps, Any]
   }
 
+  object LawfulF2 {
+    type Divariant[-CapsBoth[_[-_, +_]], -CapsLeft[_], -CapsRight[_]] =
+      ZLawfulF2.Divariant[CapsBoth, CapsLeft, CapsRight, Any]
+  }
+
   object Laws {
     type Law1[-Caps[_]]  = ZLaws.Law1[Caps]
     type Law1M[-Caps[_]] = ZLaws.Law1M[Caps, Any]
@@ -129,6 +134,17 @@ package object laws {
     }
   }
 
+  object LawsF2 {
+    type Divariant[-CapsBoth[_[-_, +_]], -CapsLeft[_], -CapsRight[_]] =
+      ZLawsF2.Divariant[CapsBoth, CapsLeft, CapsRight, Any]
+
+    object Divariant {
+      type ComposeLaw[-CapsBothF[_[-_, +_]], -Caps[_]] = ZLawsF2.Divariant.ComposeLaw[CapsBothF, Caps]
+      type Law1[CapsBothF[_[-_, +_]], -CapsLeft[_], -CapsRight[_]] =
+        ZLawsF2.Divariant.Law1[CapsBothF, CapsLeft, CapsRight]
+    }
+  }
+
   /**
    * Checks that all values generated by a the specified generator satisfy the
    * expected behavior of the lawful instance.