Parallelism, Exercise 7.6 answers missing

[otto-dev]

The answers for Exercise 7.6 are missing. Only parFilter is provided, but not map3 to map5, also not the reduce/fold function for summation/maximum/character count.

https://github.com/fpinscala/fpinscala/blob/master/answers/src/main/scala/fpinscala/parallelism/Par.scala

I'd like to be able to review my approach against a model approach. I'll provide my answers below if it's any help.

I've implemented map3 like this:

  def map3[A, B, C, D](a: Par[A], b: Par[B], c: Par[C])(f: (A, B, C) => D): Par[D] = {
    val pab = map2(a, b)((a, b) => f(a, b, _))
    map2(pab, c)((f, n) => f(n))
  }

With map5 I became a bit fancier and implemented a flapMap first. Then I implemented it like this:

  def map5[A, B, C, D, E, F](a: Par[A], b: Par[B], c: Par[C], d: Par[D], e: Par[E])(f: (A, B, C, D, E) => F): Par[F] = {
    val pa = map(a)(f.curried)
    val pb = flatMap(pa)(lift(_)(b))
    val pc = flatMap(pb)(lift(_)(c))
    val pd = flatMap(pc)(lift(_)(d))
    flatMap(pd)(lift(_)(e))
  }

For the other exercises I implemented a reduce and parReduce function first, like this:

  def reduce[A](as: List[A])(f: (A, A) => A): Par[A] = {
    val pars: List[Par[A]] = as.map(v => lazyUnit(v))
    parReduce(pars)(f)
  }

  def parReduce[A](as: List[Par[A]])(f: (A, A) => A): Par[A] = {
    if (as.isEmpty) throw new IllegalArgumentException("Trying to reduce list of zero elements")
    else if (as.size == 1) as.head
    else {
      val (left, right) = as.splitAt(as.size / 2)
      map2(parReduce(left)(f), parReduce(right)(f))(f)
    }
  }

And then solved the exercises like so:

  def max(ns: List[Int]): Par[Int] = reduce(ns)(math.max)

  def characters(ss: List[String]): Par[Int] = {
    val ls = ss.map(asyncF(_.length))
    parReduce(ls)(_ + _)
  }