Demo of recursive factorial function using anonymous lambda expressions and a "Y combinator".

YCombinator.java

/*
    A demonstration of recursive implementation of the factorial function using anonymous
    lambda expressions and a "Y combinator".
    see: https://en.wikipedia.org/wiki/Fixed-point_combinator
 */

import java.math.BigInteger;

public class YCombinator {

    interface SelfApplicable<T> {
        T apply(SelfApplicable<T> a);
    }

    interface Func<X, Y> {
        Y apply(X x);
    }

    public static void main(String[] args) {

        BigInteger zero = BigInteger.valueOf(0);
        BigInteger one = BigInteger.valueOf(1);
        BigInteger fifty = BigInteger.valueOf(50);
        BigInteger tenThousand = BigInteger.valueOf(10000);

        for (BigInteger i = BigInteger.valueOf(1); i.compareTo(fifty) != 1; i = i.add(one)) {

            System.out.print(i + "! = ");
            System.out.println(((SelfApplicable<Func<Func<Func<BigInteger, BigInteger>, Func<BigInteger, BigInteger>>, Func<BigInteger, BigInteger>>>)
                    y -> f -> x -> f.apply(y.apply(y).apply(f)).apply(x))
                    .apply(y -> f -> x -> f.apply(y.apply(y).apply(f)).apply(x))
                    .apply(f -> n -> n.compareTo(zero) == 0 ? one : n.multiply(f.apply(n.subtract(one))))
                    .apply(i));
        }
    }
}