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.
An outline of the Builder class:
Documentationpackage scala.collection.mutable
class 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 class.
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),
and b ++= xs work 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.
package scala.collection
class TraversableLike[+Elem, +Repr] {
def newBuilder: Builder[Elem, Repr] // deferred
def foreach[U](f: Elem => U) // 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 classes 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[I] 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 class
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 with
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 problem is how to achieve that without duplicating
the definition of the map method in lists and arrays. The
newBuilder/foreach framework shown in class 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 still can
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](p: Elem => B)
(implicit bf: CanBuildFrom[B, That, This]): That = {
val b = bf(this)
for (x <- this) 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 class
TraversableLike.
The principal difference is that where filter used
the newBuilder method, which is abstract in class 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: Elem
indicates the element type of the collection to be built, To indicates
the type of collection to build, and From indicates the type for which
this builder factory applies. 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 type of the collection to build
is Int. If this is not the case, you can always fall back to a
different implicit builder factory, this time implemented in
mutable.Set's companion object. The type of this more general builder
factory, where A is a generic 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 have a list value that has Iterable as its
static type, and you map some function over that value:
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 be) still 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.
What needs to be done if you want to integrate a new collection class, so that it can profit from all predefined operations at the right types? On the next few pages you'll be walked through two examples that do this.
RNA Bases:
abstract class Base
case object A extends Base
case object T extends Base
case object G extends Base
case object U extends Base
object Base {
val fromInt: Int => Base = Array(A, T, G, U)
val toInt: Base => Int = Map(A -> 0, T -> 1, G -> 2, U -> 3)
}
Say you want to create a new sequence type for RNA strands, which are sequences of bases A (adenine), T (thymine), G (guanine), and U (uracil). 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
3. 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.
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, T, A)
xs: List[Product with Base] = List(A, G, T, A)
scala> RNA1.fromSeq(xs)
res1: RNA1 = RNA1(A, G, T, A)
scala> val rna1 = RNA1(A, U, G, G, T)
rna1: RNA1 = RNA1(A, U, G, G, T)
Here are some more interactions with the RNA1 abstraction:
scala> rna1.length
res2: Int = 5
scala> rna1.last
res3: Base = T
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.
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
}
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. 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 from IndexedSeqLike[Base, RNA2]. 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, T)
rna2: RNA2 = RNA2(A, U, G, G, T)
scala> rna2 take 3
res5: RNA2 = RNA2(A, U, G)
scala> rna2 filter (U !=)
res6: RNA2 = RNA2(A, G, G, T)
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? Ideally we'd expect that mapping
bases to bases over an RNA strand would yield again an RNA strand:
scala> val rna = RNA(A, U, G, G, T)
rna: RNA = RNA(A, U, G, G, T)
scala> rna map { case A => T case b => b }
res7: RNA = RNA(T, U, G, G, T)
Likewise, appending two RNA strands with ++ should yield again
another RNA strand:
scala> rna ++ rna
res8: RNA = RNA(A, U, G, G, T, A, U, G, G, T)
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, 3, 2, 2, 1)
scala> rna ++ List("missing", "data")
res3: IndexedSeq[java.lang.Object] =
Vector(A, U, G, G, T, missing, data)
This is what you'd expect in the ideal case. But this is not what the
RNA2 class provides. In fact, if you ran the first two examples above
with instances of this class you would obtain:
scala> val rna2 = RNA2(A, U, G, G, T)
rna2: RNA2 = RNA2(A, U, G, G, T)
scala> rna2 map { case A => T case b => b }
res0: IndexedSeq[Base] = Vector(T, U, G, G, T)
scala> rna2 ++ rna2
res1: IndexedSeq[Base] = Vector(A, U, G, G, T, A, U, G, G, T)
So the result of map and ++ is never an RNA strand, even if the
element type of the generated collection is a 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. In essence, an implicit value of type
CanBuildFrom[From, Elem, To] says: "Here is a way, given a collection
of type From, to build with elements of type Elem a collection of type
To."
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
}
}
}
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
}
}
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 IndexedSeqs, and that's what you saw when applying map to
rna2.
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 on 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 such an object 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 natural types. Its implementation requires a little bit 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.
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." The idea is to store a
set or a map as a tree where subsequent character in a search key
determines uniquely a descendant tree. For instance a Patricia trie
storing the three strings "abc", "abd", "al", "all", "xy" would look
like this:
A sample patricia tree:
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.
An implementation of prefix maps with Patricia tries:
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]
}
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))
The previous listing shows the definition of PrefixMap. This class is
parameterized with the type of associated values T, and 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 did we pick 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. 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 is
elegantly expressed using flatMap. When applied to an optional value,
ov, and a closure, f, which in turn returns an optional value, ov flatMap f will succeed if both ov and f return a defined
value. Otherwise ov flatMap f will return None.
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).
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]
}
}
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. Mutable sets behave the same. The default
builders for immutable maps and sets use the non-destructive element
addition method +, instead of method +=.
However, in all these cases, to build the right kind of set or map,
you need to start with an empty set or map of this kind. This is
provided by the empty method, which is the last method defined in
PrefixMap. This method simply returns a fresh PrefixMap.
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 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.
To summarize, if you want to fully integrate a new collection class into the framework you need to pay attention to the following points:
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 build new kinds of collections. Because of Scala's rich support for abstraction, each new collection type can have a large number of methods without having to reimplement them all over again.
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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