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This question is based on the scala cats library, but I guess could apply to scalaz or general functional programming.

I'm trying the cats exercises and I thought of the following functionality with Applicative: Is there a function with the following signature and if so, what's it's name?

def foo[A[_]: Applicative, B, C, D](x: B, y: C)(f: (A[B], A[C]) => A[D]): A[D]

That is, if I have a function lying around that takes two Applicative instances and produces a third as result (f), I want to apply it to 2 values x and y without having to wrap it in an Applicative myself with pure. I can easily implement it myself like:

def pureMap[A[_]: Applicative, B, C, D](x: B, y: C)(f: (A[B], A[C]) => A[D]): A[D] = {
  val ap = Applicative[A]
  f(ap.pure(x), ap.pure(y))
}

but it looked like something that might exist already and I couldn't find anything. (pureMap sounded like a reasonable name).

An example would be, if I already had a function in a validation library like:

def div(ox: Option[Int], oy: Option[Int]): Option[Int] = 
  for {
    x <- ox
    y <- oy
    if y != 0
  } yield x / y

, then I would want to use it like:

val z:Option[Int] = pureMap(2,0)(div)
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