list.pony

class List[A] is Seq[A]
  """
  A doubly linked list.

  The following is paraphrased from [Wikipedia](https://en.wikipedia.org/wiki/Doubly_linked_list).

  A doubly linked list is a linked data structure that consists of a set of sequentially
  linked records called nodes (implemented in Pony via the collections.ListNode class). Each
  node contains four fields: two link fields (references to the previous and to the next node in
  the sequence of nodes), one data field, and the reference to the List in which it resides. A doubly
  linked list can be conceptualized as two singly linked lists formed from the same data items, but
  in opposite sequential orders.

  As you would expect. functions are provided to perform all the common list operations such as
  creation, traversal, node addition and removal, iteration, mapping, filtering, etc.

  ## Example program
  There are a _lot_ of functions in List. The following code picks out a few common examples.

  It outputs:

      A new empty list has 0 nodes.
      Adding one node to our empty list means it now has a size of 1.
      The first (index 0) node has the value: A single String
      A list created by appending our second single-node list onto our first has size: 2
      The List nodes of our first list are now:
        A single String
        Another String
      Append *moves* the nodes from the second list so that now has 0 nodes.
      A list created from an array of three strings has size: 3
        First
        Second
        Third
      Mapping over our three-node list produces a new list of size: 3
      Each node-value in the resulting list is now far more exciting:
        First BOOM!
        Second BOOM!
        Third BOOM!
      Filtering our three-node list produces a new list of size: 2
        Second BOOM!
        Third BOOM!
      The size of our first partitioned list (matches predicate): 1
      The size of our second partitioned list (doesn't match predicate): 1
      Our matching partition elements are:
        Second BOOM!

  ```pony
    use "collections"

    actor Main
      new create(env:Env) =>

        // Create a new empty List of type String
        let my_list = List[String]()

        env.out.print("A new empty list has " + my_list.size().string() + " nodes.") // 0

        // Push a String literal onto our empty List
        my_list.push("A single String")
        env.out.print("Adding one node to our empty list means it now has a size of "
                      + my_list.size().string() + ".") // 1

        // Get the first element of our List
        try env.out.print("The first (index 0) node has the value: "
                          + my_list.index(0)?()?.string()) end // A single String

        // Create a second List from a single String literal
        let my_second_list = List[String].unit("Another String")

        // Append the second List to the first
        my_list.append_list(my_second_list)
        env.out.print("A list created by appending our second single-node list onto our first has size: "
                      + my_list.size().string()) // 2
        env.out.print("The List nodes of our first list are now:")
        for n in my_list.values() do
          env.out.print("\t" + n.string())
        end
        // NOTE: this _moves_ the elements so second_list consequently ends up empty
        env.out.print("Append *moves* the nodes from the second list so that now has "
                      + my_second_list.size().string() + " nodes.") // 0

        // Create a third List from a Seq(ence)
        // (In this case a literal array of Strings)
        let my_third_list = List[String].from(["First"; "Second"; "Third"])
        env.out.print("A list created from an array of three strings has size: "
                      + my_third_list.size().string()) // 3
        for n in my_third_list.values() do
          env.out.print("\t" + n.string())
        end

        // Map over the third List, concatenating some "BOOM!'s" into a new List
        let new_list = my_third_list.map[String]({ (n) => n + " BOOM!" })
        env.out.print("Mapping over our three-node list produces a new list of size: "
                      + new_list.size().string()) // 3
        env.out.print("Each node-value in the resulting list is now far more exciting:")
        for n in new_list.values() do
          env.out.print("\t" + n.string())
        end

        // Filter the new list to extract 2 elements
        let filtered_list = new_list.filter({ (n) => n.string().contains("d BOOM!") })
        env.out.print("Filtering our three-node list produces a new list of size: "
                          + filtered_list.size().string()) // 2
        for n in filtered_list.values() do
          env.out.print("\t" + n.string()) // Second BOOM!\nThird BOOM!
        end

        // Partition the filtered list
        let partitioned_lists = filtered_list.partition({ (n) => n.string().contains("Second") })
        env.out.print("The size of our first partitioned list (matches predicate): " + partitioned_lists._1.size().string())        // 1
        env.out.print("The size of our second partitioned list (doesn't match predicate): " + partitioned_lists._2.size().string())  // 1
        env.out.print("Our matching partition elements are:")
        for n in partitioned_lists._1.values() do
          env.out.print("\t" + n.string()) // Second BOOM!
        end
  ```

  """
  var _head: (ListNode[A] | None) = None
  var _tail: (ListNode[A] | None) = None
  var _size: USize = 0

  new create(len: USize = 0) =>
    """
    Always creates an empty list with 0 nodes, `len` is ignored.

    Required method for `List` to satisfy the `Seq` interface.
    ```pony
    let my_list = List[String]
    ```
    """
    None

  new unit(a: A) =>
    """
    Creates a list with 1 node of element.

    ```pony
    let my_list = List[String].unit("element")
    ```
    """
    push(consume a)

  new from(seq: Array[A^]) =>
    """
    Creates a list equivalent to the provided Array (both node number and order are preserved).

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    ```
    """
    for value in seq.values() do
      push(consume value)
    end

  fun ref reserve(len: USize) =>
    """
    Do nothing

    Required method for `List` to satisfy the `Seq` interface.
    """
    None

  fun size(): USize =>
    """
    Returns the number of items in the list.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    my_list.size() // 3
    ```
    """
    _size

  fun apply(i: USize = 0): this->A ? =>
    """
    Get the i-th element, raising an error if the index is out of bounds.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    try my_list.apply(1)? end // "b"
    ```
    """
    index(i)?()?

  fun ref update(i: USize, value: A): A^ ? =>
    """
    Change the i-th element, raising an error if the index is out of bounds, and
    returning the previous value.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    try my_list.update(1, "z")? end // Returns "b" and List now contains ["a"; "z"; "c"]
    ```
    """
    index(i)?()? = consume value

  fun index(i: USize): this->ListNode[A] ? =>
    """
    Gets the i-th node, raising an error if the index is out of bounds.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    try my_list.index(0)? end // Returns a ListNode[String] containing "a"
    ```
    """
    if i >= _size then
      error
    end

    var node = _head as this->ListNode[A]
    var j = USize(0)

    while j < i do
      node = node.next() as this->ListNode[A]
      j = j + 1
    end

    node

  fun ref remove(i: USize): ListNode[A] ? =>
    """
    Remove the i-th node, raising an error if the index is out of bounds, and
    returning the removed node.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    try my_list.remove(0)? end // Returns a ListNode[String] containing "a" and List now contains ["b"; "c"]
    ```
    """
    index(i)? .> remove()

  fun ref clear() =>
    """
    Empties the list.
    """
    _head = None
    _tail = None
    _size = 0

  fun head(): this->ListNode[A] ? =>
    """
    Show the head of the list, raising an error if the head is empty.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    try my_list.head()? end // Returns a ListNode[String] containing "a"
    ```
    """
    _head as this->ListNode[A]

  fun tail(): this->ListNode[A] ? =>
    """
    Show the tail of the list, raising an error if the tail is empty.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    try my_list.tail()? end // Returns a ListNode[String] containing "c"
    ```
    """
    _tail as this->ListNode[A]

  fun ref prepend_node(node: ListNode[A]) =>
    """
    Adds a node to the head of the list.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let new_head = ListNode[String]("0")
    my_list.prepend_node(new_head) // ["0", "a"; "b"; "c"]
    ```
    """
    match _head
    | let head': ListNode[A] =>
      head'.prepend(node)
    else
      _set_both(node)
    end

  fun ref append_node(node: ListNode[A]) =>
    """
    Adds a node to the tail of the list.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let new_tail = ListNode[String]("0")
    my_list.append_node(new_head) // ["a"; "b"; "c", "0"]
    ```
    """
    match _tail
    | let tail': ListNode[A] =>
      tail'.append(node)
    else
      _set_both(node)
    end

  fun ref append_list(that: List[A]) =>
    """
    Empties the provided List by appending all elements onto the receiving List.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = List[String].from(["d"; "e"; "f"])
    my_list.append_list(other_list)  // my_list is ["a"; "b"; "c"; "d"; "e"; "f"], other_list is empty
    ```
    """
    if this isnt that then
      while that._size > 0 do
        try append_node(that.head()?) end
      end
    end

  fun ref prepend_list(that: List[A]) =>
    """
    Empties the provided List by prepending all elements onto the receiving List.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = List[String].from(["d"; "e"; "f"])
    my_list.prepend_list(other_list)  // my_list is ["d"; "e"; "f"; "a"; "b"; "c"], other_list is empty
    ```
    """
    if this isnt that then
      while that._size > 0 do
        try prepend_node(that.tail()?) end
      end
    end

  fun ref push(a: A) =>
    """
    Adds a new tail value.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    my_list.push("d")  // my_list is ["a"; "b"; "c"; "d"]
    ```
    """
    append_node(ListNode[A](consume a))

  fun ref pop(): A^ ? =>
    """
    Removes the tail value, raising an error if the tail is empty.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    try my_list.pop() end  // Returns "c" and my_list is ["a"; "b"]
    ```
    """
    tail()? .> remove().pop()?

  fun ref unshift(a: A) =>
    """
    Adds a new head value.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    my_list.unshift("d")  // my_list is ["d"; "a"; "b"; "c"]
    ```
    """
    prepend_node(ListNode[A](consume a))

  fun ref shift(): A^ ? =>
    """
    Removes the head value, raising an error if the head is empty.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    try my_list.shift() end  // Returns "a" and my_list is ["b"; "c"]
    ```
    """
    head()? .> remove().pop()?

  fun ref append(
    seq: (ReadSeq[A] & ReadElement[A^]),
    offset: USize = 0,
    len: USize = -1)
  =>
    """
    Append len elements from a sequence, starting from the given offset.

    When len is -1, all elements of sequence are pushed.

    Does not remove elements from sequence.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = List[String].from(["d"; "e"; "f"])
    my_list.append(other_list)  // my_list is ["a"; "b"; "c"; "d"; "e"; "f"], other_list is unchanged
    ```
    """
    if offset >= seq.size() then
      return
    end

    let copy_len = len.min(seq.size() - offset)
    reserve(_size + copy_len)

    let cap = copy_len + offset
    var i = offset

    try
      while i < cap do
        push(seq(i)?)
        i = i + 1
      end
    end

  fun ref concat(iter: Iterator[A^], offset: USize = 0, len: USize = -1) =>
    """
    Add len iterated elements to the tail of the list, starting from the given
    offset.

    When len is -1, all elements of iterator are pushed.

    Does not remove elements from iterator.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = List[String].from(["d"; "e"; "f"])
    my_list.concat(other_list.values())  // my_list is ["a"; "b"; "c"; "d"; "e"; "f"], other_list is unchanged
    ```
    """
    try
      for i in Range(0, offset) do
        if iter.has_next() then
          iter.next()?
        else
          return
        end
      end

      for i in Range(0, len) do
        if iter.has_next() then
          push(iter.next()?)
        else
          return
        end
      end
    end

  fun ref truncate(len: USize) =>
    """
    Pop tail elements until the list is len size.
    If the list is already smaller than len, do nothing.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    my_list.truncate(1)  // my_list is ["a"]
    ```
    """
    try
      while _size > len do
        pop()?
      end
    end

  fun clone(): List[this->A!]^ =>
    """
    Clone all elements into a new List.

    Note: elements are not copied, an additional reference to each element is created in the new List.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = my_list.clone()  // my_list is ["a"; "b"; "c"], other_list is ["a"; "b"; "c"]
    ```
    """
    let out = List[this->A!]

    for v in values() do
      out.push(v)
    end
    out

  fun map[B](f: {(this->A!): B^} box): List[B]^ =>
    """
    Builds a new `List` by applying a function to every element of the `List`.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = my_list.map[String]( {(s: String): String => "m: " + s } )  // other_list is ["m: a"; "m: b"; "m: c"]
    ```
    """
    try
      _map[B](head()?, f, List[B])
    else
      List[B]
    end

  fun _map[B](
    ln: this->ListNode[A],
    f: {(this->A!): B^} box,
    acc: List[B])
    : List[B]^
  =>
    """
    Private helper for `map`, recursively working with `ListNode`s.
    """
    try acc.push(f(ln()?)) end

    try
      _map[B](ln.next() as this->ListNode[A], f, acc)
    else
      acc
    end

  fun flat_map[B](f: {(this->A!): List[B]} box): List[B]^ =>
    """
    Builds a new `List` by applying a function to every element of the `List`, 
    producing a new `List` for each element, then flattened into a single `List`.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = my_list.flat_map[String]( {(s: String): List[String] => List[String].from( ["m"; s] )} )  // other_list is ["m"; "a"; "m"; "b"; "m"; c"]
    ```
    """
    try
      _flat_map[B](head()?, f, List[B])
    else
      List[B]
    end

  fun _flat_map[B](
    ln: this->ListNode[A],
    f: {(this->A!): List[B]} box,
    acc: List[B]): List[B]^
  =>
    """
    Private helper for `flat_map`, recursively working with `ListNode`s.
    """
    try acc.append_list(f(ln()?)) end

    try
      _flat_map[B](ln.next() as this->ListNode[A], f, acc)
    else
      acc
    end

  fun filter(f: {(this->A!): Bool} box): List[this->A!]^ =>
    """
    Builds a new `List` with those elements that satisfy the predicate.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = my_list.filter( {(s: String): Bool => s == "b" } )  // other_list is ["b"]
    ```
    """
    try
      _filter(head()?, f, List[this->A!])
    else
      List[this->A!]
    end

  fun _filter(
    ln: this->ListNode[A],
    f: {(this->A!): Bool} box,
    acc: List[this->A!]): List[this->A!]
  =>
    """
    Private helper for `filter`, recursively working with `ListNode`s.
    """
    try
      let cur = ln()?
      if f(cur) then acc.push(cur) end
    end

    try
      _filter(ln.next() as this->ListNode[A], f, acc)
    else
      acc
    end

  fun fold[B](f: {(B!, this->A!): B^} box, acc: B): B =>
    """
    Folds the elements of the `List` using the supplied function.

    On the first iteration, the `B` argument in `f` is the value `acc`, 
    on the second iteration `B` is the result of the first iteration,
    on the third iteration `B` is the result of the second iteration, and so on.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let folded = my_list.fold[String]( {(str: String, s: String): String => str + s }, "z")  // "zabc"
    ```
    """
    let h = try
      head()?
    else
      return acc
    end

    _fold[B](h, f, consume acc)

  fun _fold[B](
    ln: this->ListNode[A],
    f: {(B!, this->A!): B^} box,
    acc: B)
    : B
  =>
    """
    Private helper for `fold`, recursively working with `ListNode`s.
    """
    let nextAcc: B = try f(acc, ln()?) else consume acc end
    let h = try
      ln.next() as this->ListNode[A]
    else
      return nextAcc
    end

    _fold[B](h, f, consume nextAcc)

  fun every(f: {(this->A!): Bool} box): Bool =>
    """
    Returns `true` if every element satisfies the predicate, otherwise returns `false`.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let all_z = my_list.every( {(s: String): Bool => s == "z"} ) // false
    ```
    """
    try
      _every(head()?, f)
    else
      true
    end

  fun _every(ln: this->ListNode[A], f: {(this->A!): Bool} box): Bool =>
    """
    Private helper for `every`, recursively working with `ListNode`s.
    """
    try
      if not(f(ln()?)) then
        false
      else
        _every(ln.next() as this->ListNode[A], f)
      end
    else
      true
    end

  fun exists(f: {(this->A!): Bool} box): Bool =>
    """
    Returns `true` if at least one element satisfies the predicate, otherwise returns `false`.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let b_exists = my_list.exists( {(s: String): Bool => s == "b"} ) // true
    ```
    """
    try
      _exists(head()?, f)
    else
      false
    end

  fun _exists(ln: this->ListNode[A], f: {(this->A!): Bool} box): Bool =>
    """
    Private helper for `exists`, recursively working with `ListNode`s.
    """
    try
      if f(ln()?) then
        true
      else
        _exists(ln.next() as this->ListNode[A], f)
      end
    else
      false
    end

  fun partition(
    f: {(this->A!): Bool} box)
    : (List[this->A!]^, List[this->A!]^)
  =>
    """
    Builds a pair of `List`s, the first of which is made up of the elements
    satisfying the predicate and the second of which is made up of
    those that do not.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    (let lt_b, let gt_b) = my_list.partition( {(s: String): Bool => s < "b"} )  // lt_b is ["a"], while gt_b is ["b"; "c"]
    ```
    """
    let l1 = List[this->A!]
    let l2 = List[this->A!]
    for item in values() do
      if f(item) then l1.push(item) else l2.push(item) end
    end
    (l1, l2)

  fun drop(n: USize): List[this->A!]^ =>
    """
    Builds a `List` by dropping the first `n` elements.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = my_list.drop(1)  // ["b"; "c"]
    ```
    """
    let l = List[this->A!]

    if size() > n then
      try
        var node = index(n)?

        for i in Range(n, size()) do
          l.push(node()?)
          node = node.next() as this->ListNode[A]
        end
      end
    end
    l

  fun take(n: USize): List[this->A!] =>
    """
    Builds a `List` by keeping the first `n` elements.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = my_list.drop(1)  // ["a"]
    ```
    """
    let l = List[this->A!]

    if size() > 0 then
      try
        var node = head()?

        for i in Range(0, n.min(size())) do
          l.push(node()?)
          node = node.next() as this->ListNode[A]
        end
      end
    end
    l

  fun take_while(f: {(this->A!): Bool} box): List[this->A!]^ =>
    """
    Builds a `List` of elements satisfying the predicate, stopping at the first `false` return.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = my_list.take_while( {(s: String): Bool => s < "b"} )  // ["a"]
    ```
    """
    let l = List[this->A!]

    if size() > 0 then
      try
        var node = head()?

        for i in Range(0, size()) do
          let item = node()?
          if f(item) then l.push(item) else return l end
          node = node.next() as this->ListNode[A]
        end
      end
    end
    l

  fun reverse(): List[this->A!]^ =>
    """
    Builds a new `List` by reversing the elements in the `List`.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let other_list = my_list.reverse() // ["c"; "b"; "a"]
    ```
    """
    try
      _reverse(head()?, List[this->A!])
    else
      List[this->A!]
    end

  fun _reverse(ln: this->ListNode[A], acc: List[this->A!]): List[this->A!]^ =>
    """
    Private helper for `reverse`, recursively working with `ListNode`s.
    """
    try acc.unshift(ln()?) end

    try
      _reverse(ln.next() as this->ListNode[A], acc)
    else
      acc
    end

  fun contains[B: (A & HasEq[A!] #read) = A](a: box->B): Bool =>
    """
    Returns `true` if the `List` contains the provided element, otherwise returns `false`.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let contains_b = my_list.contains[String]("b") // true
    ```
    """
    try
      _contains[B](head()?, a)
    else
      false
    end

  fun _contains[B: (A & HasEq[A!] #read) = A](
    ln: this->ListNode[A],
    a: box->B)
    : Bool
  =>
    """
    Private helper for `contains`, recursively working with `ListNode`s.
    """
    try
      if a == ln()? then
        true
      else
        _contains[B](ln.next() as this->ListNode[A], a)
      end
    else
      false
    end

  fun nodes(): ListNodes[A, this->ListNode[A]]^ =>
    """
    Return an iterator on the nodes in the `List` in forward order.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let nodes = my_list.nodes()  // node with "a" is before node with "c"
    ```
    """
    ListNodes[A, this->ListNode[A]](_head)

  fun rnodes(): ListNodes[A, this->ListNode[A]]^ =>
    """
    Return an iterator on the nodes in the `List` in reverse order.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let rnodes = my_list.rnodes()  // node with "c" is before node with "a"
    ```
    """
    ListNodes[A, this->ListNode[A]](_head, true)

  fun values(): ListValues[A, this->ListNode[A]]^ =>
    """
    Return an iterator on the values in the `List` in forward order.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let values = my_list.values()  // value "a" is before value "c"
    ```
    """
    ListValues[A, this->ListNode[A]](_head)

  fun rvalues(): ListValues[A, this->ListNode[A]]^ =>
    """
    Return an iterator on the values in the `List` in reverse order.

    ```pony
    let my_list = List[String].from(["a"; "b"; "c"])
    let rvalues = my_list.rvalues()  // value "c" is before value "a"
    ```
    """
    ListValues[A, this->ListNode[A]](_head, true)

  fun ref _increment() =>
    """
    Private method to control mutating `_size` field.
    """
    _size = _size + 1

  fun ref _decrement() =>
    """
    Private method to control mutating `_size` field.
    """
    _size = _size - 1

  fun ref _set_head(head': (ListNode[A] | None)) =>
    """
    Private method to control mutating `_head` field.
    """
    _head = head'

  fun ref _set_tail(tail': (ListNode[A] | None)) =>
    """
    Private method to control mutating `_tail` field.
    """
    _tail = tail'

  fun ref _set_both(node: ListNode[A]) =>
    """
    Private method to set both `_head` and `_tail` to the same node,
    creating a `List` with a `_size` of 1.
    """
    node._set_list(this)
    _head = node
    _tail = node
    _size = 1

class ListNodes[A, N: ListNode[A] #read] is Iterator[N]
  """
  Iterate over the nodes in a `List`.
  """
  var _next: (N | None)
  let _reverse: Bool

  new create(head: (N | None), reverse: Bool = false) =>
    """
    Build the iterator over nodes.

    `reverse` of `false` iterates forward, while
    `reverse` of `true` iterates in reverse.
    """
    _next = head
    _reverse = reverse

  fun has_next(): Bool =>
    """
    Indicates whether there are any nodes remaining in the iterator.
    """
    _next isnt None

  fun ref next(): N ? =>
    """
    Return the next node in the iterator, advancing the iterator by one element.
    
    Order of return is determined by `reverse` argument during creation.
    """
    match _next
    | let next': N =>
      if _reverse then
        _next = next'.prev()
      else
        _next = next'.next()
      end

      next'
    else
      error
    end

class ListValues[A, N: ListNode[A] #read] is Iterator[N->A]
  """
  Iterate over the values in a `List`.
  """
  var _next: (N | None)
  let _reverse: Bool

  new create(head: (N | None), reverse: Bool = false) =>
    """
    Build the iterator over values.

    `reverse` of `false` iterates forward, while
    `reverse` of `true` iterates in reverse.
    """
    _next = head
    _reverse = reverse

  fun has_next(): Bool =>
    """
    Indicates whether there are any values remaining in the iterator.
    """
    _next isnt None

  fun ref next(): N->A ? =>
    """
    Return the next node in the iterator, advancing the iterator by one element.
    
    Order of return is determined by `reverse` argument during creation.
    """
    match _next
    | let next': N =>
      if _reverse then
        _next = next'.prev()
      else
        _next = next'.next()
      end

      next'()?
    else
      error
    end