Higher-Order Java Parallelism, Part 1: Parallel Strategies and the Callable Monad

Now that even budget desktop and laptop computers are shipping with multi-core processors, it’s more important than ever to design programs so that they can take advantage of parallel processing. If you’re already writing software in Erlang or Parallel Haskell, then lucky you. But if you’re writing in Java (and are unable or unwilling to take up Scala), you will need to get organized.

Since Java 5, the JDK comes with a concurrency library that makes concurrent programming a lot easier than it used to be, and the library has been improved further in Java 6. This provides some basic abstractions that take care of the nitty-gritty of thread management for us. In this short series of articles, I’m going to show how we can build on top of that library to achieve concurrent programming of a higher order. We will employ some design patterns and simple abstract building blocks from functional programming. This style of writing concurrent programs will afford us the ability to:

• Compose ordinary functions into concurrent programs.
• Decouple parallel behavior from the algorithm itself.
• Turn existing code into parallel code, without refactoring, at runtime.
• Work with hypothetical results of concurrent computations, before they finish.

We will not use any locking or explicit synchronization. Basic familiarity with the java.util.concurrent package is assumed but not required. Familiarity with generics is highly recommended, and I recommend reading parts 1 and 2 of my Lazy Error Handling series as it explains some preliminaries. Most of the source code herein is already part of the Functional Java library, and I’ll use a fair bit of interfaces and classes from it, which I’ll introduce as we go along.

When we’re through, I will have demonstrated that a functional style of programming promotes code-reuse and modularity of parallel programs, above and beyond what can be achieved with the canonical object-orientated style.

The Callable Monad

The Callable interface is new in Java 5. It’s similar to the old Runnable interface that we all know and love, except that its call() method returns a result, and it may throw an Exception. If you followed my Lazy Error Handling articles, you will immediately notice that Callable is nearly identical to the Thrower interface described in that series, and you’ll know that it is indeed a potential monad. Treating Callable as a monad will allow us to work with it at a higher level of abstraction, letting us compose Callables, chain them, and project computations into them.

As you may already know, we need three ingredients (and only these three) to have a monad:

1. Type construction. This comes free with the Callable interface, since it takes a type parameter (i.e. it’s generic).
2. A unit function. This allows us to turn any value into a Callable that returns that value again.
3. A binding function. This allows us to chain together Callables with functions, without actually calling them.

Here is the unit function for Callable (we will refer to it as unit in the text to avoid ambiguity):

  public static <A> Callable<A> callable(final A a) {
    return new Callable<A>() {
      public A call() {
        return a;
      }
    };
  }

And here is its binding function:

  public static <A, B> Callable<B> bind(final Callable<A> a, final F<A, Callable<B>> f) {
    return new Callable<B>() {
      public B call() throws Exception {
        return f.f(a.call()).call();
      }
    };
  }

Note: The F interface is from Functional Java. It represents a first-class function (a function that can be treated like any other value). F<A, B> has one method that takes an argument of type A and returns a value of type B.

Given the above two methods, Callable is now a monad. All monads are also functors, so we can define a Callable functor. What I mean by “functor” is that we can define a method to turn any existing function into a function on Callables, or, in other words, to apply any function to a value wrapped in a Callable, without actually calling it (i.e. lazily). This method is called fmap, and we can define it in terms of bind:

  public static <A, B> F<Callable<A>, Callable<B>> fmap(final F<A, B> f) {
    return new F<Callable<A>, Callable<B>>() {
      public Callable<B> f(final Callable<A> a) {
        return bind(a, new F<A, Callable<B>>() {
          public Callable<B> f(final A ab) {
            return new Callable<B>() {
              public B call() {
                return f.f(ab);
              }
            };
          }
        });
      }
    };
  }

Useful operations on Callables, that the methods above allow us to implement, include sequence—which is a method of turning a list of Callables into a single Callable that returns a list—and join, which peels one layer of Callables from a Callable<Callable<A>> so that it becomes just Callable<A>. You will find the source code for those as part of Functional Java.

Parallel Strategies

When working with the java.util.concurrent library, you normally don’t work with Threads directly. You might instead implement Callable<A> and submit instances of your implementation to an ExecutorService, which yields values of type Future<A> which represents a running computation that yields an A. Future has a method called get() that returns the result as soon as it’s ready. This is a great improvement over managing threads and Runnables ourselves, but it still ties our hands somewhat to the ExecutorService, and encourages tight coupling of our code to the parallelisation library.

Inspired by Haskell’s “Parallel Strategies”, let’s instead work with parallelisation in the abstract. For what is ExecutorService, really? It’s a method of turning Callables into Futures. That means it’s a kind of function, so we can abstract from it, using a function type: F<Callable<A>, Future<A>>. Such a function can then be backed by an ExecutorService, or by something else entirely, such as a load-balancing facility that serializes Callables to be executed on remote servers.

We will use a new class, Strategy<A>, that allows us to effectively separate parallelism from the algorithm itself:

  public final class Strategy<A> {

    private F<Callable<A>, Future<A>> f;

    private Strategy(final F<Callable<A>, Future<A>> f) {
      this.f = f;
    }

    public F<Callable<A>, Future<A>> f() {
      return f;
    }

    public static <A> Strategy<A> strategy(final F<Callable<A>, Future<A>> f) {
      return new Strategy<A>(f);
    }

  }

We’ll add a couple of static functions to create simple strategies:

  public static <A> Strategy<A> simpleThreadStrategy() {
    return strategy(new F<Callable<A>, Future<A>>() {
      public Future<A> f(final Callable<A> p) {
        final FutureTask<A> t = new FutureTask<A>(p);
        new Thread(t).start();
        return t;
      }
    });
  }

  public static <A> Strategy<A> executorStrategy(final ExecutorService s) {
    return strategy(new F<Callable<A>, Future<A>>() {
      public Future<A> f(final Callable<A> p) {
        return s.submit(p);
      }
    });
  }

One of the neat things that working with Strategies as functions allows us to do is use the Callable monad to compose them with existing functions. Any function can be lifted into the Callable monad using fmap, and then composed with a Strategy to yield a concurrent function. Moreover, we can use Strategies to convert existing functions to concurrent functions. The following method on Strategy will take any function and return the equivalent function that executes concurrently. Calling such a function will give you a Future value from which you can get the computed result whenever it’s ready.

  public <B> F<B, Future<A>> lift(final F<B, A> f) {
    final Strategy<A> self = this;
    return new F<B, Future<A>>() {
      public Future<A> f(final B b) {
        return self.f().f(new Callable<A>() {
          public A call() {
            return f.f(b);
          }
        });
      }
    };
  }

Alert readers will note that lift represents the Kleisli arrow for the Future monad. As for most monads, this arrow is a very useful kind of thing (see Lazy Error Handling, Part 2). In the Future monad, the Kleisli arrow provides parallel function application. If you already have a function f, then calling lift(f).f(x) will apply that function to x while simultaneously continuing with the next statement in the current program.

Lazy Futures

For functions involving Futures, we generally always want to have the Future type in the codomain (on the right-hand side, in the return type). If you think about it, you’ll see that functions that take Futures in their arguments won’t be able to do much without blocking on Future.get(). However, that doesn’t mean we can’t compose Future-valued functions together. It just means that we can only compose two of them together in such a way that we either wait for the first Future to obtain a value before firing off the second one, or we have to spark a new thread that does nothing but wait on the first Future. We’re much better off composing Callables and then turning those into Futures as needed. In fact, we might want to wrap values of type Future<A> inside of a Callable<A> again so that we can manipulate their return values while they are running:

  public static <A> Callable<A> obtain(final Future<A> x) {
    return new Callable<A>() {
      public A call() throws Exception {
        return x.get();
      }
    };
  }

And this takes us full circle back into the Callable monad, where we can compose computations, bind them to functions and map functions over them, all lazily. Which means: without actually asking what their values are until we absolutely need to know.

So we have accomplished what we set out to do in this first part of the series. We’ve written a Callable monad that lets us compose existing code into concurrent programs. We’ve implemented parallel strategies to run those programs in parallel, without regard to the actual parallelisation implementation. We have a Kleisli arrow that lets us run ordinary functions concurrently with each other, and finally we have a way of taking concurrently running computations back into the Callable monad. Not bad for a day’s work.

In the next part of this series, we will employ what we’ve built here to develop some higher-order parallel functions, including a parallel list functor. I hope you join me.