LinkedList.lua

-- Circular, doubly linked list --
----------------------------------

local linkedList = {}

-- Creates a list from table or variable n. of values --
function linkedList.construct(...)
	local args = {...}
	local tail = linkedList.newNode(args[1])
	for i = 2, #args do
		linkedList.insert(tail, args[i])
		tail = tail.next
	end
	return tail.next
end

-- Creates a new instance of node --
function linkedList.newNode(val)
	local node = {}
	node.value = val
	node.next = node
	node.prev = node
	return node
end

-- Inserts a node after the given node && returns a reference --
function linkedList.insert(node, val)
	local newnode = linkedList.newNode(val)
	newnode.next = node.next
	newnode.prev = node
	node.next = newnode
	return newnode
end

-- Remove an element of the list, return reference to next element --
function linkedList.erase(node)
	local index = node.next
	node.prev.next = node.next
	node = nil
	return index
end

-- Print the whole list, avoiding circularity --
function linkedList.print(node)
	local it = node
	repeat
		print(it.value)
		it = it.next
	until it == node
end

return linkedList

SampleUse.lua

local list = require("LinkedList")

foo = list.construct(1, 2, 3, 4, 5, 6)
list.print(foo) print()
-- Output: 1, 2, 3, 4, 5, 6 --

list.print(foo.next.next) print()
-- Output: 3, 4, 5, 6, 1, 2 --

last = list.insert(foo.prev, 'bar')
list.print(last) print()
-- Output: 'bar', 2, 3, 4, 5, 6, 1
-- Oops: first in list doesn't refer to last --
-- Don't know how to do this without storing additional information --

last = list.erase(last)
list.print(last)
-- Output: 2, 3, 4, 5, 6, 1

For all of you visiting this, two years old, gist, the problem is that the construct function is not updating the head about the current last item the insert and the erase functions do not update both the adjacent nodes.

Also, I think that clearing the links of the erased node is a good thing for the garbage collector.

The solution is to add after the line 13 the following update them as:

  -- Ignore this.
  -- tail.next.prev = tail

-- Inserts a node after the given node && returns a reference --
function linkedList.insert(node, val)
  local newnode = linkedList.newNode(val)
  newnode.next = node.next
  newnode.next.prev = newnode
  newnode.prev = node
  newnode.prev.next = newnode
  return newnode
end

-- Remove an element of the list, return reference to next element --
function linkedList.erase(node)
  local head = node.next
  node.prev.next = node.next
  node.next.prev = node.prev
  node.prev, node.next = nil, nil
  return head
end

Not tested thoroughly though.