http://bartoszmilewski.com/2014/11/04/category-the-essence-of-composition/

CategoryTheory.java

public class CategoryTheory {

    public static <T> Function<T, T> id() {
        return new Function<T, T>() {
            @Override
            public T apply(T arg) {
                return arg;
            }
        };
    }

    interface Function<A, B> {
        public B apply(A arg);
    }

    public static <A, B, C> Function<A, C> compose(final Function<A, B> f, final Function<B, C> g) {
        return new Function<A, C>() {
            @Override
            public C apply(A arg) {
                return g.apply(f.apply(arg));
            }
        };
    }

    public static void main(String[] args) {
        Object a = id().apply(2);
        System.out.println("a = " + a);

        Function<Object, Object> increment = new Function<Object, Object>() {
            @Override
            public Object apply(Object arg) {
                return (Integer)arg + 1;
            }
        };

        Function<Object, Object> show = new Function<Object, Object>() {
            @Override
            public Object apply(Object arg) {
                return arg.toString();
            }
        };

        Function<Object, Object> incrementThenShow = compose(increment, show);

        System.out.println("incrementThenShow.apply(2) = " + incrementThenShow.apply(2));


        // f . id == f

        Function<Object, Object> five = new Function<Object, Object>() {
            @Override
            public Object apply(Object arg) {
                return 5;
            }
        };

        Object res = compose(id(), five).apply("any");

        System.out.println("res = " + res);


        // id . f == f

        Object res2 = compose(five, id()).apply("any");

        System.out.println("res = " + res2);

    }




}