trait FunctorLayer[M[_], Inner[_]] extends Serializable
FunctorLayer[M, Inner]
has the following functionality:
- lifts values from the Functor
Inner
to the Functor
M
.
- lifts Functor
isomorphisms in Inner
((Inner ~> Inner, Inner ~> Inner)
)
into Functor
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.
FunctorLayer[M, Inner]
has two external laws:
def mapForwardRespectsLayer[A](in: Inner[A])(forward: Inner ~> Inner, backward: Inner ~> Inner) = { layer(forward(in)) <-> layerImapK(layer(in))(forward, backward) } def layerImapRespectsId[A](in: M[A]) = { in <-> layerImapK(in)(FunctionK.id, FunctionK.id) }
FunctorLayer
has one free law, i.e. a law guaranteed by parametricity:
def layerRespectsMap[A, B](in: Inner[A])(f: A => B) = { layer(in.map(f)) <-> layer(in).map(f) } // this is free because all `FunctionK`'s (including `layer`, despite not being an instance of the class) // are natural transformations (i.e., they follow this law exactly)
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