SetIsNotAFullyFaithfulFunctor.java

    public static class SetIsNotAFullyFaithfulFunctor {
        public static void main(String[] args) {
            class Mod {
                private final int mod;
                private final int value;

                Mod(int mod, int value) {
                    this.mod = mod;
                    this.value = value;
                }

                int getValue() {
                    return value;
                }

                @Override
                public int hashCode() {
                    return mod * 31;
                }

                @Override
                public boolean equals(Object other) {
                    // the problem is Set's reliance on structural equality, which is not guaranteed, nor should it be
                    return other instanceof Mod && (value % mod) == (((Mod) other).value % mod);
                }
            }

            Function<Integer, Mod> g = x -> new Mod(2, x);
            Function<Mod, Integer> f = Mod::getValue;

            // map f . map g
            Map.<Mod, Integer>map(f).andThen(toCollection(HashSet::new)) // Set[1, 2]
                    .compose(map(g)).andThen(toCollection(HashSet::new)) // Set[Mod(2,1), Mod(2,2)]
                    .apply(asList(1, 2, 3));

            System.out.println();
            System.out.println("vs");
            System.out.println();

            // map (f . g)
            map(f.compose(g)).andThen(toCollection(HashSet::new)) // Set[1, 2, 3]
                    .apply(asList(1, 2, 3))
                    .forEach(System.out::println);
        }
    }