Code block

for(mbr <- collection) {
  println(mbr)
}

Not surprisingly, this loop prints out the members of the collection, in order that they are returned by the collection’s iterator. In fact, this loop construct is translated exactly to

Code block

collection.foreach(mbr => println(mbr))

Code block

val transformed = for(mbr <- collection) {
  yield transform(mbr)
}

Each time through this example loop, the result of the loop is yielded out. All the yielded results are collected in to a single iterator. This type of for loop is syntactic sugar for the following statement

Code block

val transformed = collection.map(mbr => transform(mbr))

That’s right, a simple for…yield loop is just syntactic sugar for Iteratable.map().

Infinite (or extremely large) iterables, usually implemented as Streams or Ranges, are a bit tricky. For example, it probably wouldn’t surprise you to learn that the following traditional for loop will not terminate (at least not in your lifetime):

Code block

for(i <- 0 to 100000000000) println(i)

But executing this next for…yield loop does not cause an indefinite wait — it works fine! (Go ahead, try it out!)

Code block

val numberStrings = for(i <- 0 to 100000000000) yield ("" + i)

How can this be so? You need to know that o to 10000000000 results in a Range object, which is a non-strict iterator. That is, it is an iterator that calculates the “next” value as you iterate through it, rather than pre-computing all members up front and storing them in memory when the Range is created.

Iteratable functions that yield a scalar result, like foldLeft() or length() or any catamorphic function, are not safe to use with non-strict iterators, because these methods must iterate over the entire iteratable’s contents to produce a result. The foreach() method falls in to this unsafe category — foreach()’s return type is Unit, which is considered scalar.

Remember the traditional for loop is just syntactic sugar for a foreach() call, and this explains why looping over the range with a traditional loop causes an indefinite wait.

Iteratable functions that yield results of similar size to the input, such as map() and flatMap(), are perfectly safe to use with non-strict iterators. These methods themselves yield non-strict iterators, and don’t need to iterate over the source iterator’s contents to yield a result.

The for…yield loop is just syntactic sugar for a map() call, and this explains why looping over the Range with a for…yield loop doesn’t cause an indefinite wait.

End of Interlude

Code block

// Using the guarded for...yield loop syntactic sugar
val oddSquares =
  for(i <- 0 to 10000000000 if i % 2 == 1) yield (i*i)
 
// Exactly the same thing as
val oddSquares = (0 to 10000000000).filter(i=>i % 2 == 1).map(i=>i*i)

And as the example implies, this for loop style is non-strict collection safe (because both filter() and map() are non-strict safe).

Code block

// Long-winded nested for loop
val pairsThatSumTo100 =
  for(i <- 0 to 100;
      j <- i to 100 if i + j == 100)
    yield Pair(i, j)
 
// Slightly shorter but harder to read raw form that gets compiled
val pairsThatSumTo100 =
  (0 to 100).flatMap(i=>(i to 100).filter(j=>i+j==100).map(j=>Pair(i,j)))

Note that nested for loops are also non-strict safe, because filter(), map() and flatMap() are all non-strict safe. Only the traditional for loop is not safe for non-strict use.

In functional programming, catamorphisms are embodied in the folds functions. I like Scala, so I’ll discuss some catamorphic function examples in found in the standard Scala library’s Iterable trait.

The Iterable trait in Scala represents the concept of an ordered series of same-typed values. This trait is common to all the collection types (Lists, Seqs, and Streams, and many other “series like” things). The Iterable trait defines several catamorphic functions — functions which reduce the series of values down to a single value.

Perhaps the simplest to start with is the forall() and exists() methods. These methods each take a Boolean test operation, applies it to each member of the Iterable, and returns the logical AND (forall()), or OR (exists) of the test values. Despite the fact that they act differently, both methods have the same type signature, because both are Boolean catamorphisms:

Code block

trait Iterable[A] {
  ...
  def forall(test: (A) => Boolean): Boolean = ...
  def find(test: (A) => Boolean): Boolean = ...
  ...
}

Event more generic are the foldLeft() and foldRight() methods in Iterable. foldRight() is really just a slight tweak on foldLeft(), so I’ll just explain left-hand version and for the right-hand version I’ll just do some… erm… hand-waving.

The foldLeft() method receives an aggregator function used to combine each member of the Iterable successively in to an aggregated value. foldLeft() starts with an initial value, which it combines with the first Iterable value using the aggregator function. The result is then aggregated with the second Iterable value; and then the third, and so on, until the entire Iterable has been reduce down to a single aggregated value. Thus foldLeft() is a catamorphism, as it combines and reduces the series of values represented by an Iterable down to a single value.

foldRight() is the same as foldLeft() — the only difference being which end of the series each starts with. The foldLeft() function starts with the head of the series (traditionally drawn to the left of the tail — hence the name) and proceeds to the coda; foldRight() starts with the series coda and proceeds to the head.

Code block

trait Iterable[A] {
  ...
  def foldLeft[B] (initialValue: B)(aggregatorFunc: (B, A) => B): B = ...
  def foldRight[B](initialValue: B)(aggregatorFunc: (B, A) => B): B = ...
  ...
}

If you think for a second, you can see how forall() and exists() could be implemented using foldLeft():

Code block

trait Iterable[A] {
  ...
  def foldLeft[B] (initialValue: B)(aggregatorFunc: (B, A) => B): B = ...
  ...
  def forall(test: (A) => Boolean): Boolean =
      foldLeft(true)(_ && test(_))
 
  def exists(test: (A) => Boolean): Boolean =
      foldLeft(false)(_ || test(_))
  ...
}

In addition to forall() and exists() there are other catamorphic convenience functions in Iterable, and as it turns out each of them could be re-implemented using foldLeft() (or foldRight()) as well. For example, mkString() creates a string representation of the Iterable series by combining each member’s toString() value, along with a prefix, a suffix, and a list separator string.

Code block

trait Iterable[A] {
  ...
  def foldLeft[B] (initialValue: B)(aggregatorFunc: (B, A) => B): B = ...
  ...
  def mkString(prefix: String, separator: String, suffix: String): String =
      foldLeft(prefix)(_ + separator + _) + suffix
  ...
}