What is a Cohoist in scalaz?

Question

The scalaz defines a Cohoist:

  trait Cohoist[F[_[_], _]] extends ComonadTrans[F] {
    def cohoist[M[_], N[_]: Comonad](f: M ~> N): F[M, ?] ~> F[N, ?]
  }

where ComonadTrans is defined:

 trait ComonadTrans[F[_[_], _]] {
   def lower[G[_]: Cobind, A](a: F[G, A]): G[A]
 }

The question is how to treat this type? Can someone give an explanation in a few words or give an example?

Answer 1

ComonadTrans isn't really important to understanding cohoist, which is similar to a higher-order version of map.

map can be reformulated, by flipping the arguments around, as

[A, B](A => B) => (F[A] => F[B])

In other words it lifts a function into F. ~> is just

F ~> G
[A]F[A] => G[A]

With that you can expand the signature of cohoist

[M[_], N[_]: Comonad]([A]M[A] => N[A]) => ([A]F[M, A] => F[N, A])

(the two As cannot be combined and pulled to the initial tparam list; I don't want to go into detail here beyond saying "that would not work")

So just like map, it lifts a function (M to N transformer) into F, making an "F of M" to "F of N" transformer.