What Is A No-Argument Function?

The other day, I was reading Eric Lippert’s blog—specifically the second post in his series on implementing a Z-machine in OCaml—and something he wrote reminded me of a conversation I had with Tom Denley many years ago:

This declares a variable called word, though “variable” is a bit of a misnomer in OCaml. Variables do not (typically) vary. (There are ways to make variables that vary – they are somewhat akin to “ref” parameters in C# – but I’m not going to use them in this project.) Variables are actually a name associated with a value.

In that conversation, we were talking about Google’s Guava library, and some of its functional interfaces. Here’s one, cut down to the bare essentials:

package com.google.common.base;

public interface Function<F, T> {
  T apply(F input);
}

If you’ve written any Java since Java 8 came out, you’ll notice that it has an interface that’s basically identical. The fact that interfaces like this existed before Java 8 was one of the main reasons for a lambda design that works with any functional interface, not just the ones in the standard library.

There’s another interface, also in both Guava and Java now:

package com.google.common.base;

public interface Supplier<T> {
  T get();
}

There’s two differences between Function<F, T> and Supplier<T>. The first is obvious: Function::apply takes a single parameter—an input—and returns a single value—an output, whereas Supplier::get takes no parameters but returns a value. The second is more insidious. To make it clear, let me give you an example of each.

Function<F, T> is normally used in code like the following:

Iterable<Integer> numbers = ImmutableList.of(1, 2, 3, 4, 5);
Iterable<Integer> doubled = FluentIterable.from(numbers)
        .map(new Function<Integer, Integer>() {
            @Override public Integer apply(Integer input) {
                return input * 2;
            }
        });

Or, with lambda expressions:

Iterable<Integer> numbers = ImmutableList.of(1, 2, 3, 4, 5);
Iterable<Integer> doubled = FluentIterable.from(numbers)
        .map(n -> n * 2);

That’s your average Function<F, T>. Supplier<T>, on the other hand, is normally used like this:

public class RandomNumberGenerator implements Supplier<Double> {
    private final Random random = new Random();

    @Override
    public Double get() {
        return random.nextDouble();
    }
}

public class Game {
    public static void main(String[] args) {
        Language language = Language.fromArguments(args);
        Game game = new Game(
                new RandomNumberGenerator(),
                Assets.from("assets.zip"),
                Translation.forLanguage(language));
        game.play();
    }
}

The example’s contrived, but you get the idea. Whereas Function<F, T> is typically used for a transformation of the input in a deterministic fashion, Supplier<T> is often a mechanism for supplying non-deterministic or computationally-expensive dependencies.

Back to Tom (and Eric). In this conversation, I remarked that Supplier<T>, while useful for functional-like programming in Java, wasn’t really very functional, as it isn’t referentially transparent. Tom’s response to was to ask me what, in FP, a no-argument function would be called.

I thought for a while. It didn’t come to me immediately. But when it did, it was obvious.

A function with no arguments is a value.

Think about it. If you have no side effects, and therefore all behaviour is deterministic, then a no-argument function will return the same value every time. It is therefore interchangeable with that value—the two can be seen to be one and the same. Our random number generator above wouldn’t work, and indeed, in Haskell, the random number generator’s next function is declared as follows:

next :: RandomGen g => g -> (Int, g)

Note that RandomGen g => states that g is an instance of the RandomGen type class, which is similar to saying that g implements the RandomGen interface. In Java, this could be written as follows:

<G extends RandomGen> Tuple<Integer, G> next(G generator);

next accepts a generator, g and returns a tuple, (Int, g), where the Int is the random number and the g returned is the next random number generator to be used. If you used the same generator twice as input, you’d get the same output twice. This means we have to store the output and plug it into the next incarnation of the function.

Now, procedures without arguments…