How is this piece of Recursive lambda call in Java working

Question

I recently came across this piece of code in Java. It involves Function and printing fibonacci numbers and it works.

public class AppLambdaSubstitution {

public static Function<Integer, Integer> Y(Function<Function<Integer, Integer>, Function<Integer, Integer>> f) {
    return x -> f.apply(Y(f)).apply(x);
}

public static void main(String[] args) {
    Function<Integer, Integer> fib = Y(
            func -> x -> {
        if (x < 2)
            return x;
        else
            return func.apply(x - 1) + func.apply(x - 2);
    });

    IntStream.range(1,11).
    mapToObj(Integer::valueOf).
    map(fib).forEach(System.out::println);
  }
}

The part that has me confused is return x -> f.apply(Y(f)).apply(x);. Isn't Y(f) a recursive call to the method Y? We keep calling it with the Function f as a parameter. To me, there's no base case for this recursive call to return from. Why is there no overflow resulting from an endless recursive call?

Answer 1

Fundamentally you are missing the point that x -> f.apply(Y(f)).apply(x); will not call apply, it will return a Function.

That's just a very complicated (and non-intuitive?) way of showing currying and recursive function IMO. Things would be much simpler if you would replace a couple of things and make it a bit more readable.

This construction:

 Function<Function<Integer, Integer>, Function<Integer, Integer>>

is not needed at all, since the left parameter is not used at all. It's simply needed to get a hold of the right one. As such the left parameter could be anything at all (I will later replace it with Supplier - that is not needed either, but just to prove a point).

Actually all you care about here is this Function that does the actual computation for each element of the Stream:

 public static Function<Integer, Integer> right() {

    return new Function<Integer, Integer>() {
        @Override
        public Integer apply(Integer x) {
            if (x < 2) {
                return x;
            } else {
                return apply(x - 1) + apply(x - 2);
            }
        }
    };
}

Now you could write that entire construct with:

 Supplier<Function<Integer, Integer>> toUse = () -> right();
 Function<Integer, Integer> fib = curry(toUse);
 IntStream.range(1, 11)
          .mapToObj(Integer::valueOf)
          .map(fib)
          .forEach(System.out::println);

This Supplier<Function<Integer, Integer>> toUse = () -> right(); should make you understand why in the previous example (Function<Function, Function>) the left part was needed - just to get a hold of the right one.

If you look even closer, you might notice that the Supplier is entirely not needed, thus you could even further simplify it with:

IntStream.range(1, 11)
         .mapToObj(Integer::valueOf)
         .map(right())
         .forEach(System.out::println);