WIP Selective applicative functors

[cb372]

This is a collaboration with @hamishdickson. Made a first stab at implementing Selective Applicative Functors as suggested in #2745.

• Add Selective type class
• Add instance for Validated
• Start writing laws
• Start writing combinators

Here is the "shapes" example from the paper using Validated:

scala> import cats._, cats.data._, cats.data.Validated._
import cats._
import cats.data._
import cats.data.Validated._

scala> type Radius = Int
defined type alias Radius

scala> type Width = Int
defined type alias Width

scala> type Height = Int
defined type alias Height

scala> :paste
// Entering paste mode (ctrl-D to finish)

sealed trait Shape
case class Circle(r: Radius) extends Shape
case class Rectangle(w: Width, h: Height) extends Shape

// Exiting paste mode, now interpreting.

defined trait Shape
defined class Circle
defined class Rectangle

scala> def shape[F[_]](x: F[Boolean], r: F[Radius], w: F[Width], h: F[Height])(implicit F: Selective[F]): F[Shape] =
  F.ifS(x)(F.map(r)(radius => Circle(radius): Shape))(F.applicative.map2(w, h){ case (width, height) => Rectangle(width, height): Shape })
shape: [F[_]](x: F[Boolean], r: F[Radius], w: F[Width], h: F[Height])(implicit F: cats.Selective[F])F[Shape]

scala> type V[A] = Validated[String, A]
defined type alias V

scala> import cats.instances.string._
import cats.instances.string._

scala> shape[V](valid(true), valid(1), invalid("width?"), invalid("height?"))
res1: V[Shape] = Valid(Circle(1))

scala> shape[V](valid(false), invalid("radius?"), valid(2), valid(3))
res2: V[Shape] = Valid(Rectangle(2,3))

scala> shape[V](valid(false), valid(1), invalid("width?"), invalid("height?"))
res3: V[Shape] = Invalid(width?height?)

scala> shape[V](invalid("choice?"), invalid("radius?"), valid(2), invalid("height?"))
res4: V[Shape] = Invalid(choice?)

This is a work in progress (see the TODO comments) but happy to receive feedback at this stage.

After getting this far, we're still not sure about whether it's better for Selective to extend Applicative or to have it as a member. We went for the latter, but it's a bit clumsy to work with.

[dwijnand]

Close in favour of implementation ideas and experimentation in https://github.com/cb372/cats-selective and theoretical discussions in #2745?

[cb372]

Sounds good to me. I really need to get back to work on that repo I started...