list,scala,scalaz,applicative , ZipList with Scalaz


ZipList with Scalaz

Question:

Tag: list,scala,scalaz,applicative

Suppose I have a list of numbers and list of functions to apply to numbers:

val xs: List[Int] = List(1, 2, 3)
val fs: List[Int => Int] = List(f1, f2, f3)

Now I would like to use an Applicative to apply f1 to 1, f2 to 2, etc.

val ys: List[Int] = xs <*> fs // expect List(f1(1), f2(2), f3(3))

How can I do it with Scalaz ?


Answer:

pure for zip lists repeats the value forever, so it's not possible to define a zippy applicative instance for Scala's List (or for anything like lists). Scalaz does provide a Zip tag for Stream and the appropriate zippy applicative instance, but as far as I know it's still pretty broken. For example, this won't work (but should):

import scalaz._, Scalaz._

val xs = Tags.Zip(Stream(1, 2, 3))
val fs = Tags.Zip(Stream[Int => Int](_ + 3, _ + 2, _ + 1))

xs <*> fs

You can use the applicative instance directly (as in the other answer), but it's nice to have the syntax, and it's not too hard to write a "real" (i.e. not tagged) wrapper. Here's the workaround I've used, for example:

case class ZipList[A](s: Stream[A])

import scalaz._, Scalaz._, Isomorphism._

implicit val zipListApplicative: Applicative[ZipList] =
  new IsomorphismApplicative[ZipList, ({ type L[x] = Stream[x] @@ Tags.Zip })#L] {
    val iso =
      new IsoFunctorTemplate[ZipList, ({ type L[x] = Stream[x] @@ Tags.Zip })#L] {
        def to[A](fa: ZipList[A]) = Tags.Zip(fa.s)
        def from[A](ga: Stream[A] @@ Tags.Zip) = ZipList(Tag.unwrap(ga))
      }
    val G = streamZipApplicative
  }

And then:

scala> val xs = ZipList(Stream(1, 2, 3))
xs: ZipList[Int] = ZipList(Stream(1, ?))

scala> val fs = ZipList(Stream[Int => Int](_ + 10, _ + 11, _ + 12))
fs: ZipList[Int => Int] = ZipList(Stream(<function1>, ?))

scala> xs <*> fs
res0: ZipList[Int] = ZipList(Stream(11, ?))

scala> res0.s.toList
res1: List[Int] = List(11, 13, 15)

For what it's worth, it looks like this has been broken for at least a couple of years.


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