ApplicativeLayer

ApplicativeLayer[M, Inner] has the following functionality: - the capability to lift values from the Applicative Inner to the Applicative M, preserving the Applicative structure - lifts Applicative isomorphisms in Inner ((Inner ~> Inner, Inner ~> Inner)) into Applicative homomorphisms in M (M ~> M). This allows you to "map" a natural transformation over the Inner inside M, but only if you can provide an inverse of that natural transformation.

ApplicativeLayer[M, Inner] has two external laws:

def layerRespectsPure[A](a: A) = {
  layer(a.pure[Inner]) <-> a.pure[M]
}
def layerRespectsAp[A, B](m: Inner[A])(f: Inner[A => B]) = {
  layer(m).ap(layer(f)) <-> layer(m.ap(f))
}