FPOO Chapter 6 in Scala

This is the second in a series of articles working though the exercises in Brian Marick’s Functional Programming for the Object-Oriented Programmer, but implemented in Scala instead of Clojure. (Hat tip to Mr. Avdi Grimm for the idea.) The full source code is available on GitHub. Read the previous article on the exercises in chapter 1.

Exercise 1: Factorial

We did a factorial function in chapter 1, but Mr. Marick introduces us to recursion in chapter 6. Therefore we’ll use recursion in this implementation, in particular, recursion that uses the following form:

def factorial(n: Int): Int = n match {
  case endingCase => endingValue(n)
  case _ => combine(n, factorial(smallerValFromN(n)))
}

As with last time, the test first using the table-driven method:

class FactorialSpec extends UnitSpec with TableDrivenPropertyChecks {
  "Chapter 6, Exercise 1: factorial" should "compute the factorial, i.e., n!, of a given integer n >= 0" in {
    val factorials = Table(
      ("n", "fact"),
      (0,   1),
      (1,   1),
      (2,   2),
      (3,   6),
      (4,  24),
      (5, 120)
    )

    forAll (factorials) { (n: Int, fact: Int) =>
      whenever (n >= 0) {
        factorial(n) should be (fact)
      }
    }
  }
}

… and now the implementation:

object Chapter06 {
  def factorial(n: Int): Int = n match {
    case 0 => 1
    case _ => n * factorial(n - 1)
  }
}

In one of Mr. Marick’s hints, he suggests not worrying about the zero case, but it’s easy enough. Another case to handle is a negative n, which I handled in the exercises for chapter 1, but decided not to bother with this time.

Exercise 2: A Second Factorial

Yet another implementation of factorial, but this time we use a slightly different recursive form:

def factorial(n: Int): Int = {
  def factorialAcc(n: Int, soFar: Int) = n match {
    case endingCase => soFar
    case _ => factorialAcc(smallerValFromN(n), combine(n, soFar))
  }
  factorialAcc(n, 1)
}

My test is almost exactly the same as the test for Exercise #1:

class Factorial2Spec extends UnitSpec with TableDrivenPropertyChecks {
  "Chapter 6, Exercise 2: factorial2" should "compute the factorial, i.e., n!, of a given integer n >= 0" in {
    val factorials = Table(
      ("n", "fact"),
      (0,   1),
      (1,   1),
      (2,   2),
      (3,   6),
      (4,  24),
      (5, 120)
    )

    forAll (factorials) { (n: Int, fact: Int) =>
      whenever (n >= 0) {
        factorial2(n) should be (fact)
      }
    }
  }
}

The implementation using the second form of recursion is as follows:

object Chapter06 {
  def factorial2(n: Int): Int = {
    @tailrec
    def fact_(something: Int, soFar: Int): Int = something match {
      case 0 => soFar
      case _ => fact_(something - 1, something * soFar)
    }
    fact_(n, 1)
  }
}

Two points about this form of recursion: First, this form uses an accumulator, a value that we use to build our way up to the final answer with each step of the recursion (in contrast to the first pattern, which piles up a stack of recursive calls until the end case, at which point we combine the return values of the entire stack). The soFar parameter of the fact_ inner function serves as the accumulator in the implementation above.

Second, this form of recursion uses tail recursion, wherein the return value on the recursive branch is the recursive call and nothing else. The call to fact_ in the recursive branch is called a tail call. The compiler can optimize tail recursion as a loop. As Mr. Marick informs us, in Clojure, one must employ the recur function to make tail call optimization happen. Similarly, Scala requires the @tailrec annotation, as highlighted above.

Exercise 3: Summing a Sequence of Numbers

This exercise is to implement a function that sums the number of a sequence together using the second pattern of recursion, i.e., using a tail call with an accumulator. The test is as follows:

class SumSequenceSpec extends UnitSpec {
  "Chapter 6, Exercise 3: sumSequence" should "sum all of the elements in a sequence starting with an initial value" in {
    sumSequence(Seq(2, 4, 6, 8), 0) should be (20)
  }
  it should "return 0 if the sequence is empty" in {
    sumSequence(Seq[Int](), 0) should be (0)
  }
}

… and the implementation:

object Chapter06 {
  @tailrec
  def sumSequence[T](seq: Seq[T], init: T)(implicit n: Numeric[T]): T = seq match {
    case Seq() => init
    case _ => sumSequence(seq.tail, n.plus(init, seq.head))
  }
}

This time, instead of using an inner function to do the recursion, sumSequence itself takes an accumulator, init. Consequently, I can annotate it with @tailrec. Also I employed the trick from the exercises in chapter 1 of using an implicit Numeric parameter to enforce the constraint that this only works for sequences of numbers.

Exercise 4: Multiplying a Sequence of Numbers

The only difference between this exercise and the last one is the operation we perform on the sequence elements. Here’s the test:

class ProdSequenceSpec extends UnitSpec {
  "Chapter 6, Exercise 4: prodSequence" should "multiply all of the elements in a sequence starting with an initial value" in {
    prodSequence(Seq(2, 4, 6, 8), 1) should be (384)
  }
  it should "return 1 if the sequence is empty" in {
    prodSequence(Seq[Int](), 1) should be (1)
  }
}

… and here’s the implementation:

object Chapter06 {
  @tailrec
  def prodSequence[T](seq: Seq[T], init: T)(implicit n: Numeric[T]): T = seq match {
    case Seq() => init
    case _ => prodSequence(seq.tail, n.times(init, seq.head))
  }
}

Exercise 4a: Extracting the Combiner

Mr. Marick notes that the only difference between exercises 3 and 4 is the operation performed on the elements in the sequence, or the combiner, to borrow the parlance in Mr. Marick’s pseudocode. The test reflects the difference in the way we call the function now by passing in the combiner as a parameter with the sequence:

class ReduceSequenceSpec extends UnitSpec {
  val op = (a: Int, b: Int) => a * b
  "Chapter 6, Exercise 4a: reduceSequence" should "apply an operation all of the elements in a sequence starting with an initial value" in {
    reduceSequence(op, Seq(2, 4, 6, 8), 1) should be (384)
  }
  it should "return init if the sequence is empty" in {
    reduceSequence(op, Seq[Int](), 1) should be (1)
  }
}

And here is how I have implemented it:

object Chapter06 {
  @tailrec
  def reduceSequence[A](op: (A, A) => A, seq: Seq[A], init: A): A = seq match {
    case Seq() => init
    case _ => reduceSequence(op, seq.tail, op(seq.head, init))
  }
}

That works, but there is a problem. Exercise 5 exposes it.

Exercise 5: Building a Map from a Sequence

Mr. Marick stresses that we should perform this next exercise without changing the implementation of reduceSequence. So let’s try with our test:

class ReduceSequenceVecToMapSpec extends UnitSpec {
  val op = (a: String, b: Map[String, Int]) => b + (a -> 0)
  "Chapter 6, Exercise 5: reduceSequence" should "convert a sequence of strings into a map keyed to those strings with values of zero" in {
    reduceSequence(op, Vector("a", "b", "c"), Map[String, Int]()) should be (Map("a" -> 0, "b" -> 0, "c" -> 0))
  }
  it should "return init if the sequence is empty" in {
    reduceSequence(op, Seq[String](), Map[String, Int]()) should be (Map[String, Int]())
  }
  val op2 = (a: String, b: Map[String, Int]) => b + (a -> (b.size + 1))
  "Chapter 6, Exercise 5a: reduceSequence" should "convert a sequence of strings into a map keyed to those strings with values that increment by 1" in {
    reduceSequence(op2, Vector("a", "b", "c"), Map[String, Int]()) should be (Map("a" -> 1, "b" -> 2, "c" -> 3))
  }
}

And now the error bites us. Clojure is dynamically typed, so the implementation we would have come up with in Clojure probably would still work for this exercise if it worked for the last one.

Scala, in contrast, is statically typed. Our implementation worked in the last exercise because the type of the elements in the input sequence is the same as the type of the return value: we’re taking a sequence of integers and multiplying/adding them together, which produces an integer. In this exercise, however, we need to take a sequence of strings and produce a map—ain’t nothin’ the same about them types there! Therefore the implementation has to change to allow for a return type different from the type of the input elements:

object Chapter06 {
  @tailrec
  def reduceSequence[A, B](op: (A, B) => B, seq: Seq[A], init: B): B = seq match {
    case Seq() => init
    case _ => reduceSequence(op, seq.tail, op(seq.head, init))
  }
}

That wraps up chapter 6. Exercises from later chapters to come in future posts.

FPOO Chapter 1 in Scala

This is the first in a series of articles working though the exercises in Brian Marick’s Functional Programming for the Object-Oriented Programmer, but implemented in Scala instead of Clojure. (Hat tip to Mr. Avdi Grimm for the idea.) The full source code is available on GitHub.

For each exercise, I first wrote a specification in ScalaTest and then wrote the implementation. I followed the recommendation of the ScalaTest user guide and created the UnitSpec base class that all of my specs extend:

class UnitSpec extends FlatSpec
  with Matchers
  with OptionValues
  with Inside

Exercise 1: second

First the test:

class SecondSpec extends UnitSpec {
  "Exercise 1: second" should "return the second item in a given list" in {
    val list = List("Lorem", "ipsum", "dolor", "sit", "amet")
    second(list) should be ("ipsum")
  }
  it should "throw IndexOutOfBoundsException if called on a list with fewer than 2 elements" in {
    val listOf1 = List("sole")
    a [IndexOutOfBoundsException] should be thrownBy {
      second(listOf1)
    }
  }
}

… and then the implementation—pretty simple:

object Chapter01 {
  def second[A](list: List[A]): A = list(1)
}

Exercise 2: third

Mr. Marick asked for two implementations. First the tests, then the implementations:

class ThirdSpec extends UnitSpec {
  "Exercise 2a: third" should "return the third item in a given list" in {
    val list = List("Lorem", "ipsum", "dolor", "sit", "amet")
    third(list) should be ("dolor")
  }
  it should "throw IndexOutOfBoundsException if called on a list with fewer than 3 elements" in {
    val listOf2 = List("penultimate", "ultimate")
    a [IndexOutOfBoundsException] should be thrownBy {
      third(listOf2)
    }
  }

  "Exercise 2b: third2" should "return the third item in a given list" in {
    val list = List("Lorem", "ipsum", "dolor", "sit", "amet")
    third2(list) should be ("dolor")
  }
  it should "throw NoSuchElementException if called on a list with fewer than 3 elements" in {
    val listOf2 = List("penultimate", "ultimate")
    a [NoSuchElementException] should be thrownBy {
      third2(listOf2)
    }
  }
}

Again, both are pretty simple:

object Chapter01 {
  def third[A](list: List[A]): A = list(2)
  def third2[A](list: List[A]): A = list.tail.tail.head
}

Exercise 3: addSquares

The test for this one is pretty straightforward:

class AddSquaresSpec extends UnitSpec {
  "Exercise 3: addSquares" should "square each item in a list and sum them" in {
    val list = List(1, 2, 5)
    addSquares(list) should be (30)
  }
  it should "return 0 if called on an empty list" in {
    val emptyList = List[Int]()
    addSquares(emptyList) should be (0)
  }
}

I found the implementation somewhat challenging because I was not sure how to limit my input parameter to be a list of numbers. A second argument list that takes a single implicit parameter did the trick:

object Chapter01 {
  def addSquares[T](list: List[T])(implicit n: Numeric[T]): T =
    list.map( x => n.times(x, x) ).sum
}

Exercise 4: bizarreFactorial

In order to have a list of several inputs and the expected result for each, I used ScalaTest’s TableDrivenPropertyChecks trait.

class BizarreFactorialSpec extends UnitSpec with TableDrivenPropertyChecks {
  "Exercise 4: bizarreFactorial" should "compute the factorial, i.e., n!, of a given integer n >= 0" in {
    val factorials = Table(
      ("n", "factorial"),
      (0,   1),
      (1,   1),
      (2,   2),
      (3,   6),
      (4,  24),
      (5, 120)
    )

    forAll (factorials) { (n: Int, factorial: Int) =>
      whenever (n >= 0) {
        bizarreFactorial(n) should be (factorial)
      }
    }
  }
}

Mr. Marick’s constraints were to use apply, but not to use either iteration or recursion. Scala has apply, but its purpose is to allow you to use an object as if it were a function. Clojure’s apply is effectively used more like the way Scala uses reduce on collections. Consequently, I could have implemented bizarreFactorial this way:

object Chapter01 {
  def bizarreFactorial(n: Int): Int = n match {
    case x if x < 0 => throw new IllegalArgumentException("Factorial only works for positive integers")
    case 0 => 1
    case _ => 1 to n reduce (_ * _)
  }
}

But Scala has a shorthand for that: product (like sum in Exercise 3 above), which yields slightly more readable code.

object Chapter01 {
  def bizarreFactorial(n: Int): Int = n match {
    case x if x < 0 => throw new IllegalArgumentException("Factorial only works for positive integers")
    case 0 => 1
    case _ => 1 to n product
  }
}

Exercise 5: Other Functions

As this exercise required the demonstration of a handful of functions that Clojure already has defined, I was able to use the Scala analogues in most cases:

class OtherFunctionsSpec extends UnitSpec {
  "Exercise 5a: take" should "create a new sequence of the first n elements of an existing sequence" in {
    1 to 10 take 3 should be (List(1, 2, 3))
  }

  "Exercise 5b: distinct" should "remove duplicates from an existing sequence" in {
    val dupes = Seq(1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6)
    dupes.distinct should be (1 to 6)
  }

  "Exercise 5c: ++" should "concatenate two sequences together" in {
    val a = 1 to 3
    val b = 4 to 6
    a ++ b should be (1 to 6)
  }

  "Exercise 5d: fill" should "create a sequence containing n copies of the same value" in {
    Seq.fill(5)(2) should be (Seq(2, 2, 2, 2, 2))
  }

  "Exercise 5e: interleave" should "interleave the elements of two sequences together" in {
    val evens = 0 to 8 by 2
    val odds = 1 to 9 by 2
    evens interleave odds should be (0 to 9)
  }

  "Exercise 5f.i: drop" should "remove the first n items from the sequence" in {
    1 to 10 drop 3 should be (4 to 10)
  }
  "Exercise 5f.ii: dropRight" should "remove the last n items from the sequence" in {
    1 to 10 dropRight 3 should be (1 to 7)
  }

  "Exercise 5g: flatten" should "turn a sequence of sequences into a sequence containing all of the values of each subsequence" in {
    Seq(1 to 3, 4 to 6, 7 to 9).flatten should be (1 to 9)
  }

  "Exercise 5h: grouped" should "yield an iterator that turns the given sequence into a sequence of subsequences, each n items long" in {
    (1 to 9 grouped 3).toSeq should be (Seq(1 to 3, 4 to 6, 7 to 9))
  }

  "Exercise 5i: forall" should "test whether all items in a sequence meet a certain condition" in {
    1 to 9 forall { _ < 10 } should be (true)
  }

  "Exercise 5j: filterNot" should "remove items meeting a certain criterion from a given sequence" in {
    1 to 10 filterNot { _ % 3 == 0 } should be (Seq(1, 2, 4, 5, 7, 8, 10))
  }
}

Nevertheless, Clojure has one function interleave that Scala does not have out of the box, so I had to implement it myself as an extension method:

object Chapter01 {
  implicit class Ops[A](val seq: Seq[A]) extends AnyVal {
    def interleave(that: Seq[A]): Seq[A] = {
      (seq, that).zipped flatMap { Seq(_, _) }
    }
  }
}

Exercise 6: prefixOf

class PrefixOfSpec extends UnitSpec {
  "Exercise 6: prefixOf" should "test whether a sequence consists of the first few elements of another sequence" in {
    (1 to 3) prefixOf (1 to 10) should be (true)
  }
}

Scala already has startsWith, but it seemed like cheating to use it to implement prefixOf:

object Chapter01 {
  implicit class Ops[A](val seq: Seq[A]) extends AnyVal {
    def prefixOf(that: Seq[A]): Boolean = {
      that startsWith seq
    }
  }
}

So I used take:

object Chapter01 {
  implicit class Ops[A](val seq: Seq[A]) extends AnyVal {
    def prefixOf(that: Seq[A]): Boolean = {
      (that take seq.length) == seq
    }
  }
}

Exercise 7: tails

I came up with three implementations.

class TailsSpec extends UnitSpec {
  val seq = 1 to 4
  val expected = Seq(1 to 4, 2 to 4, 3 to 4, 4 to 4, 4 until 4)
  "Exercise 7a: tails1" should "return a sequence of successively smaller subsequences of the argument" in {
    seq.tails1 should be (expected)
  }
}

Scala already has an implementation of tails although it returns an iterator instead of a fully constructed sequence. Implementing the version of Mr. Marick’s tails function was no harder than calling toSeq:

object Chapter01 {
  implicit class Ops[A](val seq: Seq[A]) extends AnyVal {
    def tails1: Seq[Seq[A]] = seq.tails.toSeq
  }
}

But again, that seems like cheating, so my second implementation was my own.

class TailsSpec extends UnitSpec {
  val seq = 1 to 4
  val expected = Seq(1 to 4, 2 to 4, 3 to 4, 4 to 4, 4 until 4)
  "Exercise 7b: tails2" should "return a sequence of successively smaller subsequences of the argument" in {
    seq.tails2 should be (expected)
  }
}

The solution that first occurred to me was to use pattern matching and recursion:

object Chapter01 {
  implicit class Ops[A](val seq: Seq[A]) extends AnyVal {
    def tails2: Seq[Seq[A]] = {
      def tailn(s: Seq[A]): Seq[Seq[A]] = s match {
        case Seq() => Seq(s)
        case _ => s +: tailn(s.tail)
      }
      tailn(seq)
    }
  }
}

A perfectly valid implementation, and yet I wanted one more.

class TailsSpec extends UnitSpec {
  val seq = 1 to 4
  val expected = Seq(1 to 4, 2 to 4, 3 to 4, 4 to 4, 4 until 4)
  "Exercise 7c: tails3" should "return a sequence of successively smaller subsequences of the argument" in {
    seq.tails3 should be (expected)
  }
}

I took a peek at Mr. Marick’s Clojure implementation. I wanted to do a Scala version of it:

object Chapter01 {
  implicit class Ops[A](val seq: Seq[A]) extends AnyVal {
    def tails3: Seq[Seq[A]] = {
      val seqs = Seq.fill(seq.length + 1)(seq)
      val nToDrop = 0 to seq.length
      (seqs, nToDrop).zipped map (_ drop _)
    }
  }
}

Well, that’s all for Chapter 1. Look for my take on Chapter 2 to come soon. Chapters 2–5 cover embedding an object-oriented language in Clojure. Because Scala is a hybrid functional–object-oriented language, I didn’t really see the point of doing them in Scala. Therefore the next post will cover chapter 6.