    indexing
    	description: "Trees implemented using a two way linked list representation"
    	legal: "See notice at end of class."
    	status: "See notice at end of class."
    	names: two_way_tree, tree, two_way_list
    	representation: recursive, linked
    	access: cursor, membership
    	contents: generic
    	date: "$Date: 2006-09-15 17:28:10 -0700 (Fri, 15 Sep 2006) $"
    	revision: "$Revision: 63620 $"

    class interface
    	TWO_WAY_TREE [G]

    create
    	make (v: like item)
    			-- Create single node with item `v'.

    create {TWO_WAY_TREE}
    	twl_make
    			-- Create an empty list.
    			-- (from LINKED_LIST)
    		ensure -- from LINKED_LIST
    			is_before: child_before

    	make_sublist (first_item, last_item: like first_child; n: INTEGER_32)
    			-- Create sublist
    			-- (from TWO_WAY_LIST)

    feature -- Initialization

    	make (v: like item)
    			-- Create single node with item `v'.

    feature -- Access

    	child_cursor: TWO_WAY_TREE_CURSOR [G]
    			-- Current cursor position
    		require -- from  CURSOR_STRUCTURE
    			True
    		require -- from  TREE
    			True
    		ensure -- from CURSOR_STRUCTURE
    			cursor_not_void: Result /= Void

    	first: like child_item
    			-- Item at first position
    			-- (from LINKED_LIST)
    		require -- from CHAIN
    			not_empty: not is_leaf

    	first_child: like parent
    			-- Leftmost child

    	generating_type: STRING_8
    			-- Name of current object's generating type
    			-- (type of which it is a direct instance)
    			-- (from ANY)

    	generator: STRING_8
    			-- Name of current object's generating class
    			-- (base class of the type of which it is a direct instance)
    			-- (from ANY)

    	i_th alias "[]" (i: INTEGER_32): like child_item assign put_i_th
    			-- Item at `i'-th position
    			-- Was declared in CHAIN as synonym of infix "@".
    			-- (from CHAIN)
    		require -- from TABLE
    			valid_key: valid_index (i)

    	child_index: INTEGER_32
    			-- Index of current position
    			-- (from LINKED_LIST)
    		require -- from  LINEAR
    			True
    		require -- from  TREE
    			True
    		ensure -- from TREE
    			valid_index: Result >= 0 and Result <= arity + 1

    	index_of (v: like child_item; i: INTEGER_32): INTEGER_32
    			-- Index of `i'-th occurrence of item identical to `v'.
    			-- (Reference or object equality,
    			-- based on object_comparison.)
    			-- 0 if none.
    			-- (from CHAIN)
    		require -- from LINEAR
    			positive_occurrences: i > 0
    		ensure -- from LINEAR
    			non_negative_result: Result >= 0

    	child_item: G
    			-- Current item
    			-- (from LINKED_LIST)
    		require -- from TRAVERSABLE
    			not_off: not child_off
    		require -- from ACTIVE
    			readable: child_readable
    		require -- from TREE
    			readable: child_readable

    	item: G
    			-- Content of cell.
    			-- (from CELL)

    	last: like child_item
    			-- Item at last position
    			-- (from LINKED_LIST)
    		require -- from CHAIN
    			not_empty: not is_leaf

    	last_child: like parent

    	left_sibling: like Current
    			-- Left neighbor
    			-- (from BI_LINKABLE)

    	sequential_occurrences (v: like child_item): INTEGER_32
    			-- Number of times `v' appears.
    			-- (Reference or object equality,
    			-- based on object_comparison.)
    			-- (from LINEAR)
    		require -- from  BAG
    			True
    		ensure -- from BAG
    			non_negative_occurrences: Result >= 0

    	parent: TWO_WAY_TREE [G]
    			-- Parent node

    	right_sibling: like Current
    			-- Right neighbor
    			-- (from LINKABLE)

    	sublist: like Current
    			-- Result produced by last split
    			-- (from TWO_WAY_LIST)

    	infix "@" (i: INTEGER_32): like child_item assign put_i_th
    			-- Item at `i'-th position
    			-- Was declared in CHAIN as synonym of i_th.
    			-- (from CHAIN)
    		require -- from TABLE
    			valid_key: valid_index (i)

    feature -- Measurement

    	child_capacity: INTEGER_32
    			-- Maximal number of children
    			-- (from TREE)

    	count: INTEGER_32
    			-- Number of items
    			-- (from TREE)

    	arity: INTEGER_32
    			-- Number of items
    			-- (from LINKED_LIST)

    	index_set: INTEGER_INTERVAL
    			-- Range of acceptable indexes
    			-- (from CHAIN)
    		require -- from  INDEXABLE
    			True
    		ensure -- from INDEXABLE
    			not_void: Result /= Void
    		ensure then -- from CHAIN
    			count_definition: Result.count = arity

    	occurrences (v: like child_item): INTEGER_32
    			-- Number of times `v' appears.
    			-- (Reference or object equality,
    			-- based on object_comparison.)
    			-- (from CHAIN)
    		require -- from  BAG
    			True
    		require -- from  LINEAR
    			True
    		ensure -- from BAG
    			non_negative_occurrences: Result >= 0

    feature -- Comparison

    	frozen deep_equal (some: ANY; other: like arg #1): BOOLEAN
    			-- Are `some' and `other' either both void
    			-- or attached to isomorphic object structures?
    			-- (from ANY)
    		ensure -- from ANY
    			shallow_implies_deep: standard_equal (some, other) implies Result
    			both_or_none_void: (some = Void) implies (Result = (other = Void))
    			same_type: (Result and (some /= Void)) implies some.same_type (other)
    			symmetric: Result implies deep_equal (other, some)

    	frozen equal (some: ANY; other: like arg #1): BOOLEAN
    			-- Are `some' and `other' either both void or attached
    			-- to objects considered equal?
    			-- (from ANY)
    		ensure -- from ANY
    			definition: Result = (some = Void and other = Void) or else ((some /= Void and other /= Void) and then some.is_equal (other))

    	is_equal (other: like Current): BOOLEAN
    			-- Does `other' contain the same elements?
    			-- (Reference or object equality,
    			-- based on object_comparison.)
    			-- (from TREE)
    		require -- from ANY
    			other_not_void: other /= Void
    		ensure -- from ANY
    			symmetric: Result implies other.is_equal (Current)
    			consistent: standard_is_equal (other) implies Result
    		ensure then -- from LIST
    			indices_unchanged: child_index = old child_index and other.child_index = old other.child_index
    			true_implies_same_size: Result implies arity = other.arity

    	node_is_equal (other: like Current): BOOLEAN
    			-- Is `other' equal to Current?
    			-- (from TREE)
    		require -- from TREE
    			other_not_void: other /= Void

    	frozen standard_equal (some: ANY; other: like arg #1): BOOLEAN
    			-- Are `some' and `other' either both void or attached to
    			-- field-by-field identical objects of the same type?
    			-- Always uses default object comparison criterion.
    			-- (from ANY)
    		ensure -- from ANY
    			definition: Result = (some = Void and other = Void) or else ((some /= Void and other /= Void) and then some.standard_is_equal (other))

    	frozen standard_is_equal (other: like Current): BOOLEAN
    			-- Is `other' attached to an object of the same type
    			-- as current object, and field-by-field identical to it?
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    		ensure -- from ANY
    			same_type: Result implies same_type (other)
    			symmetric: Result implies other.standard_is_equal (Current)

    feature -- Status report

    	child_after: BOOLEAN
    			-- Is there no valid cursor position to the right of cursor?
    			-- (from LINKED_LIST)

    	child_before: BOOLEAN
    			-- Is there no valid cursor position to the left of cursor?
    			-- (from LINKED_LIST)

    	changeable_comparison_criterion: BOOLEAN
    			-- May object_comparison be changed?
    			-- (Answer: yes by default.)
    			-- (from CONTAINER)

    	child_isfirst: BOOLEAN
    			-- Is cursor under first child?
    			-- (from TREE)
    		require -- from  CHAIN
    			True
    		ensure -- from CHAIN
    			valid_position: Result implies not is_leaf
    		ensure -- from TREE
    			not_is_leaf: Result implies not is_leaf

    	child_islast: BOOLEAN
    			-- Is cursor under last child?
    		require -- from  CHAIN
    			True
    		require -- from  TREE
    			True
    		ensure -- from CHAIN
    			valid_position: Result implies not is_leaf
    		ensure -- from TREE
    			not_is_leaf: Result implies not is_leaf

    	child_readable: BOOLEAN
    			-- Is there a current child_item to be read?
    			-- (from TREE)
    		require -- from  ACTIVE
    			True

    	child_writable: BOOLEAN
    			-- Is there a current child_item that may be modified?
    			-- (from TREE)
    		require -- from  ACTIVE
    			True

    	conforms_to (other: ANY): BOOLEAN
    			-- Does type of current object conform to type
    			-- of `other' (as per Eiffel: The Language, chapter 13)?
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void

    	exhausted: BOOLEAN
    			-- Has structure been completely explored?
    			-- (from LINEAR)
    		ensure -- from LINEAR
    			exhausted_when_off: child_off implies Result

    	extendible: BOOLEAN is True
    			-- May new items be added?
    			-- (from DYNAMIC_TREE)

    	child_extendible: BOOLEAN is True
    			-- May new items be added? (Answer: yes.)
    			-- (from DYNAMIC_CHAIN)

    	has (v: G): BOOLEAN
    			-- Does subtree include `v'?
    			-- (Reference or object equality,
    			-- based on object_comparison.)
    			-- (from TREE)
    		ensure -- from CONTAINER
    			not_found_in_empty: Result implies not is_leaf

    	is_empty: BOOLEAN
    			-- Is structure empty of items?
    			-- (from TREE)

    	is_inserted (v: G): BOOLEAN
    			-- Has `v' been inserted at the end by the most recent put or
    			-- extend?
    			-- (from LINKED_LIST)

    	is_leaf: BOOLEAN
    			-- Are there no children?
    			-- (from TREE)
    		require -- from  CONTAINER
    			True

    	is_root: BOOLEAN
    			-- Is there no parent?
    			-- (from TREE)

    	is_sibling (other: like parent): BOOLEAN
    			-- Are current node and `other' siblings?
    			-- (from TREE)
    		require -- from TREE
    			other_exists: other /= Void
    		ensure -- from TREE
    			not_root: Result implies not is_root
    			other_not_root: Result implies not other.is_root
    			same_parent: Result = not is_root and other.parent = parent

    	object_comparison: BOOLEAN
    			-- Must search operations use equal rather than `='
    			-- for comparing references? (Default: no, use `='.)
    			-- (from CONTAINER)

    	child_off: BOOLEAN
    			-- Is there no current item?
    			-- (from LINKED_LIST)
    		require -- from  TRAVERSABLE
    			True
    		require -- from  TREE
    			True

    	prunable: BOOLEAN
    			-- May items be removed? (Answer: yes.)
    			-- (from DYNAMIC_CHAIN)
    		require -- from  COLLECTION
    			True

    	readable: BOOLEAN is True
    			-- (from TREE)

    	readable_child: BOOLEAN
    			-- Is there a current child to be read?
    			-- (from TREE)

    	same_type (other: ANY): BOOLEAN
    			-- Is type of current object identical to type of `other'?
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    		ensure -- from ANY
    			definition: Result = (conforms_to (other) and other.conforms_to (Current))

    	valid_cursor (p: CURSOR): BOOLEAN
    			-- Can the cursor be moved to position `p'?
    			-- (from LINKED_LIST)

    	valid_cursor_index (i: INTEGER_32): BOOLEAN
    			-- Is `i' correctly bounded for cursor movement?
    			-- (from TREE)
    		require -- from  CHAIN
    			True
    		ensure -- from CHAIN
    			valid_cursor_index_definition: Result = ((i >= 0) and (i <= arity + 1))
    		ensure -- from TREE
    			valid_cursor_index_definition: Result = (i >= 0) and (i <= child_capacity + 1)

    	valid_index (i: INTEGER_32): BOOLEAN
    			-- Is `i' within allowable bounds?
    			-- (from CHAIN)
    		require -- from  TABLE
    			True
    		ensure then -- from INDEXABLE
    			only_if_in_index_set: Result implies ((i >= index_set.lower) and (i <= index_set.upper))
    		ensure then -- from CHAIN
    			valid_index_definition: Result = ((i >= 1) and (i <= arity))

    	writable: BOOLEAN is True
    			-- Is there a current item that may be modified?
    			-- (from TREE)

    	writable_child: BOOLEAN
    			-- Is there a current child that may be modified?
    			-- (from TREE)

    feature -- Status setting

    	compare_objects
    			-- Ensure that future search operations will use equal
    			-- rather than `=' for comparing references.
    			-- (from CONTAINER)
    		require -- from CONTAINER
    			changeable_comparison_criterion: changeable_comparison_criterion
    		ensure -- from CONTAINER
    			object_comparison

    	compare_references
    			-- Ensure that future search operations will use `='
    			-- rather than equal for comparing references.
    			-- (from CONTAINER)
    		require -- from CONTAINER
    			changeable_comparison_criterion: changeable_comparison_criterion
    		ensure -- from CONTAINER
    			reference_comparison: not object_comparison

    feature -- Cursor movement

    	child_back
    			-- Move cursor to previous position, if any.
    			-- (from TWO_WAY_LIST)
    		require -- from BILINEAR
    			not_before: not child_before
    		require -- from  TREE
    			True

    	child_finish
    			-- Move cursor to last position.
    			-- (Go before if empty)
    			-- (from TWO_WAY_LIST)
    		require -- from  LINEAR
    			True
    		require -- from  TREE
    			True
    		ensure then -- from CHAIN
    			at_last: not is_leaf implies child_islast
    		ensure then -- from LINKED_LIST
    			empty_convention: is_leaf implies child_before
    		ensure then -- from TWO_WAY_LIST
    			not_after: not child_after

    	child_forth
    			-- Move cursor to next position, if any.
    			-- (from TWO_WAY_LIST)
    		require -- from LINEAR
    			not_after: not child_after
    		require -- from  TREE
    			True
    		ensure then -- from LIST
    			moved_forth: child_index = old child_index + 1

    	child_go_i_th (i: INTEGER_32)
    			-- Move cursor to `i'-th position.
    			-- (from LINKED_LIST)
    		require -- from CHAIN
    			valid_cursor_index: valid_cursor_index (i)
    		require -- from  TREE
    			True
    		ensure -- from CHAIN
    			position_expected: child_index = i
    		ensure then -- from TREE
    			position: child_index = i

    	child_go_to (p: CURSOR)
    			-- Move cursor to position `p'.
    			-- (from LINKED_LIST)
    		require -- from CURSOR_STRUCTURE
    			cursor_position_valid: valid_cursor (p)
    		require -- from  TREE
    			True

    	move (i: INTEGER_32)
    			-- Move cursor `i' positions. The cursor
    			-- may end up `off' if the offset is to big.
    			-- (from TWO_WAY_LIST)
    		require -- from  CHAIN
    			True
    		ensure -- from CHAIN
    			too_far_right: (old child_index + i > arity) implies exhausted
    			too_far_left: (old child_index + i < 1) implies exhausted
    			expected_index: (not exhausted) implies (child_index = old child_index + i)
    		ensure then -- from LINKED_LIST
    			moved_if_inbounds: ((old child_index + i) >= 0 and (old child_index + i) <= (arity + 1)) implies child_index = (old child_index + i)
    			before_set: (old child_index + i) <= 0 implies child_before
    			after_set: (old child_index + i) >= (arity + 1) implies child_after

    	search_child (v: like child_item)
    			-- Move to first position (at or after current
    			-- position) where item and `v' are equal.
    			-- If structure does not include `v' ensure that
    			-- exhausted will be true.
    			-- (Reference or object equality,
    			-- based on object_comparison.)
    			-- (from BILINEAR)
    		ensure -- from LINEAR
    			object_found: (not exhausted and object_comparison) implies equal (v, child_item)
    			item_found: (not exhausted and not object_comparison) implies v = child_item

    	child_start
    			-- Move cursor to first position.
    			-- (from LINKED_LIST)
    		require -- from  TRAVERSABLE
    			True
    		require -- from  TREE
    			True
    		ensure then -- from CHAIN
    			at_first: not is_leaf implies child_isfirst
    		ensure then -- from LINKED_LIST
    			empty_convention: is_leaf implies child_after

    feature -- Element change

    	append (s: SEQUENCE [G])
    			-- Append a copy of `s'.
    			-- (from CHAIN)
    		require -- from SEQUENCE
    			argument_not_void: s /= Void
    		ensure -- from SEQUENCE
    			new_count: arity >= old arity

    	extend (v: like item)
    			-- Add `v' as new child.
    			-- (from DYNAMIC_TREE)

    	child_extend (v: like child_item)
    			-- Add `v' to end.
    			-- Do not move cursor.
    			-- (from TWO_WAY_LIST)
    		require -- from COLLECTION
    			extendible: child_extendible
    		require -- from  DYNAMIC_TREE
    			True
    		ensure -- from COLLECTION
    			item_inserted: is_inserted (v)
    		ensure then -- from BAG
    			one_more_occurrence: occurrences (v) = old (occurrences (v)) + 1

    	fill (other: TREE [G])
    			-- Fill with as many items of `other' as possible.
    			-- The representations of `other' and current node
    			-- need not be the same.
    			-- (from TREE)

    	force (v: like child_item)
    			-- Add `v' to end.
    			-- (from SEQUENCE)
    		require -- from SEQUENCE
    			extendible: child_extendible
    		ensure then -- from SEQUENCE
    			new_count: arity = old arity + 1
    			item_inserted: has (v)

    	twl_merge_left (other: like Current)
    			-- Merge `other' into current structure before cursor
    			-- position. Do not move cursor. Empty `other'.
    			-- (from TWO_WAY_LIST)
    		require -- from DYNAMIC_CHAIN
    			extendible: child_extendible
    			not_before: not child_before
    			other_exists: other /= Void
    			not_current: other /= Current
    		ensure -- from DYNAMIC_CHAIN
    			new_count: arity = old arity + old other.arity
    			new_index: child_index = old child_index + old other.arity
    			other_is_empty: other.is_leaf

    	twl_merge_right (other: like Current)
    			-- Merge `other' into current structure after cursor
    			-- position. Do not move cursor. Empty `other'.
    			-- (from TWO_WAY_LIST)
    		require -- from DYNAMIC_CHAIN
    			extendible: child_extendible
    			not_after: not child_after
    			other_exists: other /= Void
    			not_current: other /= Current
    		ensure -- from DYNAMIC_CHAIN
    			new_count: arity = old arity + old other.arity
    			same_index: child_index = old child_index
    			other_is_empty: other.is_leaf

    	merge_tree_after (other: like first_child)
    			-- Merge children of `other' into current structure
    			-- after cursor position. Do not move cursor.
    			-- Make `other' a leaf.
    		require -- from DYNAMIC_TREE
    			not_child_off: not child_off
    			other_exists: (other /= Void)
    		ensure -- from DYNAMIC_TREE
    			other_is_leaf: other.is_leaf

    	merge_tree_before (other: like first_child)
    			-- Merge children of `other' into current structure
    			-- before cursor position. Do not move cursor.
    			-- Make `other' a leaf.
    		require -- from DYNAMIC_TREE
    			not_child_off: not child_off
    			other_exists: (other /= Void)
    		ensure -- from DYNAMIC_TREE
    			other_is_leaf: other.is_leaf

    	prune (n: like first_child)
    			-- Prune `n' from children.
    		require -- from TREE
    			is_child: n.parent = Current
    		ensure -- from TREE
    			n_is_root: n.is_root

    	put (v: like item)
    			-- Make `v' the cell's item.
    			-- Was declared in CELL as synonym of replace.
    			-- (from CELL)
    		require -- from TREE
    			is_writable: writable
    		ensure -- from TREE
    			item_inserted: item = v
    		ensure -- from CELL
    			item_inserted: item = v

    	child_put (v: like child_item)
    			-- Replace current item by `v'.
    			-- (Synonym for replace)
    			-- (from CHAIN)
    		require -- from COLLECTION
    			extendible: child_extendible
    		require -- from TREE
    			child_writable: child_writable
    		ensure -- from COLLECTION
    			item_inserted: is_inserted (v)
    		ensure -- from TREE
    			item_inserted: child_item = v
    		ensure then -- from CHAIN
    			same_count: arity = old arity

    	put_child (n: like parent)
    			-- Add `n' to the list of children.
    			-- Do not move child cursor.
    		require -- from TREE
    			non_void_argument: n /= Void

    	put_child_left (n: like parent)
    			-- Add `n' to the left of cursor position.
    			-- Do not move cursor.
    		require -- from DYNAMIC_TREE
    			not_child_before: not child_before
    			non_void_argument: n /= Void

    	put_child_right (n: like parent)
    			-- Add `n' to the right of cursor position.
    			-- Do not move cursor.
    		require -- from DYNAMIC_TREE
    			not_child_after: not child_after
    			non_void_argument: n /= Void

    	put_front (v: like child_item)
    			-- Add `v' to beginning.
    			-- Do not move cursor.
    			-- (from TWO_WAY_LIST)
    		require -- from  DYNAMIC_CHAIN
    			True
    		ensure -- from DYNAMIC_CHAIN
    			new_count: arity = old arity + 1
    			item_inserted: first = v

    	put_i_th (v: like child_item; i: INTEGER_32)
    			-- Put `v' at `i'-th position.
    			-- (from CHAIN)
    		require -- from TABLE
    			valid_key: valid_index (i)
    		ensure then -- from INDEXABLE
    			insertion_done: i_th (i) = v

    	child_put_left (v: like child_item)
    			-- Add `v' to the left of cursor position.
    			-- Do not move cursor.
    			-- (from TWO_WAY_LIST)
    		require -- from DYNAMIC_CHAIN
    			extendible: child_extendible
    			not_before: not child_before
    		require -- from DYNAMIC_TREE
    			not_child_before: not child_before
    		ensure -- from DYNAMIC_CHAIN
    			new_count: arity = old arity + 1
    			new_index: child_index = old child_index + 1
    		ensure then -- from LINKED_LIST
    			previous_exists: previous /= Void
    			item_inserted: previous.item = v

    	child_put_right (v: like child_item)
    			-- Add `v' to the right of cursor position.
    			-- Do not move cursor.
    			-- (from TWO_WAY_LIST)
    		require -- from DYNAMIC_CHAIN
    			extendible: child_extendible
    			not_after: not child_after
    		require -- from DYNAMIC_TREE
    			not_child_after: not child_after
    		ensure -- from DYNAMIC_CHAIN
    			new_count: arity = old arity + 1
    			same_index: child_index = old child_index
    		ensure then -- from LINKED_LIST
    			next_exists: next /= Void
    			item_inserted: not old child_before implies next.item = v
    			item_inserted_before: old child_before implies child.item = v

    	replace (v: like item)
    			-- Make `v' the cell's item.
    			-- Was declared in CELL as synonym of put.
    			-- (from CELL)
    		require -- from TREE
    			is_writable: writable
    		ensure -- from TREE
    			item_inserted: item = v
    		ensure -- from CELL
    			item_inserted: item = v

    	child_replace (v: like child_item)
    			-- Replace current item by `v'.
    			-- (from LINKED_LIST)
    		require -- from ACTIVE
    			writable: child_writable
    		require -- from TREE
    			child_writable: child_writable
    		ensure -- from ACTIVE
    			item_replaced: child_item = v
    		ensure -- from TREE
    			item_inserted: child_item = v

    	replace_child (n: like parent)
    			-- Replace current child by `n'.
    		require -- from TREE
    			writable_child: writable_child
    		ensure -- from TREE
    			child_replaced: child = n

    	sprout
    			-- Make current node a root.
    			-- (from TREE)

    feature -- Removal

    	twl_prune (v: like child_item)
    			-- Remove first occurrence of `v', if any,
    			-- after cursor position.
    			-- If found, move cursor to right neighbor;
    			-- if not, make structure exhausted.
    			-- (from DYNAMIC_CHAIN)
    		require -- from COLLECTION
    			prunable: prunable

    	prune_all (v: like child_item)
    			-- Remove all occurrences of `v'.
    			-- (Reference or object equality,
    			-- based on object_comparison.)
    			-- Leave structure exhausted.
    			-- (from DYNAMIC_CHAIN)
    		require -- from COLLECTION
    			prunable: prunable
    		ensure -- from COLLECTION
    			no_more_occurrences: not has (v)
    		ensure then -- from DYNAMIC_CHAIN
    			is_exhausted: exhausted

    	remove_child
    			-- Remove current item.
    			-- Move cursor to right neighbor
    			-- (or `after' if no right neighbor).
    			-- (from TWO_WAY_LIST)
    		require -- from ACTIVE
    			prunable: prunable
    			writable: child_writable
    		require -- from DYNAMIC_TREE
    			child_not_off: not child_off
    		ensure then -- from DYNAMIC_LIST
    			after_when_empty: is_leaf implies child_after
    		ensure -- from DYNAMIC_TREE
    			new_arity: arity = old arity - 1
    			new_child_index: child_index = old child_index

    	remove_left_child
    			-- Remove item to the left of cursor position.
    			-- Do not move cursor.
    			-- (from TWO_WAY_LIST)
    		require -- from DYNAMIC_CHAIN
    			left_exists: child_index > 1
    		require -- from DYNAMIC_TREE
    			is_not_first: not child_isfirst
    		ensure -- from DYNAMIC_CHAIN
    			new_count: arity = old arity - 1
    			new_index: child_index = old child_index - 1
    		ensure -- from DYNAMIC_TREE
    			new_arity: arity = old arity - 1
    			new_child_index: child_index = old child_index - 1

    	remove_right_child
    			-- Remove item to the right of cursor position.
    			-- Do not move cursor.
    			-- (from TWO_WAY_LIST)
    		require -- from DYNAMIC_CHAIN
    			right_exists: child_index < arity
    		require -- from DYNAMIC_TREE
    			is_not_last: not child_islast
    		ensure -- from DYNAMIC_CHAIN
    			new_count: arity = old arity - 1
    			same_index: child_index = old child_index
    		ensure -- from DYNAMIC_TREE
    			new_arity: arity = old arity - 1
    			new_child_index: child_index = old child_index

    	remove_sublist
    			-- (from TWO_WAY_LIST)

    	split (n: INTEGER_32)
    			-- Remove from current list
    			-- min (`n', count - `index' - 1) items
    			-- starting at cursor position.
    			-- Move cursor right one position.
    			-- Make extracted sublist accessible
    			-- through attribute sublist.
    			-- (from TWO_WAY_LIST)
    		require -- from TWO_WAY_LIST
    			not_off: not child_off
    			valid_sublist: n >= 0

    	wipe_out
    			-- Remove all items.
    			-- (from TWO_WAY_LIST)
    		require -- from COLLECTION
    			prunable: prunable
    		require -- from  TREE
    			True
    		ensure -- from COLLECTION
    			wiped_out: is_leaf
    		ensure then -- from DYNAMIC_LIST
    			is_before: child_before
    		ensure -- from TREE
    			is_leaf: is_leaf

    feature -- Transformation

    	swap (i: INTEGER_32)
    			-- Exchange item at `i'-th position with item
    			-- at cursor position.
    			-- (from CHAIN)
    		require -- from CHAIN
    			not_off: not child_off
    			valid_index: valid_index (i)
    		ensure -- from CHAIN
    			swapped_to_item: child_item = old i_th (i)
    			swapped_from_item: i_th (i) = old child_item

    feature -- Conversion

    	binary_representation: BINARY_TREE [G]
    			-- Convert to binary tree representation:
    			-- first child becomes left child,
    			-- right sibling becomes right child.
    			-- (from TREE)
    		ensure -- from TREE
    			result_is_root: Result.is_root
    			result_has_no_right_child: not Result.has_right

    	fill_from_binary (b: BINARY_TREE [G])
    			-- Fill from a binary tree representation.
    			-- Left child becomes first child.
    			-- Right child becomes right sibling.
    			-- Any right child of `b' is ignored.
    			-- (from DYNAMIC_TREE)

    	linear_representation: LINEAR [G]
    			-- Representation as a linear structure
    			-- (from TREE)
    		require -- from  CONTAINER
    			True

    feature -- Duplication

    	copy (other: like Current)
    			-- Copy contents from `other'.
    			-- (from TREE)
    		require -- from ANY
    			other_not_void: other /= Void
    			type_identity: same_type (other)
    		ensure -- from ANY
    			is_equal: is_equal (other)

    	frozen deep_copy (other: like Current)
    			-- Effect equivalent to that of:
    			--		copy (`other' . deep_twin)
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    		ensure -- from ANY
    			deep_equal: deep_equal (Current, other)

    	frozen deep_twin: like Current
    			-- New object structure recursively duplicated from Current.
    			-- (from ANY)
    		ensure -- from ANY
    			deep_equal: deep_equal (Current, Result)

    	duplicate (n: INTEGER_32): like Current
    			-- Copy of sub-tree beginning at cursor position and
    			-- having min (`n', arity - child_index + 1)
    			-- children
    			-- (from DYNAMIC_TREE)
    		require -- from TREE
    			not_child_off: not child_off
    			valid_sublist: n >= 0

    	frozen standard_copy (other: like Current)
    			-- Copy every field of `other' onto corresponding field
    			-- of current object.
    			-- (from ANY)
    		require -- from ANY
    			other_not_void: other /= Void
    			type_identity: same_type (other)
    		ensure -- from ANY
    			is_standard_equal: standard_is_equal (other)

    	frozen standard_twin: like Current
    			-- New object field-by-field identical to `other'.
    			-- Always uses default copying semantics.
    			-- (from ANY)
    		ensure -- from ANY
    			standard_twin_not_void: Result /= Void
    			equal: standard_equal (Result, Current)

    	frozen twin: like Current
    			-- New object equal to `Current'
    			-- twin calls copy; to change copying/twining semantics, redefine copy.
    			-- (from ANY)
    		ensure -- from ANY
    			twin_not_void: Result /= Void
    			is_equal: Result.is_equal (Current)

    feature -- Basic operations

    	frozen default: like Current
    			-- Default value of object's type
    			-- (from ANY)

    	frozen default_pointer: POINTER
    			-- Default value of type `POINTER'
    			-- (Avoid the need to write `p'.default for
    			-- some `p' of type `POINTER'.)
    			-- (from ANY)

    	default_rescue
    			-- Process exception for routines with no Rescue clause.
    			-- (Default: do nothing.)
    			-- (from ANY)

    	frozen do_nothing
    			-- Execute a null action.
    			-- (from ANY)

    feature -- Implementation

    	child: like first_child
    			-- Element at cursor position
    			-- (from LINKED_LIST)

    	forget_left
    			-- Remove links with left neighbor.
    			-- (from BI_LINKABLE)
    		require -- from  TREE
    			True
    		ensure -- from BI_LINKABLE
    			left_not_chained: left_sibling = Void or else (old left_sibling /= Void) implies ((old left_sibling).right_sibling = Void)

    	forget_right
    			-- Remove links with right neighbor.
    			-- (from BI_LINKABLE)
    		require -- from  LINKABLE
    			True
    		require -- from  TREE
    			True
    		ensure -- from LINKABLE
    			not_chained: right_sibling = Void
    		ensure then -- from BI_LINKABLE
    			right_not_chained: (old right_sibling /= Void) implies ((old right_sibling).left_sibling = Void)

    feature -- Iteration

    	do_all (action: PROCEDURE [ANY, TUPLE [G]])
    			-- Apply `action' to every item.
    			-- Semantics not guaranteed if `action' changes the structure;
    			-- in such a case, apply iterator to clone of structure instead.
    			-- (from LINEAR)
    		require -- from TRAVERSABLE
    			action_exists: action /= Void

    	do_if (action: PROCEDURE [ANY, TUPLE [G]]; test: FUNCTION [ANY, TUPLE [G], BOOLEAN])
    			-- Apply `action' to every item that satisfies `test'.
    			-- Semantics not guaranteed if `action' or `test' changes the structure;
    			-- in such a case, apply iterator to clone of structure instead.
    			-- (from LINEAR)
    		require -- from TRAVERSABLE
    			action_exists: action /= Void
    			test_exits: test /= Void

    	for_all (test: FUNCTION [ANY, TUPLE [G], BOOLEAN]): BOOLEAN
    			-- Is `test' true for all items?
    			-- Semantics not guaranteed if `test' changes the structure;
    			-- in such a case, apply iterator to clone of structure instead.
    			-- (from LINEAR)
    		require -- from TRAVERSABLE
    			test_exits: test /= Void
    		ensure then -- from LINEAR
    			empty: is_leaf implies Result

    	there_exists (test: FUNCTION [ANY, TUPLE [G], BOOLEAN]): BOOLEAN
    			-- Is `test' true for at least one item?
    			-- Semantics not guaranteed if `test' changes the structure;
    			-- in such a case, apply iterator to clone of structure instead.
    			-- (from LINEAR)
    		require -- from TRAVERSABLE
    			test_exits: test /= Void

    feature -- Output

    	io: STD_FILES
    			-- Handle to standard file setup
    			-- (from ANY)

    	out: STRING_8
    			-- New string containing terse printable representation
    			-- of current object
    			-- Was declared in ANY as synonym of tagged_out.
    			-- (from ANY)

    	print (some: ANY)
    			-- Write terse external representation of `some'
    			-- on standard output.
    			-- (from ANY)

    	frozen tagged_out: STRING_8
    			-- New string containing terse printable representation
    			-- of current object
    			-- Was declared in ANY as synonym of out.
    			-- (from ANY)

    feature -- Platform

    	operating_environment: OPERATING_ENVIRONMENT
    			-- Objects available from the operating system
    			-- (from ANY)

    invariant
    	off_constraint: (child = Void) implies child_off

    		-- from DYNAMIC_TREE
    	extendible_definition: extendible
    	child_after_definition: child_after = (child_index = arity + 1)

    		-- from TREE
    	tree_consistency: child_readable implies child.parent = Current
    	leaf_definition: is_leaf = (arity = 0)
    	child_off_definition: child_off = child_before or child_after
    	child_before_definition: child_before = (child_index = 0)
    	child_isfirst_definition: child_isfirst = (not is_leaf and child_index = 1)
    	child_islast_definition: child_islast = (not is_leaf and child_index = child_capacity)
    	child_after_definition: child_after = (child_index >= child_capacity + 1)

    		-- from ANY
    	reflexive_equality: standard_is_equal (Current)
    	reflexive_conformance: conforms_to (Current)

    		-- from BI_LINKABLE
    	right_symmetry: (right_sibling /= Void) implies (right_sibling.left_sibling = Current)
    	left_symmetry: (left_sibling /= Void) implies (left_sibling.right_sibling = Current)

    		-- from TWO_WAY_LIST
    	non_empty_list_has_two_endpoints: not is_leaf implies (first_child /= Void and last_child /= Void)
    	first_element_constraint: first_child /= Void implies first_child.left_sibling = Void
    	last_element_constraint: last_child /= Void implies last_child.right_sibling = Void

    		-- from LINKED_LIST
    	prunable: prunable
    	empty_constraint: is_leaf implies ((first_child = Void) and (child = Void))
    	not_void_unless_empty: (child = Void) implies is_leaf
    	before_constraint: child_before implies (child = first_child)
    	after_constraint: child_after implies (child = last_child)

    		-- from LIST
    	before_definition: child_before = (child_index = 0)
    	after_definition: child_after = (child_index = arity + 1)

    		-- from CHAIN
    	non_negative_index: child_index >= 0
    	index_small_enough: child_index <= arity + 1
    	off_definition: child_off = ((child_index = 0) or (child_index = arity + 1))
    	isfirst_definition: child_isfirst = ((not is_leaf) and (child_index = 1))
    	islast_definition: child_islast = ((not is_leaf) and (child_index = arity))
    	item_corresponds_to_index: (not child_off) implies (child_item = i_th (child_index))
    	index_set_has_same_count: index_set.count = arity

    		-- from ACTIVE
    	writable_constraint: child_writable implies child_readable
    	empty_constraint: is_leaf implies (not child_readable) and (not child_writable)

    		-- from INDEXABLE
    	index_set_not_void: index_set /= Void

    		-- from BILINEAR
    	not_both: not (child_after and child_before)
    	before_constraint: child_before implies child_off

    		-- from LINEAR
    	after_constraint: child_after implies child_off

    		-- from TRAVERSABLE
    	empty_constraint: is_leaf implies child_off

    		-- from FINITE
    	empty_definition: is_leaf = (arity = 0)
    	non_negative_count: arity >= 0

    		-- from DYNAMIC_CHAIN
    	extendible: child_extendible

    indexing
    	library: "EiffelBase: Library of reusable components for Eiffel."
    	copyright: "Copyright (c) 1984-2006, Eiffel Software and others"
    	license: "Eiffel Forum License v2 (see http://www.eiffel.com/licensing/forum.txt)"
    	source: "[
    		Eiffel Software
    		356 Storke Road, Goleta, CA 93117 USA
    		Telephone 805-685-1006, Fax 805-685-6869
    		Website http://www.eiffel.com
    		Customer support http://support.eiffel.com
    	]"

    end -- class TWO_WAY_TREE