/**
* Maps this elements to a {@code Monoid} and applies {@code foldLeft}, starting with {@code
* monoid.zero()}:
*
* <pre><code>
* foldLeft(monoid.zero(), (ys, x) -> monoid.combine(ys, mapper.apply(x)));
* </code></pre>
*
* @param monoid A Monoid
* @param foldable A foldable
* @param mapper A mapper
* @param <T> type of the foldable elements
* @param <U> Component type of the given monoid.
* @return the folded monoid value.
* @throws NullPointerException if {@code monoid} or {@code mapper} is null
*/
static <T, U> U foldMap(
Monoid<U> monoid, Foldable<T> foldable, Function<? super T, ? extends U> mapper) {
Objects.requireNonNull(monoid, "monoid is null");
Objects.requireNonNull(foldable, "foldable is null");
Objects.requireNonNull(mapper, "mapper is null");
return foldable.foldLeft(monoid.zero(), (ys, x) -> monoid.combine(ys, mapper.apply(x)));
}
/**
* Folds the elements of {@code Foldable} from the left, starting with {@code monoid.zero()} and
* successively calling {@code monoid::combine}.
*
* @param monoid A monoid, providing a {@code zero} and a {@code combine} function.
* @param foldable A foldable
* @param <T> type of the foldable elements
* @return a folded value
* @throws NullPointerException if {@code monoid} or {@code foldable} is null
*/
static <T> T fold(Monoid<T> monoid, Foldable<T> foldable) {
Objects.requireNonNull(monoid, "monoid is null");
Objects.requireNonNull(foldable, "foldable is null");
return foldable.foldLeft(monoid.zero(), monoid::combine);
}
/**
* The monoid of endomorphisms under composition.
*
* @param <A> Value type
* @return The monoid of endomorphisms of type A.
*/
static <A> Monoid<Function<A, A>> endoMonoid() {
return Monoid.of(Function.identity(), Function::compose);
}