How to define <*> for Option[List[_]] n Scala - scala

Question

This is a followup to my previous question with an example found on the Internet.
Suppose I define a typeclass Applicative as follows:
trait Functor[T[_]]{
def map[A,B](f:A=>B, ta:T[A]):T[B]
}
trait Applicative[T[_]] extends Functor[T] {
def unit[A](a:A):T[A]
def ap[A,B](tf:T[A=>B], ta:T[A]):T[B]
}
I can define an instance of Applicative for List
object AppList extends Applicative[List] {
def map[A,B](f:A=>B, as:List[A]) = as.map(f)
def unit[A](a: A) = List(a)
def ap[A,B](fs:List[A=>B], as:List[A]) = for(f <- fs; a <- as) yield f(a)
}
For convenience I can define an implicit conversion to add a method <*> to List[A=>B]
implicit def toApplicative[A, B](fs: List[A=>B]) = new {
def <*>(as: List[A]) = AppList.ap(fs, as)
}
Now I can do a cool thing !
zip two lists List[String] and apply f2 to every pair in applicative style
val f2: (String, String) => String = {(first, last) => s"$first $last"}
val firsts = List("a", "b", "c")
val lasts = List("x", "y", "z")
scala> AppList.unit(f2.curried) <*> firsts <*> lasts
res31: List[String] = List(a x, a y, a z, b x, b y, b z, c x, c y, c z)
So far, so good but now I have:
val firstsOpt = Some(firsts)
val lastsOpt = Some(lasts)
I would like to zip firsts and lasts, apply f2, and get Option[List[String]] in applicative style. In other words I need <*> for Option[List[_]]. How can I do it ?

Answer 1

Firstly, you need an instance of applicative for Option:
implicit object AppOption extends Applicative[Option] {
def map[A, B](f: A => B, o: Option[A]) = o.map(f)
def unit[A](a: A): Option[A] = Some(a)
def ap[A, B](of: Option[A => B], oa: Option[A]) = of match {
case Some(f) => oa.map(f)
case None => None
}
}
Then you can also create an applicative instance for the composition of two applicatives (note, based on the Haskell version):
class AppComp[F[_], G[_]](fa: Applicative[F], ga: Applicative[G]) extends Applicative[({ type f[A] = F[G[A]]})#f] {
def map[A, B](f: A => B, a: F[G[A]]): F[G[B]] = fa.map((g: G[A]) => ga.map(f, g), a)
def unit[A](a: A) = fa.unit(ga.unit(a))
def ap[A, B](f: F[G[A => B]], a: F[G[A]]): F[G[B]] = {
val liftg: G[A => B] => (G[A] => G[B]) = gf => (gx => ga.ap(gf, gx))
val ffg: F[G[A] => G[B]] = fa.map(liftg, f)
fa.ap(ffg, a)
}
}
implicit def toComp[F[_], G[_]](implicit fa: Applicative[F], ga: Applicative[G]) = new AppComp[F, G](fa, ga)
Finally you can now do:
val ola = toComp[Option, List]
ola.ap(ola.ap(ola.unit(f2.curried), firstsOpt), lastsOpt)
You could probably also remove some of the noise by generalising <*> to work for any applicative.