The Architecture of Scala Collections

Language

    Martin Odersky and Lex Spoon

    These pages describe the architecture of the Scala collections framework in detail. Compared to the Scala 2.8 Collections API you will find out more about the internal workings of the framework. You will also learn how this architecture helps you define your own collections in a few lines of code, while reusing the overwhelming part of collection functionality from the framework.

    The Scala 2.8 Collections API contains a large number of collection operations, which exist uniformly on many different collection implementations. Implementing every collection operation anew for every collection type would lead to an enormous amount of code, most of which would be copied from somewhere else. Such code duplication could lead to inconsistencies over time, when an operation is added or modified in one part of the collection library but not in others. The principal design objective of the new collections framework was to avoid any duplication, defining every operation in as few places as possible. (Ideally, everything should be defined in one place only, but there are a few exceptions where things needed to be redefined.) The design approach was to implement most operations in collection “templates” that can be flexibly inherited from individual base classes and implementations. The following pages explain these templates and other classes and traits that constitute the “building blocks” of the framework, as well as the construction principles they support.

    Builders

    An outline of the Builder trait:

    package scala.collection.mutable

trait Builder[-Elem, +To] {
  def +=(elem: Elem): this.type
  def result(): To
  def clear(): Unit
  def mapResult[NewTo](f: To => NewTo): Builder[Elem, NewTo] = ...
}

    Almost all collection operations are implemented in terms of traversals and builders. Traversals are handled by Traversable’s foreach method, and building new collections is handled by instances of class Builder. The listing above presents a slightly abbreviated outline of this trait.

    You can add an element x to a builder b with b += x. There’s also syntax to add more than one element at once, for instance b += (x, y). Adding another collection with b ++= xs works as for buffers (in fact, buffers are an enriched version of builders). The result() method returns a collection from a builder. The state of the builder is undefined after taking its result, but it can be reset into a new empty state using clear(). Builders are generic in both the element type, Elem, and in the type, To, of collections they return.

    Often, a builder can refer to some other builder for assembling the elements of a collection, but then would like to transform the result of the other builder, for example to give it a different type. This task is simplified by method mapResult in class Builder. Suppose for instance you have an array buffer buf. Array buffers are builders for themselves, so taking the result() of an array buffer will return the same buffer. If you want to use this buffer to produce a builder that builds arrays, you can use mapResult like this:

    scala> val buf = new ArrayBuffer[Int]
buf: scala.collection.mutable.ArrayBuffer[Int] = ArrayBuffer()

scala> val bldr = buf mapResult (_.toArray)
bldr: scala.collection.mutable.Builder[Int,Array[Int]]
  = ArrayBuffer()

    The result value, bldr, is a builder that uses the array buffer, buf, to collect elements. When a result is demanded from bldr, the result of buf is computed, which yields the array buffer buf itself. This array buffer is then mapped with _.toArray to an array. So the end result is that bldr is a builder for arrays.

    Factoring out common operations

    Outline of trait TraversableLike

    package scala.collection

trait TraversableLike[+Elem, +Repr] {
  def newBuilder: Builder[Elem, Repr] // deferred
  def foreach[U](f: Elem => U): Unit  // deferred
          ...
  def filter(p: Elem => Boolean): Repr = {
    val b = newBuilder
    foreach { elem => if (p(elem)) b += elem }
    b.result
  }
}

    The main design objectives of the collection library redesign were to have, at the same time, natural types and maximal sharing of implementation code. In particular, Scala’s collections follow the “same-result-type” principle: wherever possible, a transformation method on a collection will yield a collection of the same type. For instance, the filter operation should yield, on every collection type, an instance of the same collection type. Applying filter on a List should give a List; applying it on a Map should give a Map, and so on. In the rest of this section, you will find out how this is achieved.

    The Scala collection library avoids code duplication and achieves the “same-result-type” principle by using generic builders and traversals over collections in so-called implementation traits. These traits are named with a Like suffix; for instance, IndexedSeqLike is the implementation trait for IndexedSeq, and similarly, TraversableLike is the implementation trait for Traversable. Collection traits such as Traversable or IndexedSeq inherit all their concrete method implementations from these traits. Implementation traits have two type parameters instead of one for normal collections. They parameterize not only over the collection’s element type, but also over the collection’s representation type, i.e., the type of the underlying collection, such as Seq[T] or List[T]. For instance, here is the header of trait TraversableLike:

    trait TraversableLike[+Elem, +Repr] { ... }

    The type parameter, Elem, stands for the element type of the traversable whereas the type parameter Repr stands for its representation. There are no constraints on Repr. In particular Repr might be instantiated to a type that is itself not a subtype of Traversable. That way, classes outside the collections hierarchy such as String and Array can still make use of all operations defined in a collection implementation trait.

    Taking filter as an example, this operation is defined once for all collection classes in the trait TraversableLike. An outline of the relevant code is shown in the above outline of trait TraversableLike. The trait declares two abstract methods, newBuilder and foreach, which are implemented in concrete collection classes. The filter operation is implemented in the same way for all collections using these methods. It first constructs a new builder for the representation type Repr, using newBuilder. It then traverses all elements of the current collection, using foreach. If an element x satisfies the given predicate p (i.e., p(x) is true), it is added to the builder. Finally, the elements collected in the builder are returned as an instance of the Repr collection type by calling the builder’s result method.

    A bit more complicated is the map operation on collections. For instance, if f is a function from String to Int, and xs is a List[String], then xs map f should give a List[Int]. Likewise, if ys is an Array[String], then ys map f should give an Array[Int]. The question is how do we achieve that without duplicating the definition of the map method in lists and arrays. The newBuilder/foreach framework shown in trait TraversableLike is not sufficient for this because it only allows creation of new instances of the same collection type whereas map needs an instance of the same collection type constructor, but possibly with a different element type.

    What’s more, even the result type constructor of a function like map might depend in non-trivial ways on the other argument types. Here is an example:

    scala> import collection.immutable.BitSet
import collection.immutable.BitSet

scala> val bits = BitSet(1, 2, 3)
bits: scala.collection.immutable.BitSet = BitSet(1, 2, 3)

scala> bits map (_ * 2)
res13: scala.collection.immutable.BitSet = BitSet(2, 4, 6)

scala> bits map (_.toFloat)
res14: scala.collection.immutable.Set[Float]
  = Set(1.0, 2.0, 3.0)

    If you map the doubling function _ * 2 over a bit set you obtain another bit set. However, if you map the function (_.toFloat) over the same bit set, the result is a general Set[Float]. Of course, it can’t be a bit set because bit sets contain Ints, not Floats.

    Note that map’s result type depends on the type of function that’s passed to it. If the result type of that function argument is again an Int, the result of map is a BitSet, but if the result type of the function argument is something else, the result of map is just a Set. You’ll find out soon how this type-flexibility is achieved in Scala.

    The problem with BitSet is not an isolated case. Here are two more interactions with the interpreter that both map a function over a Map:

    scala> Map("a" -> 1, "b" -> 2) map { case (x, y) => (y, x) }
res3: scala.collection.immutable.Map[Int,java.lang.String]
  = Map(1 -> a, 2 -> b)

scala> Map("a" -> 1, "b" -> 2) map { case (x, y) => y }
res4: scala.collection.immutable.Iterable[Int]
  = List(1, 2)

    The first function swaps two arguments of a key/value pair. The result of mapping this function is again a map, but now going in the other direction. In fact, the first expression yields the inverse of the original map, provided it is invertible. The second function, however, maps the key/value pair to an integer, namely its value component. In that case, we cannot form a Map from the results, but we can still form an Iterable, a supertrait of Map.

    You might ask why, not restrict map so that it can always return the same kind of collection? For instance, on bit sets map could accept only Int-to-Int functions and on Maps it could only accept pair-to-pair functions. Not only are such restrictions undesirable from an object-oriented modelling point of view, they are illegal because they would violate the Liskov substitution principle: A Map is an Iterable. So every operation that’s legal on an Iterable must also be legal on a Map.

    Scala solves this problem instead with overloading: not the simple form of overloading inherited by Java (that would not be flexible enough), but the more systematic form of overloading that’s provided by implicit parameters.

    Implementation of map in TraversableLike:

    def map[B, That](f: Elem => B)
    (implicit bf: CanBuildFrom[Repr, B, That]): That = {
  val b = bf(this)
  this.foreach(x => b += f(x))
  b.result
}

    The listing above shows trait TraversableLike’s implementation of map. It’s quite similar to the implementation of filter shown in trait TraversableLike. The principal difference is that where filter used the newBuilder method, which is abstract in TraversableLike, map uses a builder factory that’s passed as an additional implicit parameter of type CanBuildFrom.

    The CanBuildFrom trait:

    package scala.collection.generic

trait CanBuildFrom[-From, -Elem, +To] {
  // Creates a new builder
  def apply(from: From): Builder[Elem, To]
}

    The listing above shows the definition of the trait CanBuildFrom, which represents builder factories. It has three type parameters: From indicates the type for which this builder factory applies, Elem indicates the element type of the collection to be built, and To indicates the type of collection to build. By defining the right implicit definitions of builder factories, you can tailor the right typing behavior as needed. Take class BitSet as an example. Its companion object would contain a builder factory of type CanBuildFrom[BitSet, Int, BitSet]. This means that when operating on a BitSet you can construct another BitSet provided the element type of the collection to build is Int. If this is not the case, the compiler will check the superclasses, and fall back to the implicit builder factory defined in mutable.Set’s companion object. The type of this more general builder factory, where A is a type parameter, is:

    CanBuildFrom[Set[_], A, Set[A]]

    This means that when operating on an arbitrary Set (expressed by the existential type Set[_]) you can build a Set again, no matter what the element type A is. Given these two implicit instances of CanBuildFrom, you can then rely on Scala’s rules for implicit resolution to pick the one that’s appropriate and maximally specific.

    So implicit resolution provides the correct static types for tricky collection operations such as map. But what about the dynamic types? Specifically, say you map some function over a List value that has Iterable as its static type:

    scala> val xs: Iterable[Int] = List(1, 2, 3)
xs: Iterable[Int] = List(1, 2, 3)

scala> val ys = xs map (x => x * x)
ys: Iterable[Int] = List(1, 4, 9)

    The static type of ys above is Iterable, as expected. But its dynamic type is (and should still be) List! This behavior is achieved by one more indirection. The apply method in CanBuildFrom is passed the source collection as argument. Most builder factories for generic traversables (in fact all except builder factories for leaf classes) forward the call to a method genericBuilder of a collection. The genericBuilder method in turn calls the builder that belongs to the collection in which it is defined. So Scala uses static implicit resolution to resolve constraints on the types of map, and virtual dispatch to pick the best dynamic type that corresponds to these constraints.

    In the current example, the static implicit resolution will pick the Iterable’s CanBuildFrom, which calls genericBuilder on the value it received as argument. But at runtime, because of virtual dispatch, it is List.genericBuilder that gets called rather than Iterable.genericBuilder, and so map builds a List.

    Integrating a new collection: RNA sequences

    What needs to be done if you want to integrate a new collection class, so that it can profit from all predefined operations with the right types? In the next few sections you’ll be walked through two examples that do this, namely sequences of RNA bases and prefix maps implemented with Patricia tries.

    To start with the first example, we define the four RNA Bases:

    abstract class Base
case object A extends Base
case object U extends Base
case object G extends Base
case object C extends Base

object Base {
  val fromInt: Int => Base = Array(A, U, G, C)
  val toInt: Base => Int = Map(A -> 0, U -> 1, G -> 2, C -> 3)
}

    Say you want to create a new sequence type for RNA strands, which are sequences of bases A (adenine), U (uracil), G (guanine), and C (cytosine). The definitions for bases are easily set up as shown in the listing of RNA bases above.

    Every base is defined as a case object that inherits from a common abstract class Base. The Base class has a companion object that defines two functions that map between bases and the integers 0 to

    1. You can see in the examples two different ways to use collections to implement these functions. The toInt function is implemented as a Map from Base values to integers. The reverse function, fromInt, is implemented as an array. This makes use of the fact that both maps and arrays are functions because they inherit from the Function1 trait.

    The next task is to define a class for strands of RNA. Conceptually, a strand of RNA is simply a Seq[Base]. However, RNA strands can get quite long, so it makes sense to invest some work in a compact representation. Because there are only four bases, a base can be identified with two bits, and you can therefore store sixteen bases as two-bit values in an integer. The idea, then, is to construct a specialized subclass of Seq[Base], which uses this packed representation.

    First version of RNA strands class

    import collection.IndexedSeqLike
import collection.mutable.{Builder, ArrayBuffer}
import collection.generic.CanBuildFrom

final class RNA1 private (val groups: Array[Int],
    val length: Int) extends IndexedSeq[Base] {

  import RNA1._

  def apply(idx: Int): Base = {
    if (idx < 0 || length <= idx)
      throw new IndexOutOfBoundsException
    Base.fromInt(groups(idx / N) >> (idx % N * S) & M)
  }
}

object RNA1 {

  // Number of bits necessary to represent group
  private val S = 2            

  // Number of groups that fit in an Int
  private val N = 32 / S       

  // Bitmask to isolate a group
  private val M = (1 << S) - 1

  def fromSeq(buf: Seq[Base]): RNA1 = {
    val groups = new Array[Int]((buf.length + N - 1) / N)
    for (i <- 0 until buf.length)
      groups(i / N) |= Base.toInt(buf(i)) << (i % N * S)
    new RNA1(groups, buf.length)
  }

  def apply(bases: Base*) = fromSeq(bases)
}

    The RNA strands class listing above presents the first version of this class. It will be refined later. The class RNA1 has a constructor that takes an array of Ints as its first argument. This array contains the packed RNA data, with sixteen bases in each element, except for the last array element, which might be partially filled. The second argument, length, specifies the total number of bases on the array (and in the sequence). Class RNA1 extends IndexedSeq[Base]. Trait IndexedSeq, which comes from package scala.collection.immutable, defines two abstract methods, length and apply. These need to be implemented in concrete subclasses. Class RNA1 implements length automatically by defining a parametric field of the same name. It implements the indexing method apply with the code given in class RNA1. Essentially, apply first extracts an integer value from the groups array, then extracts the correct two-bit number from that integer using right shift (>>) and mask (&). The private constants S, N, and M come from the RNA1 companion object. S specifies the size of each packet (i.e., two); N specifies the number of two-bit packets per integer; and M is a bit mask that isolates the lowest S bits in a word.

    Note that the constructor of class RNA1 is private. This means that clients cannot create RNA1 sequences by calling new, which makes sense, because it hides the representation of RNA1 sequences in terms of packed arrays from the user. If clients cannot see what the representation details of RNA sequences are, it becomes possible to change these representation details at any point in the future without affecting client code. In other words, this design achieves a good decoupling of the interface of RNA sequences and its implementation. However, if constructing an RNA sequence with new is impossible, there must be some other way to create new RNA sequences, else the whole class would be rather useless. In fact there are two alternatives for RNA sequence creation, both provided by the RNA1 companion object. The first way is method fromSeq, which converts a given sequence of bases (i.e., a value of type Seq[Base]) into an instance of class RNA1. The fromSeq method does this by packing all the bases contained in its argument sequence into an array, then calling RNA1’s private constructor with that array and the length of the original sequence as arguments. This makes use of the fact that a private constructor of a class is visible in the class’s companion object.

    The second way to create an RNA1 value is provided by the apply method in the RNA1 object. It takes a variable number of Base arguments and simply forwards them as a sequence to fromSeq. Here are the two creation schemes in action:

    scala> val xs = List(A, G, U, A)
xs: List[Product with Serializable with Base] = List(A, G, U, A)

scala> RNA1.fromSeq(xs)
res1: RNA1 = RNA1(A, G, U, A)

scala> val rna1 = RNA1(A, U, G, G, C)
rna1: RNA1 = RNA1(A, U, G, G, C)

    Adapting the result type of RNA methods

    Here are some more interactions with the RNA1 abstraction:

    scala> rna1.length
res2: Int = 5

scala> rna1.last
res3: Base = C

scala> rna1.take(3)
res4: IndexedSeq[Base] = Vector(A, U, G)

    The first two results are as expected, but the last result of taking the first three elements of rna1 might not be. In fact, you see a IndexedSeq[Base] as static result type and a Vector as the dynamic type of the result value. You might have expected to see an RNA1 value instead. But this is not possible because all that was done in class RNA1 was making RNA1 extend IndexedSeq. Class IndexedSeq, on the other hand, has a take method that returns an IndexedSeq, and that’s implemented in terms of IndexedSeq’s default implementation, Vector. So that’s what you were seeing on the last line of the previous interaction.

    Now that you understand why things are the way they are, the next question should be what needs to be done to change them? One way to do this would be to override the take method in class RNA1, maybe like this:

    def take(count: Int): RNA1 = RNA1.fromSeq(super.take(count))

    This would do the job for take. But what about drop, or filter, or init? In fact there are over fifty methods on sequences that return again a sequence. For consistency, all of these would have to be overridden. This looks less and less like an attractive option. Fortunately, there is a much easier way to achieve the same effect, as shown in the next section.

    Second version of RNA strands class

    final class RNA2 private (
  val groups: Array[Int],
  val length: Int
) extends IndexedSeq[Base] with IndexedSeqLike[Base, RNA2] {

  import RNA2._

  override def newBuilder: Builder[Base, RNA2] =
    new ArrayBuffer[Base] mapResult fromSeq

  def apply(idx: Int): Base = // as before
}

    The RNA class needs to inherit not only from IndexedSeq, but also from its implementation trait IndexedSeqLike. This is shown in the above listing of class RNA2. The new implementation differs from the previous one in only two aspects. First, class RNA2 now also extends IndexedSeqLike[Base, RNA2]. Second, it provides a builder for RNA strands. The IndexedSeqLike trait implements all concrete methods of IndexedSeq in an extensible way. For instance, the return type of methods like take, drop, filter, or init is the second type parameter passed to class IndexedSeqLike, i.e., in class RNA2 it is RNA2 itself.

    To be able to do this, IndexedSeqLike bases itself on the newBuilder abstraction, which creates a builder of the right kind. Subclasses of trait IndexedSeqLike have to override newBuilder to return collections of their own kind. In class RNA2, the newBuilder method returns a builder of type Builder[Base, RNA2].

    To construct this builder, it first creates an ArrayBuffer, which itself is a Builder[Base, ArrayBuffer]. It then transforms the ArrayBuffer builder by calling its mapResult method to an RNA2 builder. The mapResult method expects a transformation function from ArrayBuffer to RNA2 as its parameter. The function given is simply RNA2.fromSeq, which converts an arbitrary base sequence to an RNA2 value (recall that an array buffer is a kind of sequence, so RNA2.fromSeq can be applied to it).

    If you had left out the newBuilder definition, you would have gotten an error message like the following:

    RNA2.scala:5: error: overriding method newBuilder in trait
TraversableLike of type => scala.collection.mutable.Builder[Base,RNA2];
 method newBuilder in trait GenericTraversableTemplate of type
 => scala.collection.mutable.Builder[Base,IndexedSeq[Base]] has
 incompatible type
class RNA2 private (val groups: Array[Int], val length: Int)
      ^
one error found

    The error message is quite long and complicated, which reflects the intricate way the collection libraries are put together. It’s best to ignore the information about where the methods come from, because in this case it detracts more than it helps. What remains is that a method newBuilder with result type Builder[Base, RNA2] needed to be defined, but a method newBuilder with result type Builder[Base,IndexedSeq[Base]] was found. The latter does not override the former. The first method, whose result type is Builder[Base, RNA2], is an abstract method that got instantiated at this type in class RNA2 by passing the RNA2 type parameter to IndexedSeqLike. The second method, of result type Builder[Base,IndexedSeq[Base]], is what’s provided by the inherited IndexedSeq class. In other words, the RNA2 class is invalid without a definition of newBuilder with the first result type.

    With the refined implementation of the RNA2 class, methods like take, drop, or filter work now as expected:

    scala> val rna2 = RNA2(A, U, G, G, C)
rna2: RNA2 = RNA2(A, U, G, G, C)

scala> rna2 take 3
res5: RNA2 = RNA2(A, U, G)

scala> rna2 filter (U !=)
res6: RNA2 = RNA2(A, G, G, C)

    Dealing with map and friends

    However, there is another class of methods in collections that are not dealt with yet. These methods do not always return the collection type exactly. They might return the same kind of collection, but with a different element type. The classical example of this is the map method. If s is a Seq[Int], and f is a function from Int to String, then s.map(f) would return a Seq[String]. So the element type changes between the receiver and the result, but the kind of collection stays the same.

    There are a number of other methods that behave like map. For some of them you would expect this (e.g., flatMap, collect), but for others you might not. For instance, the append method, ++, also might return a result of different type as its arguments–appending a list of String to a list of Int would give a list of Any. How should these methods be adapted to RNA strands? The desired behavior would be to get back an RNA strand when mapping bases to bases or appending two RNA strands with ++:

    scala> val rna = RNA(A, U, G, G, C)
rna: RNA = RNA(A, U, G, G, C)

scala> rna map { case A => U case b => b }
res7: RNA = RNA(U, U, G, G, C)

scala> rna ++ rna
res8: RNA = RNA(A, U, G, G, C, A, U, G, G, C)

    On the other hand, mapping bases to some other type over an RNA strand cannot yield another RNA strand because the new elements have the wrong type. It has to yield a sequence instead. In the same vein appending elements that are not of type Base to an RNA strand can yield a general sequence, but it cannot yield another RNA strand.

    scala> rna map Base.toInt
res2: IndexedSeq[Int] = Vector(0, 1, 2, 2, 3)

scala> rna ++ List("missing", "data")
res3: IndexedSeq[java.lang.Object] =
  Vector(A, U, G, G, C, missing, data)

    This is what you’d expect in the ideal case. But this is not what the RNA2 class provides. In fact, all examples will return instances of Vector, not just the last two. If you run the first three commands above with instances of this class you obtain:

    scala> val rna2 = RNA2(A, U, G, G, C)
rna2: RNA2 = RNA2(A, U, G, G, C)

scala> rna2 map { case A => U case b => b }
res0: IndexedSeq[Base] = Vector(U, U, G, G, C)

scala> rna2 ++ rna2
res1: IndexedSeq[Base] = Vector(A, U, G, G, C, A, U, G, G, C)

    So the result of map and ++ is never an RNA strand, even if the element type of the generated collection is Base. To see how to do better, it pays to have a close look at the signature of the map method (or of ++, which has a similar signature). The map method is originally defined in class scala.collection.TraversableLike with the following signature:

    def map[B, That](f: A => B)
  (implicit cbf: CanBuildFrom[Repr, B, That]): That

    Here A is the type of elements of the collection, and Repr is the type of the collection itself, that is, the second type parameter that gets passed to implementation classes such as TraversableLike and IndexedSeqLike. The map method takes two more type parameters, B and That. The B parameter stands for the result type of the mapping function, which is also the element type of the new collection. The That appears as the result type of map, so it represents the type of the new collection that gets created.

    How is the That type determined? In fact, it is linked to the other types by an implicit parameter cbf, of type CanBuildFrom[Repr, B, That]. These CanBuildFrom implicits are defined by the individual collection classes. Recall that an implicit value of type CanBuildFrom[Repr, B, That] says: “Here is a way, given a collection of type Repr and new elements of type B, to build a collection of type That containing those elements”.

    Now the behavior of map and ++ on RNA2 sequences becomes clearer. There is no CanBuildFrom instance that creates RNA2 sequences, so the next best available CanBuildFrom was found in the companion object of the inherited trait IndexedSeq. That implicit creates Vectors (recall that Vector is the default implementation of IndexedSeq), and that’s what you saw when applying map to rna2.

    Final version of RNA strands class

    final class RNA private (val groups: Array[Int], val length: Int)
  extends IndexedSeq[Base] with IndexedSeqLike[Base, RNA] {

  import RNA._

  // Mandatory re-implementation of `newBuilder` in `IndexedSeq`
  override protected[this] def newBuilder: Builder[Base, RNA] =
    RNA.newBuilder

  // Mandatory implementation of `apply` in `IndexedSeq`
  def apply(idx: Int): Base = {
    if (idx < 0 || length <= idx)
      throw new IndexOutOfBoundsException
    Base.fromInt(groups(idx / N) >> (idx % N * S) & M)
  }

  // Optional re-implementation of foreach,
  // to make it more efficient.
  override def foreach[U](f: Base => U): Unit = {
    var i = 0
    var b = 0
    while (i < length) {
      b = if (i % N == 0) groups(i / N) else b >>> S
      f(Base.fromInt(b & M))
      i += 1
    }
  }
}

    Final version of RNA companion object

    object RNA {

  private val S = 2            // number of bits in group
  private val M = (1 << S) - 1 // bitmask to isolate a group
  private val N = 32 / S       // number of groups in an Int

  def fromSeq(buf: Seq[Base]): RNA = {
    val groups = new Array[Int]((buf.length + N - 1) / N)
    for (i <- 0 until buf.length)
      groups(i / N) |= Base.toInt(buf(i)) << (i % N * S)
    new RNA(groups, buf.length)
  }

  def apply(bases: Base*) = fromSeq(bases)

  def newBuilder: Builder[Base, RNA] =
    new ArrayBuffer mapResult fromSeq

  implicit def canBuildFrom: CanBuildFrom[RNA, Base, RNA] =
    new CanBuildFrom[RNA, Base, RNA] {
      def apply(): Builder[Base, RNA] = newBuilder
      def apply(from: RNA): Builder[Base, RNA] = newBuilder
    }
}

    To address this shortcoming, you need to define an implicit instance of CanBuildFrom in the companion object of the RNA class. That instance should have type CanBuildFrom[RNA, Base, RNA]. Hence, this instance states that, given an RNA strand and a new element type Base, you can build another collection which is again an RNA strand. The two listings above of class RNA and its companion object show the details. Compared to class RNA2 there are two important differences. First, the newBuilder implementation has moved from the RNA class to its companion object. The newBuilder method in class RNA simply forwards to this definition. Second, there is now an implicit CanBuildFrom value in object RNA. To create this value you need to define two apply methods in the CanBuildFrom trait. Both create a new builder for an RNA collection, but they differ in their argument list. The apply() method simply creates a new builder of the right type. By contrast, the apply(from) method takes the original collection as argument. This can be useful to adapt the dynamic type of builder’s return type to be the same as the dynamic type of the receiver. In the case of RNA this does not come into play because RNA is a final class, so any receiver of static type RNA also has RNA as its dynamic type. That’s why apply(from) also simply calls newBuilder, ignoring its argument.

    That is it. The final RNA class implements all collection methods at their expected types. Its implementation requires a little of protocol. In essence, you need to know where to put the newBuilder factories and the canBuildFrom implicits. On the plus side, with relatively little code you get a large number of methods automatically defined. Also, if you don’t intend to do bulk operations like take, drop, map, or ++ on your collection you can choose to not go the extra length and stop at the implementation shown in for class RNA1.

    The discussion so far centered on the minimal amount of definitions needed to define new sequences with methods that obey certain types. But in practice you might also want to add new functionality to your sequences or to override existing methods for better efficiency. An example of this is the overridden foreach method in class RNA. foreach is an important method in its own right because it implements loops over collections. Furthermore, many other collection methods are implemented in terms of foreach. So it makes sense to invest some effort optimizing the method’s implementation. The standard implementation of foreach in IndexedSeq will simply select every i‘th element of the collection using apply, where i ranges from 0 to the collection’s length minus one. So this standard implementation selects an array element and unpacks a base from it once for every element in an RNA strand. The overriding foreach in class RNA is smarter than that. For every selected array element it immediately applies the given function to all bases contained in it. So the effort for array selection and bit unpacking is much reduced.

    Integrating a new prefix map

    As a second example you’ll learn how to integrate a new kind of map into the collection framework. The idea is to implement a mutable map with String as the type of keys by a “Patricia trie”. The term Patricia is in fact an abbreviation for “Practical Algorithm to Retrieve Information Coded in Alphanumeric” and trie comes from retrieval (a trie is also called a radix tree or prefix tree). The idea is to store a set or a map as a tree where subsequent characters in a search key uniquely determine a path through the tree. For instance a Patricia trie storing the strings “abc”, “abd”, “al”, “all” and “xy” would look like this:

    A sample patricia trie: Patricia trie

    To find the node corresponding to the string “abc” in this trie, simply follow the subtree labeled “a”, proceed from there to the subtree labelled “b”, to finally reach its subtree labelled “c”. If the Patricia trie is used as a map, the value that’s associated with a key is stored in the nodes that can be reached by the key. If it is a set, you simply store a marker saying that the node is present in the set.

    Patricia tries support very efficient lookups and updates. Another nice feature is that they support selecting a subcollection by giving a prefix. For instance, in the patricia tree above you can obtain the sub-collection of all keys that start with an “a” simply by following the “a” link from the root of the tree.

    Based on these ideas we will now walk you through the implementation of a map that’s implemented as a Patricia trie. We call the map a PrefixMap, which means that it provides a method withPrefix that selects a submap of all keys starting with a given prefix. We’ll first define a prefix map with the keys shown in the running example:

    scala> val m = PrefixMap("abc" -> 0, "abd" -> 1, "al" -> 2,
  "all" -> 3, "xy" -> 4)
m: PrefixMap[Int] = Map((abc,0), (abd,1), (al,2), (all,3), (xy,4))

    Then calling withPrefix on m will yield another prefix map:

    scala> m withPrefix "a"
res14: PrefixMap[Int] = Map((bc,0), (bd,1), (l,2), (ll,3))

    Patricia trie implementation

    import collection._

class PrefixMap[T]
extends mutable.Map[String, T]
   with mutable.MapLike[String, T, PrefixMap[T]] {

  var suffixes: immutable.Map[Char, PrefixMap[T]] = Map.empty
  var value: Option[T] = None

  def get(s: String): Option[T] =
    if (s.isEmpty) value
    else suffixes get (s(0)) flatMap (_.get(s substring 1))

  def withPrefix(s: String): PrefixMap[T] =
    if (s.isEmpty) this
    else {
      val leading = s(0)
      suffixes get leading match {
        case None =>
          suffixes = suffixes + (leading -> empty)
        case _ =>
      }
      suffixes(leading) withPrefix (s substring 1)
    }

  override def update(s: String, elem: T) =
    withPrefix(s).value = Some(elem)

  override def remove(s: String): Option[T] =
    if (s.isEmpty) { val prev = value; value = None; prev }
    else suffixes get (s(0)) flatMap (_.remove(s substring 1))

  def iterator: Iterator[(String, T)] =
    (for (v <- value.iterator) yield ("", v)) ++
    (for ((chr, m) <- suffixes.iterator;
          (s, v) <- m.iterator) yield (chr +: s, v))

  def += (kv: (String, T)): this.type = { update(kv._1, kv._2); this }

  def -= (s: String): this.type  = { remove(s); this }

  override def empty = new PrefixMap[T]
}

    The previous listing shows the definition of PrefixMap. The map has keys of type String and the values are of parametric type T. It extends mutable.Map[String, T] and mutable.MapLike[String, T, PrefixMap[T]]. You have seen this pattern already for sequences in the RNA strand example; then as now inheriting an implementation class such as MapLike serves to get the right result type for transformations such as filter.

    A prefix map node has two mutable fields: suffixes and value. The value field contains an optional value that’s associated with the node. It is initialized to None. The suffixes field contains a map from characters to PrefixMap values. It is initialized to the empty map.

    You might ask why we picked an immutable map as the implementation type for suffixes? Would not a mutable map have been more standard, since PrefixMap as a whole is also mutable? The answer is that immutable maps that contain only a few elements are very efficient in both space and execution time. For instance, maps that contain fewer than 5 elements are represented as a single object. By contrast, the standard mutable map is a HashMap, which typically occupies around 80 bytes, even if it is empty. So if small collections are common, it’s better to pick immutable over mutable. In the case of Patricia tries, we’d expect that most nodes except the ones at the very top of the tree would contain only a few successors. So storing these successors in an immutable map is likely to be more efficient.

    Now have a look at the first method that needs to be implemented for a map: get. The algorithm is as follows: To get the value associated with the empty string in a prefix map, simply select the optional value stored in the root of the tree (the current map). Otherwise, if the key string is not empty, try to select the submap corresponding to the first character of the string. If that yields a map, follow up by looking up the remainder of the key string after its first character in that map. If the selection fails, the key is not stored in the map, so return with None. The combined selection over an option value opt is elegantly expressed using opt.flatMap(x => f(x)). When applied to an optional value that is None, it returns None. Otherwise opt is Some(x) and the function f is applied to the encapsulated value x, yielding a new option, which is returned by the flatMap.

    The next two methods to implement for a mutable map are += and -=. In the implementation of PrefixMap, these are defined in terms of two other methods: update and remove.

    The remove method is very similar to get, except that before returning any associated value, the field containing that value is set to None. The update method first calls withPrefix to navigate to the tree node that needs to be updated, then sets the value field of that node to the given value. The withPrefix method navigates through the tree, creating sub-maps as necessary if some prefix of characters is not yet contained as a path in the tree.

    The last abstract method to implement for a mutable map is iterator. This method needs to produce an iterator that yields all key/value pairs stored in the map. For any given prefix map this iterator is composed of the following parts: First, if the map contains a defined value, Some(x), in the value field at its root, then ("", x) is the first element returned from the iterator. Furthermore, the iterator needs to traverse the iterators of all submaps stored in the suffixes field, but it needs to add a character in front of every key string returned by those iterators. More precisely, if m is the submap reached from the root through a character chr, and (s, v) is an element returned from m.iterator, then the root’s iterator will return (chr +: s, v) instead. This logic is implemented quite concisely as a concatenation of two for expressions in the implementation of the iterator method in PrefixMap. The first for expression iterates over value.iterator. This makes use of the fact that Option values define an iterator method that returns either no element, if the option value is None, or exactly one element x, if the option value is Some(x).

    Note that there is no newBuilder method defined in PrefixMap. There is no need to, because maps and sets come with default builders, which are instances of class MapBuilder. For a mutable map the default builder starts with an empty map and then adds successive elements using the map’s += method. For immutable maps, the non-destructive element addition method + is used instead of method +=. Sets work in the same way.

    However, in all these cases, to build the right kind of collection you need to start with an empty collection of that kind. This is provided by the empty method, which is the last method defined in PrefixMap. This method simply returns a fresh PrefixMap.

    The companion object for prefix maps

    import scala.collection.mutable.{Builder, MapBuilder}
import scala.collection.generic.CanBuildFrom

object PrefixMap extends {
  def empty[T] = new PrefixMap[T]

  def apply[T](kvs: (String, T)*): PrefixMap[T] = {
    val m: PrefixMap[T] = empty
    for (kv <- kvs) m += kv
    m
  }

  def newBuilder[T]: Builder[(String, T), PrefixMap[T]] =
    new MapBuilder[String, T, PrefixMap[T]](empty)

  implicit def canBuildFrom[T]
    : CanBuildFrom[PrefixMap[_], (String, T), PrefixMap[T]] =
      new CanBuildFrom[PrefixMap[_], (String, T), PrefixMap[T]] {
        def apply(from: PrefixMap[_]) = newBuilder[T]
        def apply() = newBuilder[T]
      }
}

    We’ll now turn to the companion object PrefixMap. In fact, it is not strictly necessary to define this companion object, as class PrefixMap can stand well on its own. The main purpose of object PrefixMap is to define some convenience factory methods. It also defines a CanBuildFrom implicit to make typing work out better.

    The two convenience methods are empty and apply. The same methods are present for all other collections in Scala’s collection framework, so it makes sense to define them here, too. With the two methods, you can write PrefixMap literals like you do for any other collection:

    scala> PrefixMap("hello" -> 5, "hi" -> 2)
res0: PrefixMap[Int] = Map(hello -> 5, hi -> 2)

scala> PrefixMap.empty[String]
res2: PrefixMap[String] = Map()

    The other member in object PrefixMap is an implicit CanBuildFrom instance. It has the same purpose as the CanBuildFrom definition in the RNA companion object from the last section: to make methods like map return the best possible type. For instance, consider mapping a function over the key/value pairs of a PrefixMap. As long as that function produces pairs of strings and some second type, the result collection will again be a PrefixMap. Here’s an example:

    scala> res0 map { case (k, v) => (k + "!", "x" * v) }
res8: PrefixMap[String] = Map(hello! -> xxxxx, hi! -> xx)

    The given function argument takes the key/value bindings of the prefix map res0 and produces pairs of strings. The result of the map is a PrefixMap, this time with value type String instead of Int. Without the canBuildFrom implicit in PrefixMap the result would just have been a general mutable map, not a prefix map. For convenience, the PrefixMap object defines a newBuilder method, but it still just uses the default MapBuilder.

    Summary

    To summarize, if you want to fully integrate a new collection class into the framework you need to pay attention to the following points:

    1. Decide whether the collection should be mutable or immutable.
    2. Pick the right base traits for the collection.
    3. Inherit from the right implementation trait to implement most collection operations.
    4. If you want map and similar operations to return instances of your collection type, provide an implicit CanBuildFrom in your class’s companion object.

    You have now seen how Scala’s collections are built and how you can add new kinds of collections. Because of Scala’s rich support for abstraction, each new collection type has a large number of methods without having to reimplement them all over again.

    Acknowledgement

    These pages contain material adapted from the 2nd edition of Programming in Scala by Odersky, Spoon and Venners. We thank Artima for graciously agreeing to its publication.

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