Add law testing guide

build.sbt

@@ -181,7 +181,8 @@ lazy val docs = project
   .settings(noPublishSettings)
   .settings(docSettings)
   .settings(commonJvmSettings)
-  .dependsOn(coreJVM, freeJVM)
+  .settings(libraryDependencies += "com.github.alexarchambault" %% "scalacheck-shapeless_1.13" % "1.1.5" % Compile)
+  .dependsOn(coreJVM, freeJVM, kernelLawsJVM, lawsJVM, testkitJVM)
 
 lazy val cats = project.in(file("."))
   .settings(moduleName := "root")

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

@@ -0,0 +1,133 @@
+# Law testing
+
+[Laws](https://typelevel.org/cats/typeclasses.html#laws) are an important part of cats.
+Cats uses `catalysts` and `discipline` to help test instances with laws.
+To make things easier, cats ships with `cats-testkit`, which makes use of `catalysts` and `discipline` and exposes `CatsSuite` based on ScalaTest.
+
+
+## Getting started
+
+First up, you will need to specify dependencies on `cats-laws` and `cats-testkit` in your `build.sbt` file.
+To make things easier, we'll also include the `scalacheck-shapeless` library in this tutorial, so we don't have to manually write instances for ScalaCheck's `Arbitrary`.
+
+```scala
+libraryDependencies ++= Seq(
+  "org.typelevel" %% "cats-laws" % "1.0.0-MF" % Test,
+  "org.typelevel" %% "cats-testkit" % "1.0.0-MF"% Test,
+  "com.github.alexarchambault" %% "scalacheck-shapeless_1.13" % "1.1.5" % Test
+)
+```
+
+## Example: Testing a Functor instance
+
+We'll begin by creating a data type and its Functor instance.
+```tut:book
+import cats._
+
+sealed trait Tree[+A]
+case object Leaf extends Tree[Nothing]
+case class Node[A](p: A, left: Tree[A], right: Tree[A]) extends Tree[A]
+
+object Tree {
+  implicit val functorTree: Functor[Tree] = new Functor[Tree] {
+    def map[A, B](tree: Tree[A])(f: A => B) = tree match {
+      case Leaf => Leaf
+      case Node(p, left, right) => Node(f(p), map(left)(f), map(right)(f))
+    }
+  }
+}
+```
+We will also need to create an `Eq` instance, as most laws will need to compare values of a type to properly test for correctness.
+For simplicity we'll just use `Eq.fromUniversalEquals`:
+
+```tut:book
+implicit def eqTree[A: Eq]: Eq[Tree[A]] = Eq.fromUniversalEquals
+```
+
+Then we can begin to write our law tests. Start by creating a new class in your `test` folder and inheriting from `cats.tests.CatsSuite`.
+`CatsSuite` extends the standard ScalaTest `FunSuite` as well as `Matchers`.
+Furthermore it also pulls in all of cats instances and syntax, so there's no need to import from `cats.implicits._`.
+
+```tut:book
+import cats.tests.CatsSuite
+
+class TreeLawTests extends CatsSuite {
+
+}
+```
+
+The key to testing laws is the `checkAll` function, which takes a name for your test and a Discipline ruleset.
+Cats has defined rulesets for all type class laws in `cats.laws.discipline.*`.
+
+So for our example we will want to import `cats.laws.discipline.FunctorTests` and call `checkAll` with it.
+Before we do so, however,
+we will have to bring our instances into scope as well as the derived `Arbitrary` instances from `scalacheck-shapeless`:
+
+
+```tut:book
+import Tree._
+
+import org.scalacheck.Shapeless._
+
+import cats.laws.discipline.FunctorTests
+
+class TreeLawTests extends CatsSuite {
+  checkAll("Tree.FunctorLaws", FunctorTests[Tree].functor[Int, Int, String])
+}
+```
+
+Now when we run `test` in our sbt console, ScalaCheck will test if the `Functor` laws hold for our `Tree` type.
+You should see something like this:
+
+```
+[info] TreeLawTests:
+[info] - Tree.FunctorLaws.functor.covariant composition
+[info] - Tree.FunctorLaws.functor.covariant identity
+[info] - Tree.FunctorLaws.functor.invariant composition
+[info] - Tree.FunctorLaws.functor.invariant identity
+[info] ScalaTest
+[info] Run completed in 537 milliseconds.
+[info] Total number of tests run: 4
+[info] Suites: completed 1, aborted 0
+[info] Tests: succeeded 4, failed 0, canceled 0, ignored 0, pending 0
+[info] All tests passed.
+[info] Passed: Total 4, Failed 0, Errors 0, Passed 4
+[success] Total time: 1 s, completed Aug 31, 2017 2:19:22 PM
+```
+
+And voila, you've successfully proven that your data type upholds the Functor laws!
+
+### 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`.
+
+Let's test it out, by defining a `Semigroup` instance for our `Tree` type.
+
+```tut:book
+import cats.implicits._
+
+implicit def semigroupTree[A: Semigroup]: Semigroup[Tree[A]] = new Semigroup[Tree[A]] {
+  def combine(x: Tree[A], y: Tree[A]) = (x, y) match {
+    case (Leaf, _) => Leaf
+    case (_, Leaf) => Leaf
+    case (Node(xp, xLeft, xRight), Node(yp, yLeft, yRight)) =>
+      Node(xp |+| yp, xLeft |+| yLeft, xRight |+| yRight)
+  }
+}
+```
+
+Then we can again test the instance inside our class extending `CatsSuite`:
+
+```tut:book
+import cats.laws.discipline.FunctorTests
+import cats.kernel.laws.GroupLaws
+
+class TreeLawTests extends CatsSuite {
+  checkAll("Tree[Int].MonoidLaws", GroupLaws[Tree[Int]].semigroup)
+  checkAll("Tree.FunctorLaws", FunctorTests[Tree].functor[Int, Int, String])
+}
+```