List.java

package fj.data;

import fj.*;
import fj.control.Trampoline;
import fj.control.parallel.*;
import fj.data.optic.Optional;
import fj.data.optic.*;
import fj.data.vector.V2;
import fj.function.Effect1;

import java.lang.Class;
import java.util.*;

import static fj.Bottom.error;
import static fj.Function.*;
import static fj.Ord.intOrd;
import static fj.Ordering.GT;
import static fj.P.*;
import static fj.Unit.unit;
import static fj.data.Array.mkArray;
import static fj.data.Either.*;
import static fj.data.List.Buffer.*;
import static fj.data.Option.*;
import static fj.data.optic.Optional.optional;
import static fj.data.optic.Prism.prism;
import static fj.data.vector.V.v;
import static fj.function.Booleans.not;

/**
 * Provides an in-memory, immutable, singly linked list.
 */
public abstract class List<A> implements Iterable<A> {
  private List() {

  }

  /**
   * Returns an iterator for this list. This method exists to permit the use in a <code>for</code>-each loop.
   *
   * @return A iterator for this list.
   */
  public final Iterator<A> iterator() {
    return toCollection().iterator();
  }

  /**
   * The first element of the linked list or fails for the empty list.
   *
   * @return The first element of the linked list or fails for the empty list.
   */
  public abstract A head();

  /**
   * The list without the first element or fails for the empty list.
   *
   * @return The list without the first element or fails for the empty list.
   */
  public abstract List<A> tail();

  /**
   * The length of this list.
   *
   * @return The length of this list.
   */
  public final int length() {
    return foldLeft((i, a) -> i + 1, 0);
  }

  /**
   * Returns <code>true</code> if this list is empty, <code>false</code> otherwise.
   *
   * @return <code>true</code> if this list is empty, <code>false</code> otherwise.
   */
  public final boolean isEmpty() {
    return this instanceof Nil;
  }

  /**
   * Returns <code>false</code> if this list is empty, <code>true</code> otherwise.
   *
   * @return <code>false</code> if this list is empty, <code>true</code> otherwise.
   */
  public final boolean isNotEmpty() {
    return this instanceof Cons;
  }

  public final <B> B uncons(final F2<A, List<A>, B> cons, final B nil) {
    return isEmpty() ? nil : cons.f(head(), tail());
  }

  /**
   * Returns the head of this list if there is one or the given argument if this list is empty.
   *
   * @param a The argument to return if this list is empty.
   * @return The head of this list if there is one or the given argument if this list is empty.
   */
  public final A orHead(final F0<A> a) {
    return isEmpty() ? a.f() : head();
  }

  /**
   * Returns the tail of this list if there is one or the given argument if this list is empty.
   *
   * @param as The argument to return if this list is empty.
   * @return The tail of this list if there is one or the given argument if this list is empty.
   */
  public final List<A> orTail(final F0<List<A>> as) {
    return isEmpty() ? as.f() : tail();
  }

  /**
   * Returns the head of the list, if any.
   *
   * @return The optional head of the list.
   */
  public final Option<A> headOption() {
    return isEmpty() ? Option.none() : some(head());
  }

  /**
   * Returns an either projection of this list; the given argument in <code>Left</code> if empty, or
   * the first element in <code>Right</code>.
   *
   * @param x The value to return in left if this list is empty.
   * @return An either projection of this list.
   */
  public final <X> Either<X, A> toEither(final F0<X> x) {
    return isEmpty() ? Either.left(x.f()) : Either.right(head());
  }

  /**
   * Returns a stream projection of this list.
   *
   * @return A stream projection of this list.
   */
  public final Stream<A> toStream() {
    return isEmpty() ? Stream.nil() : Stream.cons(head(), () -> tail().toStream());
  }

  /**
   * Returns a array projection of this list.
   *
   * @return A array projection of this list.
   */
  @SuppressWarnings("unchecked")
  public final Array<A> toArray() {
    return mkArray(toArrayObject());
  }

  public final Object[] toArrayObject() {
    final int length = length();
    final Object[] a = new Object[length];
    List<A> x = this;
    for (int i = 0; i < length; i++) {
      a[i] = x.head();
      x = x.tail();
    }
    return a;
  }

  /**
   * Returns a array projection of this list.
   *
   * @param c The class type of the array to return.
   * @return A array projection of this list.
   */
  @SuppressWarnings({"unchecked", "UnnecessaryFullyQualifiedName"})
  public final Array<A> toArray(final Class<A[]> c) {
    final A[] a = (A[]) java.lang.reflect.Array.newInstance(c.getComponentType(), length());
    List<A> x = this;
    for (int i = 0; i < length(); i++) {
      a[i] = x.head();
      x = x.tail();
    }

    return Array.array(a);
  }

  /**
   * Returns an array from this list.
   *
   * @param c The class type of the array to return.
   * @return An array from this list.
   */
  public final A[] array(final Class<A[]> c) {
    return toArray(c).array(c);
  }

  /**
   * Prepends (cons) the given element to this list to product a new list.
   *
   * @param a The element to prepend.
   * @return A new list with the given element at the head.
   */
  public final List<A> cons(final A a) {
    return new Cons<>(a, this);
  }

  /**
   * Prepends (cons) the given element to this list to product a new list. This method is added to prevent conflict with
   * overloads.
   *
   * @param a The element to prepend.
   * @return A new list with the given element at the head.
   */
  public final List<A> conss(final A a) {
    return new Cons<>(a, this);
  }

  /**
   * Maps the given function across this list.
   *
   * @param f The function to map across this list.
   * @return A new list after the given function has been applied to each element.
   */
  public final <B> List<B> map(final F<A, B> f) {
    final Buffer<B> bs = empty();

    for (List<A> xs = this; xs.isNotEmpty(); xs = xs.tail()) {
      bs.snoc(f.f(xs.head()));
    }

    return bs.toList();
  }

  /**
   * Performs a side-effect for each element of this list.
   *
   * @param f The side-effect to perform for the given element.
   * @return The unit value.
   */
  public final Unit foreach(final F<A, Unit> f) {
    for (List<A> xs = this; xs.isNotEmpty(); xs = xs.tail()) {
      f.f(xs.head());
    }

    return unit();
  }

  /**
   * Performs a side-effect for each element of this list.
   *
   * @param f The side-effect to perform for the given element.
   */
  public final void foreachDoEffect(final Effect1<A> f) {
    for (List<A> xs = this; xs.isNotEmpty(); xs = xs.tail()) {
      f.f(xs.head());
    }
  }

  /**
   * Filters elements from this list by returning only elements which produce <code>true</code> when
   * the given function is applied to them.
   *
   * @param f The predicate function to filter on.
   * @return A new list whose elements all match the given predicate.
   */
  public final List<A> filter(final F<A, Boolean> f) {
    final Buffer<A> b = empty();

    for (List<A> xs = this; xs.isNotEmpty(); xs = xs.tail()) {
      final A h = xs.head();
      if (f.f(h)) {
        b.snoc(h);
      }
    }

    return b.toList();
  }

  /**
   * Filters elements from this list by returning only elements which produce <code>false</code> when
   * the given function is applied to them.
   *
   * @param f The predicate function to filter on.
   * @return A new list whose elements do not match the given predicate.
   */
  public final List<A> removeAll(final F<A, Boolean> f) {
    return filter(compose(not, f));
  }

  /**
   * Removes the first element that equals the given object.
   * To remove all matches, use <code>removeAll(e.eq(a))</code>
   *
   * @param a The element to remove
   * @param e An <code>Equals</code> instance for the element's type.
   * @return A new list whose elements do not match the given predicate.
   */
  public final List<A> delete(final A a, final Equal<A> e) {
    final P2<List<A>, List<A>> p = span(compose(not, e.eq(a)));
    return p._2().isEmpty() ? p._1() : p._1().append(p._2().tail());
  }

  /**
   * Returns the first elements of the head of this list that match the given predicate function.
   *
   * @param f The predicate function to apply on this list until it finds an element that does not
   *          hold, or the list is exhausted.
   * @return The first elements of the head of this list that match the given predicate function.
   */
  public final List<A> takeWhile(final F<A, Boolean> f) {
    final Buffer<A> b = empty();
    boolean taking = true;

    for (List<A> xs = this; xs.isNotEmpty() && taking; xs = xs.tail()) {
      final A h = xs.head();
      if (f.f(h)) {
        b.snoc(h);
      } else {
        taking = false;
      }
    }

    return b.toList();
  }

  /**
   * Removes elements from the head of this list that do not match the given predicate function
   * until an element is found that does match or the list is exhausted.
   *
   * @param f The predicate function to apply through this list.
   * @return The list whose first element does not match the given predicate function.
   */
  public final List<A> dropWhile(final F<A, Boolean> f) {
    List<A> xs;

    //noinspection StatementWithEmptyBody
    for (xs = this; xs.isNotEmpty() && f.f(xs.head()); xs = xs.tail()) ;

    return xs;
  }

  /**
   * Returns a tuple where the first element is the longest prefix of this list that satisfies
   * the given predicate and the second element is the remainder of the list.
   *
   * @param p A predicate to be satisfied by a prefix of this list.
   * @return A tuple where the first element is the longest prefix of this list that satisfies
   *         the given predicate and the second element is the remainder of the list.
   */
  public final P2<List<A>, List<A>> span(final F<A, Boolean> p) {
    final Buffer<A> b = empty();
    for (List<A> xs = this; xs.isNotEmpty(); xs = xs.tail()) {
      if (p.f(xs.head()))
        b.snoc(xs.head());
      else
        return p(b.toList(), xs);
    }
    return p(b.toList(), List.nil());
  }

  /**
   * Returns a tuple where the first element is the longest prefix of this list that does not satisfy
   * the given predicate and the second element is the remainder of the list.
   *
   * @param p A predicate for an element to not satisfy by a prefix of this list.
   * @return A tuple where the first element is the longest prefix of this list that does not satisfy
   *         the given predicate and the second element is the remainder of the list.
   */
  public final P2<List<A>, List<A>> breakk(final F<A, Boolean> p) {
    return span(a -> !p.f(a));
  }

  /**
   * Groups elements according to the given equality implementation by longest
   * sequence of equal elements.
   *
   * @param e The equality implementation for the elements.
   * @return A list of grouped elements.
   */
  public final List<List<A>> group(final Equal<A> e) {
    if (isEmpty())
      return nil();
    else {
      final P2<List<A>, List<A>> z = tail().span(e.eq(head()));
      return cons(z._1().cons(head()), z._2().group(e));
    }
  }


  /**
   * Binds the given function across each element of this list with a final join.
   *
   * @param f The function to apply to each element of this list.
   * @return A new list after performing the map, then final join.
   */
  public final <B> List<B> bind(final F<A, List<B>> f) {
    final Buffer<B> b = empty();

    for (List<A> xs = this; xs.isNotEmpty(); xs = xs.tail()) {
      b.append(f.f(xs.head()));
    }

    return b.toList();
  }

  /**
   * Binds the given function across each element of this list and the given list with a final
   * join.
   *
   * @param lb A given list to bind the given function with.
   * @param f  The function to apply to each element of this list and the given list.
   * @return A new list after performing the map, then final join.
   */
  public final <B, C> List<C> bind(final List<B> lb, final F<A, F<B, C>> f) {
    return lb.apply(map(f));
  }

  /**
   * Binds the given function across each element of this list and the given list with a final
   * join.
   *
   * @param lb A given list to bind the given function with.
   * @param f  The function to apply to each element of this list and the given list.
   * @return A new list after performing the map, then final join.
   */
  public final <B, C> List<C> bind(final List<B> lb, final F2<A, B, C> f) {
    return bind(lb, curry(f));
  }

  /**
   * Promotes the given function of arity-2 to a function on lists.
   *
   * @param f The function to promote to a function on lists.
   * @return The given function, promoted to operate on lists.
   */
  public static <A, B, C> F<List<A>, F<List<B>, List<C>>> liftM2(final F<A, F<B, C>> f) {
    return curry((as, bs) -> as.bind(bs, f));
  }

  /**
   * Binds the given function across each element of this list and the given lists with a final
   * join.
   *
   * @param lb A given list to bind the given function with.
   * @param lc A given list to bind the given function with.
   * @param f  The function to apply to each element of this list and the given lists.
   * @return A new list after performing the map, then final join.
   */
  public final <B, C, D> List<D> bind(final List<B> lb, final List<C> lc, final F<A, F<B, F<C, D>>> f) {
    return lc.apply(bind(lb, f));
  }

  /**
   * Binds the given function across each element of this list and the given lists with a final
   * join.
   *
   * @param lb A given list to bind the given function with.
   * @param lc A given list to bind the given function with.
   * @param ld A given list to bind the given function with.
   * @param f  The function to apply to each element of this list and the given lists.
   * @return A new list after performing the map, then final join.
   */
  public final <B, C, D, E> List<E> bind(final List<B> lb, final List<C> lc, final List<D> ld,
                                   final F<A, F<B, F<C, F<D, E>>>> f) {
    return ld.apply(bind(lb, lc, f));
  }

  /**
   * Binds the given function across each element of this list and the given lists with a final
   * join.
   *
   * @param lb A given list to bind the given function with.
   * @param lc A given list to bind the given function with.
   * @param ld A given list to bind the given function with.
   * @param le A given list to bind the given function with.
   * @param f  The function to apply to each element of this list and the given lists.
   * @return A new list after performing the map, then final join.
   */
  public final <B, C, D, E, F$> List<F$> bind(final List<B> lb, final List<C> lc, final List<D> ld, final List<E> le,
                                        final F<A, F<B, F<C, F<D, F<E, F$>>>>> f) {
    return le.apply(bind(lb, lc, ld, f));
  }

  /**
   * Binds the given function across each element of this list and the given lists with a final
   * join.
   *
   * @param lb A given list to bind the given function with.
   * @param lc A given list to bind the given function with.
   * @param ld A given list to bind the given function with.
   * @param le A given list to bind the given function with.
   * @param lf A given list to bind the given function with.
   * @param f  The function to apply to each element of this list and the given lists.
   * @return A new list after performing the map, then final join.
   */
  public final <B, C, D, E, F$, G> List<G> bind(final List<B> lb, final List<C> lc, final List<D> ld, final List<E> le,
                                          final List<F$> lf, final F<A, F<B, F<C, F<D, F<E, F<F$, G>>>>>> f) {
    return lf.apply(bind(lb, lc, ld, le, f));
  }

  /**
   * Binds the given function across each element of this list and the given lists with a final
   * join.
   *
   * @param lb A given list to bind the given function with.
   * @param lc A given list to bind the given function with.
   * @param ld A given list to bind the given function with.
   * @param le A given list to bind the given function with.
   * @param lf A given list to bind the given function with.
   * @param lg A given list to bind the given function with.
   * @param f  The function to apply to each element of this list and the given lists.
   * @return A new list after performing the map, then final join.
   */
  public final <B, C, D, E, F$, G, H> List<H> bind(final List<B> lb, final List<C> lc, final List<D> ld, final List<E> le,
                                             final List<F$> lf, final List<G> lg,
                                             final F<A, F<B, F<C, F<D, F<E, F<F$, F<G, H>>>>>>> f) {
    return lg.apply(bind(lb, lc, ld, le, lf, f));
  }

  /**
   * Binds the given function across each element of this list and the given lists with a final
   * join.
   *
   * @param lb A given list to bind the given function with.
   * @param lc A given list to bind the given function with.
   * @param ld A given list to bind the given function with.
   * @param le A given list to bind the given function with.
   * @param lf A given list to bind the given function with.
   * @param lg A given list to bind the given function with.
   * @param lh A given list to bind the given function with.
   * @param f  The function to apply to each element of this list and the given lists.
   * @return A new list after performing the map, then final join.
   */
  public final <B, C, D, E, F$, G, H, I> List<I> bind(final List<B> lb, final List<C> lc, final List<D> ld, final List<E> le,
                                                final List<F$> lf, final List<G> lg, final List<H> lh,
                                                final F<A, F<B, F<C, F<D, F<E, F<F$, F<G, F<H, I>>>>>>>> f) {
    return lh.apply(bind(lb, lc, ld, le, lf, lg, f));
  }

  /**
   * Performs a bind across each list element, but ignores the element value each time.
   *
   * @param bs The list to apply in the final join.
   * @return A new list after the final join.
   */
  public final <B> List<B> sequence(final List<B> bs) {
    final F<A, List<B>> c = constant(bs);
    return bind(c);
  }

  /**
   * Sequence the given list and collect the output on the right side of an either.
   *
   * @param list the given list
   * @param <B>  the type of the right value
   * @param <L>  the type of the left value
   * @return the either
   */
  public static final <L, B> Either<L, List<B>> sequenceEither(final List<Either<L, B>> list) {
    return list.traverseEither(identity());
  }

  /**
   * Sequence the given list and collect the output on the left side of an either.
   *
   * @param list the given list
   * @param <R>  the type of the right value
   * @param <B>  the type of the left value
   * @return the either
   */
  public static final <R, B> Either<List<B>, R> sequenceEitherLeft(final List<Either<B, R>> list) {
    return list.traverseEitherLeft(identity());
  }

  /**
   * Sequence the given list and collect the output on the right side of an either.
   *
   * @param list the given list
   * @param <B>  the type of the right value
   * @param <L>  the type of the left value
   * @return the either
   */
  public static final <L, B> Either<L, List<B>> sequenceEitherRight(final List<Either<L, B>> list) {
    return list.traverseEitherRight(identity());
  }

  /**
   * Sequence the given list and collect the output as a function.
   *
   * @param list the given list
   * @param <C>  the type of the input value
   * @param <B>  the type of the output value
   * @return the either
   */
  public static final <C, B> F<C, List<B>> sequenceF(final List<F<C, B>> list) {
    return list.traverseF(identity());
  }

  /**
   * Sequence the given list and collect the output as an IO.
   *
   * @param list the given list
   * @param <B>  the type of the IO value
   * @return the IO
   */
  public static final <B> IO<List<B>> sequenceIO(final List<IO<B>> list) {
    return list.traverseIO(identity());
  }

  /**
   * Sequence the given list and collect the output as an list.
   *
   * @param list the given list
   * @param <B>  the type of the list value
   * @return the list
   */
  public static final <B> List<List<B>> sequenceList(final List<List<B>> list) {
    return list.traverseList(identity());
  }

  /**
   * Sequence the given list and collect the output as an list.
   *
   * @param list the given list
   * @param <B>  the type of the list value
   * @return the list
   */
  public static final <B> Option<List<B>> sequenceOption(final List<Option<B>> list) {
    return list.traverseOption(identity());
  }

  /**
   * Sequence the given list and collect the output as a P1.
   *
   * @param list the given list
   * @param <B>  the type of the P1 value
   * @return the P1
   */
  public static final <B> P1<List<B>> sequenceP1(final List<P1<B>> list) {
    return list.traverseP1(identity());
  }

  /**
   * Sequence the given list and collect the output as a seq.
   *
   * @param list the given list
   * @param <B>  the type of the seq value
   * @return the seq
   */
  public static final <B> Seq<List<B>> sequenceSeq(final List<Seq<B>> list) {
    return list.traverseSeq(identity());
  }

  /**
   * Sequence the given list and collect the output as a set; use the given ord to order the set.
   *
   * @param ord  the given ord
   * @param list the given list
   * @param <B>  the type of the set value
   * @return the either
   */
  public static final <B> Set<List<B>> sequenceSet(final Ord<B> ord, final List<Set<B>> list) {
    return list.traverseSet(ord, identity());
  }

  /**
   * Sequence the given list and collect the output as a stream.
   *
   * @param list the given list
   * @param <B>  the type of the stream value
   * @return the stream
   */
  public static final <B> Stream<List<B>> sequenceStream(final List<Stream<B>> list) {
    return list.traverseStream(identity());
  }

  /**
   * Sequence the given list and collect the output as a trampoline.
   *
   * @param list the given trampoline
   * @param <B>  the type of the stream value
   * @return the stream
   */
  public static final <B> Trampoline<List<B>> sequenceTrampoline(final List<Trampoline<B>> list) {
    return list.traverseTrampoline(identity());
  }

  /**
   * Sequence the given list and collect the output as a validation; use the given semigroup to reduce the errors.
   *
   * @param semigroup the given semigroup
   * @param list      the given list
   * @param <E>       the type of the failure value
   * @param <B>       the type of the success value
   * @return the validation
   */
  public static final <E, B> Validation<E, List<B>> sequenceValidation(final Semigroup<E> semigroup, final List<Validation<E, B>> list) {
    return list.traverseValidation(semigroup, identity());
  }

  /**
   * Traverse through the List with given function.
   *
   * @param f The function that produces Either value.
   * @return error in left or f mapped list in right.
   */
  public final <B, E> Either<E, List<B>> traverseEither(final F<A, Either<E, B>> f) {
    return foldRight(
        (a, acc) -> f.f(a).right().bind(e -> acc.right().map(es -> es.cons(e))),
        Either.right(List.nil())
    );
  }

  /**
   * Traverse this list with the given function and collect the output on the left side of an either.
   *
   * @param f   the given function
   * @param <R> the type of the left value
   * @param <B> the type of the right value
   * @return the either
   */
  public final <R, B> Either<List<B>, R> traverseEitherLeft(final F<A, Either<B, R>> f) {
    return foldRight(
        (element, either) -> f.f(element).left().bind(elementInner -> either.left().map(list -> list.cons(elementInner))),
        left(nil()));
  }

  /**
   * Traverse this list with the given function and collect the output on the right side of an either.
   *
   * @param f   the given function
   * @param <L> the type of the left value
   * @param <B> the type of the right value
   * @return the either
   */
  public final <L, B> Either<L, List<B>> traverseEitherRight(final F<A, Either<L, B>> f) {
    return foldRight(
        (element, either) -> f.f(element).right().bind(elementInner -> either.right().map(list -> list.cons(elementInner))),
        right(nil()));
  }

  /**
   * Traverse this list with the given function and collect the output as a function.
   *
   * @param f   the given function
   * @param <C> the type of the input value
   * @param <B> the type of the output value
   * @return the function
   */
  public final <C, B> F<C, List<B>> traverseF(F<A, F<C, B>> f) {
    return this.foldRight(
        (a, acc) -> Function.bind(acc,
            (bs) -> Function.compose(bs::cons, f.f(a))),
        constant(List.nil())
    );
  }

  /**
   * Traverse this list with the given function and collect the output as an IO.
   *
   * @param f   the given function
   * @param <B> the type of the IO value
   * @return the IO
   */
  public final <B> IO<List<B>> traverseIO(F<A, IO<B>> f) {
    return this.foldRight(
        (a, acc) -> IOFunctions.bind(f.f(a), b -> IOFunctions.map(acc, bs -> bs.cons(b))),
        IOFunctions.unit(List.nil())
    );
  }

  /**
   * Traverse this list with the given function and collect the output as a list.
   *
   * @param f   the given function
   * @param <B> the type of the list value
   * @return the list
   */
  public final <B> List<List<B>> traverseList(final F<A, List<B>> f) {
    return foldRight(
        (a, acc) -> f.f(a).bind(b -> acc.map(bs -> bs.cons(b))),
        single(List.nil()));
  }

  /**
   * Traverses through the List with the given function
   *
   * @param f The function that produces Option value
   * @return none if applying f returns none to any element of the list or f mapped list in some .
   */
  public final <B> Option<List<B>> traverseOption(final F<A, Option<B>> f) {
    return foldRight(
        (a, obs) -> f.f(a).bind(o -> obs.map(os -> os.cons(o))),
        some(List.nil())
    );
  }

  /**
   * Traverse this list with the given function and collect the output as a p1.
   *
   * @param f   the given function
   * @param <B> the type of the p1 value
   * @return the p1
   */
  public final <B> P1<List<B>> traverseP1(final F<A, P1<B>> f) {
    return foldRight(
        (a, acc) -> f.f(a).bind(b -> acc.map(bs -> bs.cons(b))),
        p(List.nil())
    );
  }

  /**
   * Traverse this list with the given function and collect the output as a seq.
   *
   * @param f   the given function
   * @param <B> the type of the seq value
   * @return the seq
   */
  public final <B> Seq<List<B>> traverseSeq(final F<A, Seq<B>> f) {
    return foldRight(
        (element, seq) -> f.f(element).bind(elementInner -> seq.map(list -> list.cons(elementInner))),
        Seq.single(nil()));
  }

  /**
   * Traverse this list with the given function and collect the output as a set; use the given ord to order the set.
   *
   * @param ord the given ord
   * @param f   the given function
   * @param <B> the type of the set value
   * @return the set
   */
  public final <B> Set<List<B>> traverseSet(final Ord<B> ord, final F<A, Set<B>> f) {
    final Ord<List<B>> listOption = Ord.listOrd(ord);
    return foldRight(
        (element, set) -> f.f(element).bind(listOption, elementInner -> set.map(listOption, list -> list.cons(elementInner))),
        Set.single(listOption, nil()));
  }

  /**
   * Traverse this list with the given function and collect the output as a stream.
   *
   * @param f   the given function
   * @param <B> the type of the stream value
   * @return the stream
   */
  public final <B> Stream<List<B>> traverseStream(final F<A, Stream<B>> f) {
    return foldRight(
        (a, acc) -> f.f(a).bind(s -> acc.map(ss -> ss.cons(s))),
        Stream.single(nil()));
  }

  /**
   * Traverse this list with the given function and collect the output as a trampoline.
   *
   * @param f   the given function
   * @param <B> the type of the trampoline value
   * @return the trampoline
   */
  public final <B> Trampoline<List<B>> traverseTrampoline(final F<A, Trampoline<B>> f) {
    return foldRight(
        (a, acc) -> f.f(a).bind(b -> acc.map(bs -> bs.cons(b))),
        Trampoline.pure(List.nil()));
  }

  public final <B> Promise<List<B>> traversePromise(final F<A, Promise<B>> f) {
    return foldRight(
        (a, acc) -> f.f(a).bind(b -> acc.fmap(bs -> bs.cons(b))),
        Promise.promise(Strategy.idStrategy(), p(List.nil())));
  }

  /**
   * Traverse this list with the given function and collect the output as a validation; use the given semigroup to reduce the errors.
   *
   * @param s   the given semigroup
   * @param f   the given function
   * @param <E> the type of the failure value
   * @param <B> the type of the success value
   * @return the validation
   */
  public final <E, B> Validation<E, List<B>> traverseValidation(Semigroup<E> s, final F<A, Validation<E, B>> f) {
    return Validation.sequence(s, map(f));
  }

  public final <B> V2<List<B>> traverseV2(final F<A, V2<B>> f) {
    return foldRight(
        (a, acc) -> acc.apply(f.f(a).<F<List<B>, List<B>>> map(e -> es -> es.cons(e))),
        v(List.nil(), List.nil()));
  }

    /**
   * Performs function application within a list (applicative functor pattern).
   *
   * @param lf The list of functions to apply.
   * @return A new list after applying the given list of functions through this list.
   */
  public final <B> List<B> apply(final List<F<A, B>> lf) {
    return lf.bind(this::map);
  }

  /**
   * Appends the given list to this list.
   *
   * @param as The list to append to this one.
   * @return A new list that has appended the given list.
   */
  public final List<A> append(final List<A> as) {
    return fromList(this).prependToList(as);
  }

  /**
   * Performs a right-fold reduction across this list.
   *
   * @param f The function to apply on each element of the list.
   * @param b The beginning value to start the application from.
   * @return The final result after the right-fold reduction.
   */
  public final <B> B foldRight(final F<A, F<B, B>> f, final B b) {
    return foldRight(uncurryF2(f), b);
  }

  /**
   * Performs a right-fold reduction across this list. This function uses O(length) stack space.
   *
   * @param f The function to apply on each element of the list.
   * @param b The beginning value to start the application from.
   * @return The final result after the right-fold reduction.
   */
  public final <B> B foldRight(final F2<A, B, B> f, final B b) {
    return reverse().foldLeft(flip(f), b);
  }

  /**
   * Performs a right-fold reduction across this list in O(1) stack space.
   * @param f The function to apply on each element of the list.
   * @param b The beginning value to start the application from.
   * @return A Trampoline containing the final result after the right-fold reduction.
   */
  public final <B> Trampoline<B> foldRightC(final F2<A, B, B> f, final B b) {
    return Trampoline.suspend(() -> isEmpty() ? Trampoline.pure(b) : tail().foldRightC(f, b).map(f.f(head())));
  }

  /**
   * Performs a left-fold reduction across this list. This function runs in constant space.
   *
   * @param f The function to apply on each element of the list.
   * @param b The beginning value to start the application from.
   * @return The final result after the left-fold reduction.
   */
  public final <B> B foldLeft(final F<B, F<A, B>> f, final B b) {
    return foldLeft(uncurryF2(f), b);
  }

  /**
   * Performs a left-fold reduction across this list. This function runs in constant space.
   *
   * @param f The function to apply on each element of the list.
   * @param b The beginning value to start the application from.
   * @return The final result after the left-fold reduction.
   */
  public final <B> B foldLeft(final F2<B, A, B> f, final B b) {
    B x = b;

    for (List<A> xs = this; !xs.isEmpty(); xs = xs.tail()) {
      x = f.f(x, xs.head());
    }

    return x;
  }

  /**
   * Takes the first 2 elements of the list and applies the function to them,
   * then applies the function to the result and the third element and so on.
   *
   * @param f The function to apply on each element of the list.
   * @return The final result after the left-fold reduction.
   */
  public final A foldLeft1(final F2<A, A, A> f) {
    if (isEmpty())
      throw error("Undefined: foldLeft1 on empty list");
    return tail().foldLeft(f, head());
  }

  /**
   * Takes the first 2 elements of the list and applies the function to them,
   * then applies the function to the result and the third element and so on.
   *
   * @param f The function to apply on each element of the list.
   * @return The final result after the left-fold reduction.
   */
  public final A foldLeft1(final F<A, F<A, A>> f) {
    return foldLeft1(uncurryF2(f));
  }

  /**
   * Reverse this list in constant stack space.
   *
   * @return A new list that is the reverse of this one.
   */
  public final List<A> reverse() {
    return foldLeft((as, a) -> cons(a, as), nil());
  }

  /**
   * Returns the element at the given index if it exists, fails otherwise.
   *
   * @param i The index at which to get the element to return.
   * @return The element at the given index if it exists, fails otherwise.
   */
  public final A index(final int i) {
    if (i < 0 || i > length() - 1)
      throw error("index " + i + " out of range on list with length " + length());
    else {
      List<A> xs = this;

      for (int c = 0; c < i; c++) {
        xs = xs.tail();
      }

      return xs.head();
    }
  }

  /**
   * Takes the given number of elements from the head of this list if they are available.
   *
   * @param i The maximum number of elements to take from this list.
   * @return A new list with a length the same, or less than, this list.
   */
  public final List<A> take(final int i) {
    Buffer<A> result = empty();
    List<A> list = this;
    int index = i;
    while (index > 0 && list.isNotEmpty()) {
      result.snoc(list.head());
      list = list.tail();
      index--;
    }
    return result.toList();
  }

  /**
   * Drops the given number of elements from the head of this list if they are available.
   *
   * @param i The number of elements to drop from the head of this list.
   * @return A list with a length the same, or less than, this list.
   */
  public final List<A> drop(final int i) {
    List<A> xs = this;

    for (int c = 0; xs.isNotEmpty() && c < i; xs = xs.tail())
      c++;

    return xs;
  }

  /**
   * Splits this list into two lists at the given index. If the index goes out of bounds, then it is
   * normalised so that this function never fails.
   *
   * @param i The index at which to split this list in two parts.
   * @return A pair of lists split at the given index of this list.
   */
  public final P2<List<A>, List<A>> splitAt(final int i) {
    int c = 0;
    List<A> first = List.nil();
    List<A> second = nil();
    for (List<A> xs = this; xs.isNotEmpty(); xs = xs.tail()) {
      final A h = xs.head();
      if (c < i) {
          first = first.cons(h);
      } else {
          second = second.cons(h);
      }
      c++;
    }
    return p(first.reverse(), second.reverse());
  }

  /**
   * Splits this list into lists of the given size. If the size of this list is not evenly divisible by
   * the given number, the last partition will contain the remainder.
   *
   * @param n The size of the partitions into which to split this list.
   * @return A list of sublists of this list, of at most the given size.
   */
  public final List<List<A>> partition(final int n) {
    if (n < 1)
      throw error("Can't create list partitions shorter than 1 element long.");
    if (isEmpty())
      throw error("Partition on empty list.");
    return unfold(as -> as.isEmpty() ? Option.none() : some(as.splitAt(n)), this);
  }

  /**
   * Partitions the list into a tuple where the first element contains the
   * items that satisfy the the predicate f and the second element contains the
   * items that does not.  The relative order of the elements in the returned tuple
   * is the same as the original list.
   *
   * @param f Predicate function.
   */
  public final P2<List<A>, List<A>> partition(F<A, Boolean> f) {
    P2<List<A>, List<A>> p2 = foldLeft((acc, a) ->
      f.f(a) ? p(acc._1().cons(a), acc._2()) : p(acc._1(), acc._2().cons(a)),
      p(nil(), nil())
    );
    return p(p2._1().reverse(), p2._2().reverse());
  }

  /**
   * Returns the list of initial segments of this list, shortest first.
   *
   * @return The list of initial segments of this list, shortest first.
   */
  public final List<List<A>> inits() {
    List<List<A>> s = single(List.nil());
    if (isNotEmpty())
      s = s.append(tail().inits().map(List.<A>cons().f(head())));
    return s;
  }

  /**
   * Returns the list of final segments of this list, longest first.
   *
   * @return The list of final segments of this list, longest first.
   */
  public final List<List<A>> tails() {
    return isEmpty() ? single(List.nil()) : cons(this, tail().tails());
  }

  /**
   * Sorts this list using the given order over elements using a <em>merge sort</em> algorithm.
   *
   * @param o The order over the elements of this list.
   * @return A sorted list according to the given order.
   */
  public final List<A> sort(final Ord<A> o) {
    if (isEmpty())
      return nil();
    else if (tail().isEmpty())
      return this;
    else {
      final class Merge {
        List<A> merge(List<A> xs, List<A> ys, final Ord<A> o) {
          final Buffer<A> buf = empty();

          while (true) {
            if (xs.isEmpty()) {
              buf.append(ys);
              break;
            }

            if (ys.isEmpty()) {
              buf.append(xs);
              break;
            }

            final A x = xs.head();
            final A y = ys.head();

            if (o.isLessThanOrEqualTo(x, y)) {
              buf.snoc(x);
              xs = xs.tail();
            } else {
              buf.snoc(y);
              ys = ys.tail();
            }
          }

          return buf.toList();
        }
      }

      final P2<List<A>, List<A>> s = splitAt(length() / 2);
      return new Merge().merge(s._1().sort(o), s._2().sort(o), o);
    }
  }

  /**
   * Zips this list with the given list using the given function to produce a new list. If this list
   * and the given list have different lengths, then the longer list is normalised so this function
   * never fails.
   *
   * @param bs The list to zip this list with.
   * @param f  The function to zip this list and the given list with.
   * @return A new list with a length the same as the shortest of this list and the given list.
   */
  public final <B, C> List<C> zipWith(List<B> bs, final F<A, F<B, C>> f) {
    final Buffer<C> buf = empty();
    List<A> as = this;

    while (as.isNotEmpty() && bs.isNotEmpty()) {
      buf.snoc(f.f(as.head()).f(bs.head()));
      as = as.tail();
      bs = bs.tail();
    }

    return buf.toList();
  }

  /**
   * Zips this list with the given list using the given function to produce a new list. If this list
   * and the given list have different lengths, then the longer list is normalised so this function
   * never fails.
   *
   * @param bs The list to zip this list with.
   * @param f  The function to zip this list and the given list with.
   * @return A new list with a length the same as the shortest of this list and the given list.
   */
  public final <B, C> List<C> zipWith(final List<B> bs, final F2<A, B, C> f) {
    return zipWith(bs, curry(f));
  }

  /**
   * Provides a first-class version of zipWith
   *
   * @return The first-class version of zipWith
   */
  public static <A, B, C> F<List<A>, F<List<B>, F<F<A, F<B, C>>, List<C>>>> zipWith() {
    return curry((as, bs, f) -> as.zipWith(bs, f));
  }

  /**
   * Zips this list with the given list to produce a list of pairs. If this list and the given list
   * have different lengths, then the longer list is normalised so this function never fails.
   *
   * @param bs The list to zip this list with.
   * @return A new list with a length the same as the shortest of this list and the given list.
   */
  public final <B> List<P2<A, B>> zip(final List<B> bs) {
    final F<A, F<B, P2<A, B>>> __2 = p2();
    return zipWith(bs, __2);
  }

  /**
   * The first-class version of the zip function.
   *
   * @return A function that zips the given lists to produce a list of pairs.
   */
  public static <A, B> F<List<A>, F<List<B>, List<P2<A, B>>>> zip() {
    return curry(List::zip);
  }

  /**
   * Zips this list with the index of its element as a pair.
   *
   * @return A new list with the same length as this list.
   */
  public final List<P2<A, Integer>> zipIndex() {
    return zipWith(range(0, length()), a -> i -> p(a, i));
  }

  /**
   * Appends (snoc) the given element to this list to produce a new list.
   *
   * @param a The element to append to this list.
   * @return A new list with the given element appended.
   */
  public final List<A> snoc(final A a) {
    return fromList(this).snoc(a).toList();
  }

  /**
   * Returns <code>true</code> if the predicate holds for all of the elements of this list,
   * <code>false</code> otherwise (<code>true</code> for the empty list).
   *
   * @param f The predicate function to test on each element of this list.
   * @return <code>true</code> if the predicate holds for all of the elements of this list,
   *         <code>false</code> otherwise.
   */
  public final boolean forall(final F<A, Boolean> f) {
    return isEmpty() || f.f(head()) && tail().forall(f);
  }

  /**
   * Returns <code>true</code> if the predicate holds for at least one of the elements of this list,
   * <code>false</code> otherwise (<code>false</code> for the empty list).
   *
   * @param f The predicate function to test on the elements of this list.
   * @return <code>true</code> if the predicate holds for at least one of the elements of this
   *         list.
   */
  public final boolean exists(final F<A, Boolean> f) {
    return find(f).isSome();
  }

  /**
   * Finds the first occurrence of an element that matches the given predicate or no value if no
   * elements match.
   *
   * @param f The predicate function to test on elements of this list.
   * @return The first occurrence of an element that matches the given predicate or no value if no
   *         elements match.
   */
  public final Option<A> find(final F<A, Boolean> f) {
    for (List<A> as = this; as.isNotEmpty(); as = as.tail()) {
      if (f.f(as.head()))
        return some(as.head());
    }

    return none();
  }

  /**
   * Intersperses the given argument between each element of this list.
   *
   * @param a The separator to intersperse in this list.
   * @return A list with the given separator interspersed.
   */
  public final List<A> intersperse(final A a) {
    return isEmpty() || tail().isEmpty() ?
           this :
            cons(head(), tail().bind(a2 -> list(a, a2)));
  }

  /**
   * Intersperses this list through the given list then joins the results.
   *
   * @param as The list to intersperse through.
   * @return This list through the given list then joins the results.
   */
  @SuppressWarnings("unchecked")
  public final List<A> intercalate(final List<List<A>> as) {
    return join(as.intersperse(this));
  }

  /**
   * Removes duplicates according to object equality.
   *
   * @return A list without duplicates according to object equality.
   */
  public final List<A> nub() {
    return nub(Equal.anyEqual());
  }

  /**
   * Removes duplicates according to the given equality. Warning: O(n^2).
   *
   * @param eq Equality over the elements.
   * @return A list without duplicates.
   */
  public final List<A> nub(final Equal<A> eq) {
    return isEmpty() ? this : cons(head(), tail().filter(a -> !eq.eq(a, head())).nub(eq));
  }

  /**
   * Removes duplicates according to the given ordering. This function is O(n).
   *
   * @param o An ordering for the elements.
   * @return A list without duplicates.
   */
  @SuppressWarnings("unchecked")
  public final List<A> nub(final Ord<A> o) {
    return sort(o).group(o.equal()).map(List.head_());
  }


  /**
   * First-class head function.
   *
   * @return A function that gets the head of a given list.
   */
  public static <A> F<List<A>, A> head_() {
    return List::head;
  }


	/**
	 * Reutrns the tail of the list, if any.
	 * @return The optional tail of the list.
	 */
	public final Option<List<A>> tailOption() {
		return isEmpty() ? none() : some(tail());
	}

  /**
   * First-class tail function.
   *
   * @return A function that gets the tail of a given list.
   */
  public static <A> F<List<A>, List<A>> tail_() {
    return List::tail;
  }

  /**
   * Returns a new list of all the items in this list that do not appear in the given list.
   *
   * @param eq an equality for the items of the lists.
   * @param xs a list to subtract from this list.
   * @return a list of all the items in this list that do not appear in the given list.
   */
  public final List<A> minus(final Equal<A> eq, final List<A> xs) {
    return removeAll(compose(Monoid.disjunctionMonoid.sumLeft(), xs.mapM(curry(eq.eq()))));
  }



    /**
   * Maps the given function of arity-2 across this list and returns a function that applies all the resulting
   * functions to a given argument.
   *
   * @param f A function of arity-2
   * @return A function that, when given an argument, applies the given function to that argument and every element
   *         in this list.
   */
  public final <B, C> F<B, List<C>> mapM(final F<A, F<B, C>> f) {
    return sequence_(map(f));
  }

  /**
   * Maps the given function across this list by binding through the Option monad.
   *
   * @param f The function to apply through the this list.
   * @return A possible list of values after binding through the Option monad.
   */
  public final <B> Option<List<B>> mapMOption(final F<A, Option<B>> f) {
    return traverseOption(f);
  }

  /**
   * Maps the given function across this list by binding through the Trampoline monad.
   *
   * @param f The function to apply through the this list.
   * @return A list of values in the Trampoline monad.
   */
  public final <B> Trampoline<List<B>> mapMTrampoline(final F<A, Trampoline<B>> f) {
    return foldRight((a, bs) -> f.f(a).bind(b -> bs.map(bbs -> bbs.cons(b))), Trampoline.pure(List.nil()));
  }

  /**
   * Returns the index of the first element in this list which is equal (by the given equality) to the
   * query element, or None if there is no such element.
   *
   * @param e An equality for this list's elements.
   * @param a A query element.
   * @return The index of the first element in this list which is equal (by the given equality) to the
   *         query element, or None if there is no such element.
   */
  public final Option<Integer> elementIndex(final Equal<A> e, final A a) {
    return lookup(e, zipIndex(), a);
  }

  /**
   * Returns the last element of this list. Undefined for the empty list.
   *
   * @return The last element of this list or throws an error if this list is empty.
   */
  public final A last() {
    A a = head();
    for (List<A> xs = tail(); xs.isNotEmpty(); xs = xs.tail())
      a = xs.head();
    return a;
  }

  /**
   * Returns all but the last element of this list. Undefiend for the empty list.
   *
   * @return All but the last element of this list. Undefiend for the empty list.
   */
  public final List<A> init() {
    List<A> ys = this;
    final Buffer<A> a = empty();
    while(ys.isNotEmpty() && ys.tail().isNotEmpty()) {
      a.snoc(ys.head());
      ys = ys.tail();
    }
    return a.toList();
  }

  /**
   * Inserts the given element before the first element that is greater than or equal to it according
   * to the given ordering.
   *
   * @param f An ordering function to compare elements.
   * @param x The element to insert.
   * @return A new list with the given element inserted before the first element that is greater than or equal to
   *         it according to the given ordering.
   */
  public final List<A> insertBy(final F<A, F<A, Ordering>> f, final A x) {
    List<A> ys = this;
    Buffer<A> xs = empty();
    while (ys.isNotEmpty() && f.f(x).f(ys.head()) == GT) {
      xs = xs.snoc(ys.head());
      ys = ys.tail();
    }
    return xs.append(ys.cons(x)).toList();
  }

  /**
   * Returns the most common element in this list.
   *
   * @param o An ordering for the elements of the list.
   * @return The most common element in this list.
   */
  public final A mode(final Ord<A> o) {
    return sort(o).group(o.equal()).maximum(intOrd.contramap(List.length_())).head();
  }

  /**
   * Groups the elements of this list by a given keyFunction into a {@link TreeMap}.
   *
   * @param keyFunction The function to select the keys for the map.
   * @param keyOrd An order for the keys of the tree map.
   * @return A TreeMap containing the keys with the accumulated list of matched elements.
   */
  public final <B> TreeMap<B, List<A>> groupBy(final F<A, B> keyFunction, final Ord<B> keyOrd) {
    return groupBy(keyFunction, identity(), keyOrd);
  }

  /**
   * Groups the elements of this list by a given keyFunction into a {@link TreeMap} and transforms
   * the matching elements with the given valueFunction. The ordering of the keys is determined by
   * the keyOrd parameter.
   *
   * @param keyFunction The function to select the keys for the map.
   * @param valueFunction The function to apply on each matching value.
   * @param keyOrd An order for the keys of the tree map.
   * @return A TreeMap containing the keys with the accumulated list of matched and mapped elements.
   */
  public final <B, C> TreeMap<B, List<C>> groupBy(
      final F<A, B> keyFunction,
      final F<A, C> valueFunction,
      final Ord<B> keyOrd) {
    return this.groupBy(keyFunction, valueFunction, List.nil(), List::cons, keyOrd);
  }

  /**
   * Groups the elements of this list by a given keyFunction into a {@link TreeMap} and transforms
   * the matching elements with the given valueFunction. The ordering of the keys is determined by
   * the keyOrd parameter.
   *
   * @param keyFunction The function to select the keys for the map.
   * @param valueFunction The function to apply on each matching value.
   * @param monoid A monoid, which defines the accumulator for the values and the zero value.
   * @param keyOrd An order for the keys of the tree map.
   * @return A TreeMap containing the keys with the accumulated list of matched and mapped elements.
   */
  public final <B, C> TreeMap<B, C> groupBy(
      final F<A, B> keyFunction,
      final F<A, C> valueFunction,
      final Monoid<C> monoid,
      final Ord<B> keyOrd) {
    return groupBy(keyFunction, valueFunction, monoid.zero(),
        uncurryF2(monoid.sum()), keyOrd);
  }

  /**
   * Groups the elements of this list by a given keyFunction, applies the valueFunction and
   * accumulates the mapped values with the given grouping accumulator function on the grouping
   * identity.
   *
   * @param keyFunction The function to select the keys.
   * @param valueFunction The function to apply on each element.
   * @param groupingIdentity The identity, or start value, for the grouping.
   * @param groupingAcc The accumulator to apply on each matching value.
   * @param keyOrd An order for the keys of the tree map.
   * @return A TreeMap containing the keys with the accumulated result of matched and mapped
   * elements.
   */
  public final <B, C, D> TreeMap<B, D> groupBy(
      final F<A, B> keyFunction,
      final F<A, C> valueFunction,
      final D groupingIdentity,
      final F2<C, D, D> groupingAcc,
      final Ord<B> keyOrd) {
    java.util.TreeMap<B, D> buffer = new java.util.TreeMap<>(keyOrd.toComparator());
    foreachDoEffect(element -> {
      final B key = keyFunction.f(element);
      final C value = valueFunction.f(element);
      buffer.put(key, buffer.containsKey(key)
          ? groupingAcc.f(value, buffer.get(key))
          : groupingAcc.f(value, groupingIdentity));
    });
    return TreeMap.fromMutableMap(keyOrd, buffer);
  }



  /**
   * Returns whether or not all elements in the list are equal according to the given equality test.
   *
   * @param eq The equality test.
   * @return Whether or not all elements in the list are equal according to the given equality test.
   */
  public final boolean allEqual(final Equal<A> eq) {
    return isEmpty() || tail().isEmpty() || eq.eq(head(), tail().head()) && tail().allEqual(eq);
  }

  public final boolean isPrefixOf(final Equal<A> eq, final List<A> xs) {
    final Iterator<A> i = iterator();
    final Iterator<A> j = xs.iterator();

    while (i.hasNext() && j.hasNext()) {
      if (!eq.eq(i.next(), j.next())) {
        return false;
      }
    }

    return !i.hasNext();
  }

  public final boolean isSuffixOf(final Equal<A> eq, final List<A> xs) {
    final Iterator<A> i = iterator();
    final Iterator<A> j = xs.drop(xs.length() - length()).iterator();

    while (i.hasNext() && j.hasNext()) {
      if (!eq.eq(i.next(), j.next())) {
        return false;
      }
    }

    return !i.hasNext();
  }

  /**
   * First-class length.
   *
   * @return A function that gets the length of a given list.
   */
  public static <A> F<List<A>, Integer> length_() {
    return List::length;
  }

  /**
   * Returns the maximum element in this list according to the given ordering.
   *
   * @param o An ordering for the elements of the list.
   * @return The maximum element in this list according to the given ordering.
   */
  public final A maximum(final Ord<A> o) {
    return foldLeft1(o::max);
  }

  /**
   * Returns the maximum element in this list according to the given ordering.
   *
   * @param o An ordering for the elements of the list.
   * @return The optional maximum element in this list according to the given ordering.
   */
  public final Option<A> maximumOption(final Ord<A> o) {
    return NonEmptyList.fromList(this).map(nel -> nel.maximum(o));
  }

  /**
   * Returns the minimum element in this list according to the given ordering.
   *
   * @param o An ordering for the elements of the list.
   * @return The minimum element in this list according to the given ordering.
   */
  public final A minimum(final Ord<A> o) {
    return foldLeft1(o::min);
  }

  /**
   * Returns the minimum element in this list according to the given ordering.
   *
   * @param o An ordering for the elements of the list.
   * @return The optional minimum element in this list according to the given ordering.
   */
  public final Option<A> minimumOption(final Ord<A> o) {
    return NonEmptyList.fromList(this).map(nel -> nel.minimum(o));
  }

  public final java.util.List<A> toJavaList() {
    return new java.util.LinkedList<>(toCollection());
  }

  /**
   * Projects an immutable collection of this list.
   *
   * @return An immutable collection of this list.
   */
  public final Collection<A> toCollection() {
    return new AbstractCollection<A>() {
      public Iterator<A> iterator() {
        return new Iterator<A>() {
          private List<A> xs = List.this;

          public boolean hasNext() {
            return xs.isNotEmpty();
          }

          public A next() {
            if (xs.isEmpty())
              throw new NoSuchElementException();
            else {
              final A a = xs.head();
              xs = xs.tail();
              return a;
            }
          }

          public void remove() {
            throw new UnsupportedOperationException();
          }
        };
      }

      public int size() {
        return length();
      }
    };
  }

  private static final class Nil<A> extends List<A> {
    public static final Nil<Object> INSTANCE = new Nil<>();

    public A head() {
      throw error("head on empty list");
    }

    public List<A> tail() {
      throw error("tail on empty list");
    }
  }

  private static final class Cons<A> extends List<A> {
    private final A head;
    private List<A> tail;

    Cons(final A head, final List<A> tail) {
      this.head = head;
      this.tail = tail;
    }

    public A head() {
      return head;
    }

    public List<A> tail() {
      return tail;
    }

    private void tail(final List<A> tail) {
      this.tail = tail;
    }
  }

  /**
   * Constructs a list from the given elements.
   *
   * @param as The elements to construct a list with.
   * @return A list with the given elements.
   */
  @SafeVarargs public static <A> List<A> list(final A... as) {
    return arrayList(as);
  }

  /**
   * Constructs a list from the given elements.
   */
  @SafeVarargs
  public static <A> List<A> arrayList(final A... as) {
    return Array.array(as).toList();
  }

  /**
   * Constructs a list from the given Iterator.
   */
  public static <A> List<A> fromIterator(final Iterator<A> it) {
    return iterableList(() -> it);
  }

  /**
   * Returns an empty list.
   *
   * @return An empty list.
   */
  @SuppressWarnings("unchecked")
  public static <A> List<A> nil() {
    return (Nil<A>) Nil.INSTANCE;
  }

  /**
   * Returns a function that prepends (cons) an element to a list to produce a new list.
   *
   * @return A function that prepends (cons) an element to a list to produce a new list.
   */
  public static <A> F<A, F<List<A>, List<A>>> cons() {
    return a -> tail -> cons(a, tail);
  }

  public static <A> F2<A, List<A>, List<A>> cons_() {
      return List::cons;
  }

  /**
   * Returns a function that prepends a value to the given list.
   *
   * @param tail The list to prepend to.
   * @return A function that prepends a value to the given list.
   */
  public static <A> F<A, List<A>> cons(final List<A> tail) {
    return tail::cons;
  }

  /**
   * Returns a function that prepends the given value to a list.
   *
   * @param a The value to prepend to a list.
   * @return A function that prepends the given value to a list.
   */
  public static <A> F<List<A>, List<A>> cons_(final A a) {
    return as -> as.cons(a);
  }

  /**
   * Prepends the given head element to the given tail element to produce a new list.
   *
   * @param head The element to prepend.
   * @param tail The list to prepend to.
   * @return The list with the given element prepended.
   */
  public static <A> List<A> cons(final A head, final List<A> tail) {
    return new Cons<>(head, tail);
  }

  /**
   * Returns a function that determines whether a given list is empty.
   *
   * @return A function that determines whether a given list is empty.
   */
  public static <A> F<List<A>, Boolean> isEmpty_() {
    return List::isEmpty;
  }

  /**
   * Returns a function that determines whether a given list is not empty.
   *
   * @return A function that determines whether a given list is not empty.
   */
  public static <A> F<List<A>, Boolean> isNotEmpty_() {
    return List::isNotEmpty;
  }

  /**
   * Joins the given list of lists using a bind operation.
   *
   * @param o The list of lists to join.
   * @return A new list that is the join of the given lists.
   */
  public static <A> List<A> join(final List<List<A>> o) {
    final F<List<A>, List<A>> id = identity();
    return o.bind(id);
  }

  /**
   * A first-class version of join
   *
   * @return A function that joins a list of lists using a bind operation.
   */
  public static <A> F<List<List<A>>, List<A>> join() {
    return List::join;
  }

  /**
   * Unfolds across the given function starting at the given value to produce a list.
   *
   * @param f The function to unfold across.
   * @param b The start value to begin the unfold.
   * @return A new list that is a result of unfolding until the function does not produce a value.
   */
  public static <A, B> List<A> unfold(final F<B, Option<P2<A, B>>> f, final B b) {
    Buffer<A> buf = empty();
    for (Option<P2<A, B>> o = f.f(b); o.isSome(); o = f.f(o.some()._2())) {
      buf = buf.snoc(o.some()._1());
    }
    return buf.toList();
  }

  /**
   * Transforms a list of pairs into a list of first components and a list of second components.
   *
   * @param xs The list of pairs to transform.sp
   * @return A list of first components and a list of second components.
   */
  public static <A, B> P2<List<A>, List<B>> unzip(final List<P2<A, B>> xs) {
    Buffer<A> ba = empty();
    Buffer<B> bb = empty();
    for (final P2<A, B> p : xs) {
      ba = ba.snoc(p._1());
      bb = bb.snoc(p._2());
    }
    return p(ba.toList(), bb.toList());
  }

  /**
   * Returns a list of the given value replicated the given number of times.
   *
   * @param n The number of times to replicate the given value.
   * @param a The value to replicate.
   * @return A list of the given value replicated the given number of times.
   */
  public static <A> List<A> replicate(final int n, final A a) {
    List<A> list = nil();
    for (int i = 0; i < n; i++) { list = list.cons(a); }
    return list;
  }

  /**
   * Returns a list of integers from the given <code>from</code> value (inclusive) to the given
   * <code>to</code> value (exclusive).
   *
   * @param from The minimum value for the list (inclusive).
   * @param to   The maximum value for the list (exclusive).
   * @return A list of integers from the given <code>from</code> value (inclusive) to the given
   *         <code>to</code> value (exclusive).
   */
  public static List<Integer> range(final int from, final int to) {
    final Buffer<Integer> buf = empty();
    for (int i = from; i < to; i++) {
      buf.snoc(i);
    }
    return buf.toList();
  }

  /**
   * Returns a list of characters from the given string. The inverse of this function is {@link
   * #asString(List)}.
   *
   * @param s The string to produce the list of characters from.
   * @return A list of characters from the given string.
   */
  public static List<Character> fromString(final String s) {
    List<Character> cs = nil();

    for (int i = s.length() - 1; i >= 0; i--)
      cs = cons(s.charAt(i), cs);

    return cs;
  }

  /**
   * A first-class <code>fromString</code>.
   *
   * @return A first-class <code>fromString</code>.
   */
  public static F<String, List<Character>> fromString() {
    return List::fromString;
  }

  /**
   * Returns a string from the given list of characters. The invers of this function is {@link
   * #fromString(String)}.
   *
   * @param cs The list of characters to produce the string from.
   * @return A string from the given list of characters.
   */
  public static String asString(final List<Character> cs) {
    final StringBuilder sb = new StringBuilder();

    cs.foreach(c -> {
      sb.append(c);
      return unit();
    });
    return sb.toString();
  }

  /**
   * A first-class <code>asString</code>.
   *
   * @return A first-class <code>asString</code>.
   */
  public static F<List<Character>, String> asString() {
    return List::asString;
  }

  /**
   * Returns a list of one element containing the given value.
   *
   * @param a The value for the head of the returned list.
   * @return A list of one element containing the given value.
   */
  public static <A> List<A> single(final A a) {
    return cons(a, List.nil());
  }

  /**
   * Creates a list where the first item is calculated by applying the function on the third argument,
   * the second item by applying the function on the previous result and so on.
   *
   * @param f The function to iterate with.
   * @param p The predicate which must be true for the next item in order to continue the iteration.
   * @param a The input to the first iteration.
   * @return A list where the first item is calculated by applying the function on the third argument,
   *         the second item by applying the function on the previous result and so on.
   */
  public static <A> List<A> iterateWhile(final F<A, A> f, final F<A, Boolean> p, final A a) {
    return unfold(
            o -> Option.iif(p2 -> p.f(o), p(o, f.f(o)))
            , a);
  }

  /**
   * Returns an associated value with the given key in the list of pairs.
   *
   * @param e The test for equality on keys.
   * @param x The list of pairs to search.
   * @param a The key value to find the associated value of.
   * @return An associated value with the given key in the list of pairs.
   */
  public static <A, B> Option<B> lookup(final Equal<A> e, final List<P2<A, B>> x, final A a) {
    return x.find(p -> e.eq(p._1(), a)).map(P2.__2());
  }

  /**
   * Returns a partially applied version of {@link #lookup(Equal, List, Object)}.
   *
   * @param e The test for equality on keys.
   * @return A partially applied version of {@link #lookup(Equal , List, Object)}.
   */
  public static <A, B> F2<List<P2<A, B>>, A, Option<B>> lookup(final Equal<A> e) {
    return (x, a) -> lookup(e, x, a);
  }

  /**
   * Provides a first-class version of bind()
   *
   * @return The bind function for lists.
   */
  public static <A, B> F<F<A, List<B>>, F<List<A>, List<B>>> bind_() {
    return curry((f, as) -> as.bind(f));
  }

  /**
   * Provides a first-class version of map()
   *
   * @return The map function for lists.
   */
  public static <A, B> F<F<A, B>, F<List<A>, List<B>>> map_() {
    return curry((f, as) -> as.map(f));
  }

  /**
   * Turn a list of functions into a function returning a list.
   *
   * @param fs The list of functions to sequence into a single function that returns a list.
   * @return A function that, when given an argument, applies all the functions in the given list to it
   *         and returns a list of the results.
   */
  public static <A, B> F<B, List<A>> sequence_(final List<F<B, A>> fs) {
    return fs.foldRight(Function.lift(List.cons()), Function
        .constant(List.nil()));
  }

  /**
   * Provides a first-class version of foldLeft.
   *
   * @return The left fold function for lists.
   */
  public static <A, B> F<F<B, F<A, B>>, F<B, F<List<A>, B>>> foldLeft() {
    return curry((f, b, as) -> as.foldLeft(f, b));
  }

  /**
   * Provides a first-class version of take.
   *
   * @return First-class version of take.
   */
  public static <A> F<Integer, F<List<A>, List<A>>> take() {
    return curry((n, as) -> as.take(n));
  }

  /**
   * Takes the given iterable to a list.
   *
   * @param i The iterable to take to a list.
   * @return A list from the given iterable.
   */
  public static <A> List<A> iterableList(final Iterable<A> i) {
    final Buffer<A> bs = empty();
    for (final A a : i) {
      bs.snoc(a);
    }
    return bs.toList();
  }

  /**
   * Constructs a list from the given Iterator.
   */
  public static <A> List<A> iteratorList(final Iterator<A> it) {
    return iterableList(() -> it);
  }

  /**
   * A mutable, singly linked list. This structure should be used <em>very</em> sparingly, in favour
   * of the {@link List immutable singly linked list structure}.
   */
  public static final class Buffer<A> implements Iterable<A> {
    private List<A> start = nil();
    private Cons<A> tail;
    private boolean exported;

    /**
     * Returns an iterator for this buffer. This method exists to permit the use in a <code>for</code>-each loop.
     *
     * @return A iterator for this buffer.
     */
    public Iterator<A> iterator() {
      return start.iterator();
    }

    /**
     * Appends (snoc) the given element to this buffer to produce a new buffer.
     *
     * @param a The element to append to this buffer.
     * @return This buffer.
     */
    public Buffer<A> snoc(final A a) {
      if (exported)
        copy();

      final Cons<A> t = new Cons<>(a, List.nil());

      if (tail == null)
        start = t;
      else
        tail.tail(t);

      tail = t;

      return this;
    }

    /**
     * Appends the given list to this buffer.
     *
     * @param as The list to append to this buffer.
     * @return This buffer.
     */
    public Buffer<A> append(final List<A> as) {
      for (List<A> xs = as; xs.isNotEmpty(); xs = xs.tail())
        snoc(xs.head());

      return this;
    }

    /**
     * Prepends the elements of this buffer to the given list.
     *
     * @param as the list to which elements are prepended.
     */
    public List<A> prependToList(final List<A> as) {
      if (isEmpty()) {
        return as;
      } else {
        if (exported)
          copy();

        tail.tail(as);
        return toList();
      }
    }

    /**
     * Returns <code>true</code> if this buffer is empty, <code>false</code> otherwise.
     */
    public boolean isEmpty() { return start.isEmpty(); }

    /**
     * Returns an immutable list projection of this buffer. Modifications to the underlying buffer
     * will <em>not</em> be reflected in returned lists.
     *
     * @return An immutable list projection of this buffer.
     */
    public List<A> toList() {
      exported = !start.isEmpty();
      return start;
    }

    /**
     * Projects an immutable collection of this buffer.
     *
     * @return An immutable collection of this buffer.
     */
    public Collection<A> toCollection() {
      return start.toCollection();
    }

    /**
     * An empty buffer.
     *
     * @return An empty buffer.
     */
    public static <A> Buffer<A> empty() {
      return new Buffer<>();
    }

    /**
     * Constructs a buffer from the given list.
     *
     * @param as The list to construct a buffer with.
     * @return A buffer from the given list.
     */
    public static <A> Buffer<A> fromList(final List<A> as) {
      final Buffer<A> b = new Buffer<>();

      for (List<A> xs = as; xs.isNotEmpty(); xs = xs.tail())
        b.snoc(xs.head());

      return b;
    }

    /**
     * Takes the given iterable to a buffer.
     *
     * @param i The iterable to take to a buffer.
     * @return A buffer from the given iterable.
     */
    public static <A> Buffer<A> iterableBuffer(final Iterable<A> i) {
      final Buffer<A> b = empty();

      for (final A a : i)
        b.snoc(a);

      return b;
    }

    @SuppressWarnings("ObjectEquality")
    private void copy() {
      List<A> s = start;
      final Cons<A> t = tail;
      start = nil();
      tail = null;
      exported = false;
      while (s != t) {
        snoc(s.head());
        s = s.tail();
      }

      if (t != null)
        snoc(t.head());
    }
  }

    /**
     * Perform an equality test on this list which delegates to the .equals() method of the member instances.
     * This is implemented with Equal.listEqual using the anyEqual rule.
     *
     * @param obj the other object to check for equality against.
     * @return true if this list is equal to the provided argument
     */
    @Override public final boolean equals(final Object obj) {
        return Equal.equals0(List.class, this, obj, () -> Equal.listEqual(Equal.anyEqual()));
    }

    /**
     * Compute the hash code from this list as a function of the hash codes of its members.
     * Delegates to Hash.listHash, using the anyHash() rule, which uses the hash codes of the contents.
     *
     * @return the hash code for this list.
     */
    @Override
    public final int hashCode() {
        return Hash.listHash(Hash.<A>anyHash()).hash(this);
    }

    /**
     * Obtain a string representation of this list using the toString implementations of the members.  Uses Show.listShow with F2 argument and may
     * not be very performant.
     *
     * @return a String representation of the list
     */
    @Override public final String toString() {
        return Show.listShow(Show.<A>anyShow()).showS(this);
    }

    /**
     * True if and only if the list has one element. Runs in constant time.
     */
    public final boolean isSingle() {
        return isNotEmpty() && tail().isEmpty();
    }

  /**
   * Optic factory methods for a List
   */
  public static final class Optic {

    private Optic() {
      throw new UnsupportedOperationException();
    }

    /**
     * Polymorphic traversal
     */
    public static <A, B> PTraversal<List<A>, List<B>, A, B> pTraversal() {
      return new PTraversal<List<A>, List<B>, A, B>() {

        @Override
        public <C> F<List<A>, F<C, List<B>>> modifyFunctionF(F<A, F<C, B>> f) {
          return l -> l.traverseF(f);
        }

        @Override
        public <L> F<List<A>, Either<L, List<B>>> modifyEitherF(F<A, Either<L, B>> f) {
          return l -> l.traverseEither(f);
        }

        @Override
        public F<List<A>, IO<List<B>>> modifyIOF(F<A, IO<B>> f) {
          return l -> l.traverseIO(f);
        }

        @Override
        public F<List<A>, Trampoline<List<B>>> modifyTrampolineF(F<A, Trampoline<B>> f) {
          return l -> l.traverseTrampoline(f);
        }

        @Override
        public F<List<A>, Promise<List<B>>> modifyPromiseF(F<A, Promise<B>> f) {
          return l -> l.traversePromise(f);
        }

        @Override
        public F<List<A>, List<List<B>>> modifyListF(F<A, List<B>> f) {
          return l -> l.traverseList(f);
        }

        @Override
        public F<List<A>, Option<List<B>>> modifyOptionF(F<A, Option<B>> f) {
          return l -> l.traverseOption(f);
        }

        @Override
        public F<List<A>, Stream<List<B>>> modifyStreamF(F<A, Stream<B>> f) {
          return l -> l.traverseStream(f);
        }

        @Override
        public F<List<A>, P1<List<B>>> modifyP1F(F<A, P1<B>> f) {
          return l -> l.traverseP1(f);
        }

        @Override
        public <E> F<List<A>, Validation<E, List<B>>> modifyValidationF(Semigroup<E> s, F<A, Validation<E, B>> f) {
          return l -> l.traverseValidation(s, f);
        }

        @Override
        public F<List<A>, V2<List<B>>> modifyV2F(F<A, V2<B>> f) {
          return l -> l.traverseV2(f);
        }

        @Override
        public <M> F<List<A>, M> foldMap(Monoid<M> monoid, F<A, M> f) {
          return l -> monoid.sumLeft(l.map(f));
        }
      };
    }

    /**
     * Monomorphic traversal
     */
    public static <A> Traversal<List<A>, A> traversal() {
      return new Traversal<>(pTraversal());
    }

    /**
     * Optional targeted on Cons head.
     */
    public static <A> Optional<List<A>, A> head() {
      return optional(List::headOption, a -> l -> l.uncons((__, as) -> as.cons(a), l));
    }

    /**
     * Optional targeted on Cons tail.
     */
    public static <A> Optional<List<A>, List<A>> tail() {
      return optional(l -> l.uncons((__, tail) -> some(tail), none()),
              tail -> l -> l.uncons((h, __) -> List.cons(h, tail), l));
    }

    /**
     * Nil prism
     */
    public static <A> Prism<List<A>, Unit> nil() {
      return prism((List<A> l) -> l.isEmpty() ? some(unit()) : none(), constant(List.nil()));
    }

    /**
     * Cons prism
     */
    public static <A> Prism<List<A>, P2<A, List<A>>> cons() {
      return prism(l -> l.<Option<P2<A, List<A>>>> uncons((h, tail) -> some(p(h, tail)), none()), c -> List.cons(c._1(), c._2()));
    }

  }

  public static final class Unsafe {

  }

}