Monad Laws using Reductio (Scala)
In the spirit of yesterday’s post that denoted the Functor Laws using Reductio, I will also give the Monad Laws. Before I do however, here is an example use of the FunctorLaws object that runs 600 unit tests when testing a Functor implementation for scala.Option[A], scala.List and finally, for the scala.Either[A, _] functor just to make it a bit quirky and probably confuse a few of you (in that case, ignore it for now!) 
val prop_OptionIdentity = identity[Option, Int] val prop_OptionComposition = composition[Option, Int, String, Long] val prop_ListIdentity = identity[List, Int] val prop_ListComposition = composition[List, Int, String, Long] val prop_EitherIdentity = identity[Apply1Of2[Either, String]#Apply, Int] val prop_EitherComposition = composition[Apply1Of2[Either, String]#Apply, Int, String, Long] // OK passed 100 tests. (appears 6 times — once per property)
…and the obligatory Monad Laws follow (import statements omitted this time, but they are the same as previous)…
object MonadLaws { def leftIdentity[M[_], A, B](implicit m: Monad[M], am: Arbitrary[M[B]], aa: Arbitrary[A], ca: Coarbitrary[A]) = prop((a: A, f: A => M[B]) => m.bind(f, m.unit(a)) === f(a)) def rightIdentity[M[_], A](implicit m: Monad[M], am: Arbitrary[M[A]]) = prop((ma: M[A]) => m.bind((a: A) => m.unit(a), ma) === ma) def associativity[M[_], A, B, C](implicit m: Monad[M], am: Arbitrary[M[A]], ca: Coarbitrary[A], cb: Coarbitrary[B], amb: Arbitrary[M[B]], amc: Arbitrary[M[C]]) = prop((ma: M[A], f: A => M[B], g: B => M[C]) => m.bind(g, m.bind(f, ma)) === m.bind((a: A) => m.bind(g, f(a)), ma)) }
Woot! Woot!