Why would you want to control the number of times a method is called? Consider, for example, the common Builder Object pattern. I don’t mean the classic GoF Builder Pattern — I use builders all the time, and I don’t at all recognize this class diagram describing what a Builder is supposed to be. By Builder I mean an object with a fluid API whose job is to collect up state for the purpose of creating one or more other objects, which is pretty common in Java and many Scala DSLs.

Rafael Ferriera wrote a piece about builders and Phantom Types I’m going to use as a starting point for introduction of the topic. I’ll start with his introduction of a ScotchBuilder: a Scala object that knows how to take a proper gentleman’s order for a scotch.

Let me quote Raphael to introduce the domain:

So, let’s say you want to order a shot of scotch. You’ll need to ask for a few things: the brand of the whiskey, how it should be prepared (neat, on the rocks or with water) and if you want it doubled. Unless, of course, you are a pretentious snob, in that case you’ll probably also ask for a specific kind of glass, brand and temperature of the water and who knows what else. Limiting the snobbery to the kind of glass, here is one way to represent the order in scala.

Code block

sealed abstract class Preparation  /* This is one way of coding enum-like things in scala */
case object Neat extends Preparation
case object OnTheRocks extends Preparation
case object WithWater extends Preparation
 
sealed abstract class Glass
case object Short extends Glass
case object Tall extends Glass
case object Tulip extends Glass
 
case class OrderOfScotch(val brand:String, val mode:Preparation, val isDouble:Boolean, val glass:Option[Glass])

You can imagine providing a ScotchBuilder class to generate immutable OrderOfScotch objects with a fluid API. Below is a first-pass at such a ScotchBuilder, which is your typical fluid implementation. Its nice, but we can do better. (Code, again, taken originally from Raphael’s post, modulo changing from stateful to stateless and fixing a couple of his typos)

Code block

case class ScotchBuilder(
    theBrand        :Option[String] = None,
    theMode         :Option[Preparation] = None,
    theDoubleStatus :Option[Boolean] = None,
    theGlass        :Option[Glass] = None) {
 
  def withBrand(b:String) = copy(theBrand = Some(b))
  def withMode(p:Preparation) = copy(theMode = Some(p))
  def isDouble(b:Boolean) = copy(theDoubleStatus = Some(b))
  def withGlass(g:Glass) = copy(theGlass = Some(g))
 
  def build() = new OrderOfScotch(theBrand.get, theMode.get, theDoubleStatus.get, theGlass);
  }

There are two unattractive features with this Builder  that we are going to clean up:

1. a client can re-invoke the same setter methods over and over
2. the client can also completely forget to call other methods that should be called

Check this out, where I am able to make a non-sense scotch order:

Code block

Welcome to Scala version 2.8.1.final (Java HotSpot(TM) 64-Bit Server VM, Java 1.
6.0_21).
Type in expressions to have them evaluated.
Type :help for more information.
 
scala> val b = new ScotchBuilder
b: ScotchBuilder = ScotchBuilder@6f77e5d4
 
scala> b withBrand "Cragganmore" withMode Neat isDouble false withBrand "Macallan 25 year" isDouble true build
res3: OrderOfScotch = OrderOfScotch(Macallan 25 year,Neat,true,None)

Notice I was able to specify the brand twice, and the size as both “double” and “single”. Quite ambiguous what I meant there. Considering the price difference between a single Cragganmore (cheap) and a double Macallan 25 (expensive!), that’s maybe an ambiguity we’d like to stamp out of the system.

I’m going to now show you how to use both Phantom Types and type constraints to ensure at compile time certain Builder methods are invoked:

• with at-most-once semantics. E.g., withGlass should be called zero or one time by client code for a single ScotchBuilder instance.
• with exactly-once semantics. E.g., withBrand, withMode, and isDouble each need to be called exactly once.
• and, by the way, you can use this same technique to define one-or-more-times semantics. (Though I’m not going to go that far in this article. If you grok at-most-once and exactly-once, you will be able to figure out one-or-more-times.)

These techniques are not limited to just fluid Builder APIs. Pretty much any API where you wanted to constraint the call semantics can employ Phantom Types and type constraints to achieve the desired call semantics. This is going to apply to objects that traditionally walk through a lifecycle. For example, any API where there are init() and destroy(). The Builder under consideration also has a lifecycle: several configuration methods must be called, and then finally the build method gets invoked.

Continuing the Builder example, first I’m going to stop the build method from working if there are any builder values that haven’t been set correctly. That is, using Phantom Types and type constraints, I’m going to set things up so that compiler won’t even compile code that attempts to build a scotch when all the builder parameters have not been set. After that I’m going to stop the individual withXYZ methods from being called more than once using the same technique.

Here’s how I’m going to do make the build method uncallable except when the Builder has been fully configured: I’m going to add to the ScotchBuilder class one type parameter per method whose calls we want to track. The type parameters are going to track whether each of the withXYZ() methods have been called or not; the classes Zero and Once are defined to represent these two states. I’m then going to constrain the build method to only be callable if the appropriate type parameters are bound to the Once type.

So I’m adding 4 type parameters, each able to be bound to the type Zero or Once. So instead of having 1 ScotchBuilder class, I actually am defining 16. That is, 16 different permutations of the possible bindings to the 4 type parameters. The build method will then be constraining to be callable on ScotchBuilder[Once, Once, Once, _] (one of 2 specific bindings).

This first chunk of code adds the Zero and Once types to track the number of times the individual withXYZ() methods are called below. Note that the case class copy method allows you to specify type parameters, which I’m using in the implementation of each withXYZ method:

Code block

abstract sealed class Count
case class Zero extends Count
case class Once extends Count
 
object ScotchBuilder {
  def apply() = new ScotchBuilder[Zero, Zero, Zero, Zero]()
  }
 
case class ScotchBuilder
    [WithBrandTracking <: Count,
     WithModeTracking <: Count,
     IsDoubleTracking <:Count,
     WithGlassTracking <: Count] (
    theBrand        :Option[String] = None,
    theMode         :Option[Preparation] = None,
    theDoubleStatus :Option[Boolean] = None,
    theGlass        :Option[Glass] = None) {
 
  def withBrand(b:String) = copy[Once, WithModeTracking, IsDoubleTracking, WithGlassTracking](theBrand = Some(b))
  def withMode(p:Preparation) = copy[WithBrandTracking, Once, IsDoubleTracking, WithGlassTracking](theMode = Some(p))
  def isDouble(b:Boolean) = copy[WithBrandTracking, WithModeTracking, Once, WithGlassTracking](theDoubleStatus = Some(b))
  def withGlass(g:Glass) = copy[WithBrandTracking, WithModeTracking, IsDoubleTracking, Once](theGlass = Some(g))
 
  //...build() method definition with appropriate type constraints is just below...
  }

And below is the build method, with type constraints guaranteeing the build method can only be called on instances of type ScotchBuilder[Once, Once, Once, _].

Code block

case class ScotchBuilder[...] {
  ...
 
  type IsOnce[T] = =:=[T, Once]
 
  ...
 
  def build[B <: WithBrandTracking : IsOnce, M <: WithModeTracking : IsOnce, D <: IsDoubleTracking : IsOnce] =
      new OrderOfScotch(withBrand.get, withMode.get, isDoubleStatus.get, withGlass)
 
  ...
  }

I use the =:= type class to guarantee this constraint on the ScotchBuilder type parameters. An implicit value of =:=[A, B] only exists when A == B. (For a deeper explanation of the =:= type constraining object, check out this blog post by Debasish Ghosh). I’ve further created a type alias IsOnce[T] = =:=[T, Once], which allows me to apply =:= as a type class.

The upshot of all of this is that any attempt to invoke build on a ScotchBuilder not matching ScotchBuilder[Once, Once, Once, _] simply cannot be compiled. You literally cannot compile code that improperly uses a ScotchBuilder to build a order of scotch!

Note that in the code above we never actually create an instance of Zero or Once — these type parameter bindings are purely for compile-time bookkeeping. Hence the term Phantom Types, because these types are never instantiated nor participate at runtime.

We can even do a little better with the builder above by constraining the withXYZ methods to have exactly-once or at-most-once call semantics, as appropriate. This is going to make the compiler fail at the point where the API is being misused — i.e., where a withXYZ method is being used the second time for a single ScotchBuilkder instance. So it’ll be a lot easier when using this API to figure out what you did wrong. Here is the final version of ScotchBuilder:

Code block

sealed abstract class Preparation  /* This is one way of coding enum-like things in scala */
case object Neat extends Preparation
case object OnTheRocks extends Preparation
case object WithWater extends Preparation
 
sealed abstract class Glass
case object Short extends Glass
case object Tall extends Glass
case object Tulip extends Glass
 
case class OrderOfScotch(val brand:String, val mode:Preparation, val isDouble:Boolean, val glass:Option[Glass])
 
abstract sealed class Count
case class Zero extends Count
case class Once extends Count
 
object ScotchBuilder {
  def apply() = new ScotchBuilder[Zero, Zero, Zero, Zero]()
  }
 
case class ScotchBuilder
    [WithBrandTracking <: Count,
     WithModeTracking <: Count,
     IsDoubleTracking <:Count,
     WithGlassTracking <: Count] (
    theBrand        :Option[String] = None,
    theMode         :Option[Preparation] = None,
    theDoubleStatus :Option[Boolean] = None,
    theGlass        :Option[Glass] = None) {
 
  type IsOnce[T] = =:=[T, Once]
  type IsZero[T] = =:=[T, Zero]
 
  def withBrand[B <: WithBrandTracking : IsZero](b:String) =
      copy[Once, WithModeTracking, IsDoubleTracking, WithGlassTracking](theBrand = Some(b))
 
  def withMode[M <: WithModeTracking : IsZero](p:Preparation) =
      copy[WithBrandTracking, Once, IsDoubleTracking, WithGlassTracking](theMode = Some(p))
 
  def isDouble[D <: WithModeTracking : IsZero](b:Boolean) =
      copy[WithBrandTracking, WithModeTracking, Once, WithGlassTracking](theDoubleStatus = Some(b))
 
  def withGlass[G <: WithGlassTracking : IsZero](g:Glass) =
      copy[WithBrandTracking, WithModeTracking, IsDoubleTracking, Once](theGlass = Some(g))
 
  def build[B <: WithBrandTracking : IsOnce, M <: WithModeTracking : IsOnce, D <: IsDoubleTracking : IsOnce] =
      new OrderOfScotch(withBrand.get, withMode.get, isDoubleStatus.get, withGlass)
 
  }

All this extra type bookkeeping is well worth it for me because it means I don’t have to write a bunch more test code. I never need to worry or test for cases where client is is misusing my ScotchBuilder: it simply is not possible to do. And there’s never a need to write regression tests against a case which is impossible.

Code block

lazy val fib: Stream[Int] =
 Stream.cons(0, Stream.cons(1, fib.zip(fib.tail).map(p => p._1 + p._2)))

If you have not seen that zip trick before, follow me on a little explanation. The code defines a Stream — a non-strict iterable — that begins with two literal values “0″ and “1″. The stream then continues the Fibonacci sequence by zipping the sequence to itself. More specifically, to its own tail sequence.

This figure illustrates what the zipper is creating.

The tail value of the initial sequence is just the sequence starting with the literal value “1″. The zipper creates Pairs out of the each member of the sequence pairwise joined with the next member of the sequence.

The first pair is (0, 1).

The second pair is then (1, 0 + 1) = (1, 1).

The third pair is then (1, 1 + 1) = (1, 2).

The forth pair is then (2, 1 + 2) = (2, 3). And so on.

The coolest part is of course the complete lack of apparent recursion. The whole sequence is lazily evaluated, so the Stream takes up little space — one new Stream object per element in the sequence.

Generalizing

We can generalize this stream-zipping technique. When the value of a Stream element n can be calculated from the previous k sequence members, we can use a k-ary version of this technique. That is, if the stream theStream member n can be defined by some function s:

def theSeq(n) = s(theSeq(n-1), theSeq(n-2), …, theSeq(n-k))

We can define the stream in a single statement thus:

• Explicitly define the first k-1 stream members
• For all other members, perform k-1 zips to create a TupleK of the previous k sequence elements.
• A single closure then defines the next element from this Tuple.

Here, for example, is a rolling average of the last 4 members of a Stream[Double]:

Code block

val data: Stream[Double] = ...
val padded_data = Stream.fill(4)(0.0) ++ data ++ Stream.fill(4)(0.0)
  // Note: tail padding not a problem even if data is infinite.
 
/* Here's where the stream is joined to itself. Also,
   mapping the (((Int,Int),Int),Int) to (Int,Int,Int,Int)
   for readability. Can't be recursively defined   */
def zip4[A](str: Stream[A]): (A,A,A,A) =
 (str zip str.tail zip str.tail.tail zip str.tail.tail.tail) map { p=>
     (p._1._1._1, p._1._1._2, p._1._2, p._2)}
 
/* Could be recursively defined in terms of
   base type Product */
def avg4(p: (Double,Double,Double,Double)): Double =
 (p._1, p._2, p._3, p._4) / 4
 
/* Finally, generating the rolling-average stream */
lazy val avg_rolling: Stream[Double] =
 zip4(padded_data) map (avg4)

You can use Iterator.sliding(n) to get a similar effect. And that does work on infinite, non-strict streams. Personally, I just though this technique was so cool, and it does have the benefit of strongly-typed tuples. (Iterator.sliding() simple provides more Streams. Try it out if you’re curious.)

(Most of the documentation could be replaced by a far smaller, and more logically accurate, Operation State Modeling description. But that’s not what I’m here to talk about…)

Writing the REST-style interface, something pretty interesting occurred to me. I’ll need the casual reader to put on his thinking cap before moving on here, so please do that if you haven’t already. I’ll wait…

What is a Future?

Let’s start with what a future is: To review, as the linked document says, a future is “…a place-holder for the undetermined result of a (concurrent) computation…”. Let’s say there’s a value your program needs, but the computation or retrieval of that value takes a significant amount of time or resources. Instead of synchronizing (waiting) for the value to be computed, you could spin off an asynchronous process to compute/retrieve the value; alternatively, you could leave a placeholder object that only starts the complex computation/retrieval on demand. Either way, your program leaves in place a placeholder object know as a future.

When your program eventually comes back to the future object asking for the value, the the future either a) hands it back immediately if it has a cached copy; or b) the main program synchronizes (blocks) until the background process completes its computation/retrieval.

The object graph produced by Hibernate when you make an object query uses futures to represent unretrieved values. The query result Hibernate produces is an object graph with placeholder Collections representing lazy relationships. The lazy collections initially don’t have any data in them, but instead have just enough data in them to generate a secondary Hibernate query. When the program tries to access a lazy collection’s contents, only then does the Collection query a Hibernate entity manager for the collection of related objects it represents. The placeholder Collection objects are thus futures.

URL/URI References as Lazy Futures

When a REST-style service response contains a link URL/URI reference to another entity, you can think of that link as a kind of future in the same way as a Hibernate lazily populated Collection. One could easily populate a graph of objects from JSON source, replacing URL/URI references with lazy future objects.

In Scala, a Future[X] extends Function1[X], meaning that Future is Function subtype, so you can use a Function1[_] type to represent URL/URI-based references:

Code block

/**
 * Invoice can be deserialized from JSON such as:
 * {
 *   id: "XYZ",
 *   lineItems: "http://somewhere.com/inv/XYZ/lineItems"
 *       //      ^^^ URL; serialized representation of
 *       //          a List[LineItem] future.
 * }
 **/
class Invoice(val id: String,
              val lineItems: () => List[LineItem],
              ...) {
  ...
}

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.

Quick Explanation of the Pipe Operator

The pipe operator is syntactic sugar that makes certain patterns of code easier to read. When generating a final result by a sequence of value calculations its easier to read the sequence from left -to-right, but Scala  only supports passing values to functions in function(value) form, which basically forces the eyes to read the sequence in right-to-left order — rather unnatural.

Here is one way of expressing a sequence of calculations, relying on local vals to hold intermediate sequence values:

Code block

def shuffle(str: String): String = . . .
def randomize(str: String): String = . . .
def camelCase(str: String): String = . . .
def futzWith(str: String): String = . . .
def applySeveralStringTransforms(str: String): String = {
  val shuffled = shuffle(str)
  val randomized = randomize(shuffled)
  val camelCased = camelCase(randomized)
  futzWith(camelCased)
}

Which reads easy enough — the result of the function is the result of shuffling, randomizing, camel-casing and finally futzing with the original String. And here’s the equivalent calculation as a single expression, without local vals. Note how the sequence of calculations is performed from right to left — first shuffle, then randomize, etc.

Code block

def applySeveralStringTransforms(str: String): String = {
  futzWith(camelCase(randomize(shuffle(str)))
}

A pipe operator allows you to pass the result of an expression to the right, preserving left-to-right visual order while still being semantically equivalent to either form above:

Code block

def applySeveralStringTransforms(str: String): String = {
  str |> shuffle |> randomize |> camelCase |> futzWith
}

Attempt # 1: Right-Associative Operator

My first attempt has me defining a right-associative operator, using Odersky’s pimp-my-library technique, to generate a temporary PipeFunc object which has a “|>:” operator. That is, I’m using a couple tricks to get the compiler to automatically rewrite this

Code block

x |>: func

like this

Code block

(new PipeFunc(func)).|>:(x)

Since my operator “|>:” ends with a colon, Scala treats it as a “right-associative” function — a function of the right-operand “func”, rather than a function of the left-operand “x”. A very short-lived PipeFunc object gets created by an implicit conversion, and this object has a method named “|>:” that gets applied.

Here’s the definition of my operator:

Code block

object Pipeline {
  implicit def toPipeFunc[X, Y](func: X => Y) = new PipeFunc(func)
  class PipeFunc[X, Y](func: X => Y) {
    def |>:(value: X): Y = func(value)
  }
}

There are immediate problems with this approach. Because of how Scala 2.7.5 (the version I am using) parses this code, it is apparently unable to recognize that the right-hand side of |>: is a function reference. So the following actually causes a compiler error:

Code block

// complains "|>:" is not a function of type Unit
"Hello, World!" |>: println

I’m not sure why this is, but using parens fixes the problem, but makes the expression too surprising and ugly for my taste. I’m going to have to go back to the drawing board…

Attempt #2: Left-Associative Operator

Instead of augmenting the function argument on the right, I’ll try augmenting the value argument on the left with a “|>” operator. I’ll use the same pimp-my-library technique to use an implicit conversion of the left-hand object to a temporary object that has a “|>” operator, which takes a function as its right-hand argument. That is, I’m using a couple tricks to get the compiler to automatically convert this

Code block

x |> func

to this

Code block

(new PipeLink(x)).|>(func)

Here’s my code for the operator definition:

Code block

object Pipeline {
  implicit def toPipeLink[X](v: X): PipeLink[X] = new PipeLink[X](v)
  class PipeLink[X](value: X) {
    def |>[Y](func: X => Y): Y = func(value)
  }
}

OK, works correctly, and doesn’t have any of the problems that the right-associative operator had.

I do have a hidden performance issue: creation of an very-short-lived temporary object. Consider how the the following single expression gets rewritten by the Scala compiler:

Code block

str |> shuffle |> randomize |> camelCase |> futzWith

to this:

Code block

(new PipeLink((new PipeLink((new PipeLink((new PipeLink(str)).
    |>(shuffle)).|>(randomize)).|>(camelCase)).|>(futzWith)

Ugly – obviously; wastefully creates too many objects – also true. 4 temporary PipeLinks created and thrown away. The JVM GC is pretty good at handling short-lived objects, but this is terribly wasteful. I can’t think of a way of getting rid of temporary objects — any suggestions greatly appreciated!

Smarter Than Me

Only after implementing did I find that Steve Gilham had already posted his implementation of the pipe operator. He immediately went with a left-associative operator implementation. Must be a clever guy! Both his solution and mine suffer from creating a temp object with each invocation of the pipe operator.