    indexing
    	description: "Cursor trees implemented in two-way linked representation"
    	legal: "See notice at end of class."
    	status: "See notice at end of class."
    	names: two_way_cursor_tree, cursor_tree
    	access: cursor, membership
    	representation: recursive, linked
    	contents: generic
    	date: "$Date: 2006-01-22 18:25:44 -0800 (Sun, 22 Jan 2006) $"
    	revision: "$Revision: 56675 $"

    class interface
    	TWO_WAY_CURSOR_TREE [G]

    create
    	make
    			-- Create an empty tree.
    		ensure
    			is_above: above
    			is_empty: is_empty

    	make_root (v: G)
    			-- Create a tree with `v' as root.

    feature -- Initialization

    	make
    			-- Create an empty tree.
    		ensure
    			is_above: above
    			is_empty: is_empty

    	make_root (v: G)
    			-- Create a tree with `v' as root.

    feature {ANY} -- Initialization

    	default_create
    			-- Process instances of classes with no creation clause.
    			-- (Default: do nothing.)
    			-- (from ANY)

    feature -- Access

    	child_item (i: INTEGER_32): G
    			-- Item in `i'-th child
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			argument_within_bounds: i >= 1 and then i <= arity
    			not_off: not off

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

    	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)

    	has (v: G): BOOLEAN
    			-- Does structure include an occurrence of `v'?
    			-- (Reference or object equality,
    			-- based on object_comparison.)
    			-- (from CURSOR_TREE)
    		require -- from  CONTAINER
    			True
    		ensure -- from CONTAINER
    			not_found_in_empty: Result implies not is_empty

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

    	item: G
    			-- Item at cursor position
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from TRAVERSABLE
    			not_off: not off
    		require -- from ACTIVE
    			readable: readable

    	occurrences (v: G): INTEGER_32
    			-- (from CURSOR_TREE)
    		require -- from  BAG
    			True
    		require -- from  LINEAR
    			True
    		ensure -- from BAG
    			non_negative_occurrences: Result >= 0

    	parent_item: G
    			-- Item in parent.
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			not_on_root: not is_root

    	search (v: like item)
    			-- Move to first position (at or after current
    			-- position) where item and `v' are equal.
    			-- (Reference or object equality,
    			-- based on object_comparison.)
    			-- If no such position ensure that exhausted will be true.
    			-- (from LINEAR)
    		ensure -- from LINEAR
    			object_found: (not exhausted and object_comparison) implies equal (v, item)
    			item_found: (not exhausted and not object_comparison) implies v = item

    feature -- Measurement

    	arity: INTEGER_32
    			-- Number of children of active node.
    			-- If cursor is above, 0 if tree is empty, 1 otherwise.
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from HIERARCHICAL
    			not_off: not off
    		require else -- from RECURSIVE_CURSOR_TREE
    			valid_cursor: not off or else above

    	breadth: INTEGER_32
    			-- Breadth of current level
    			-- (from CURSOR_TREE)

    	count: INTEGER_32
    			-- Number of items in the tree
    			-- (from RECURSIVE_CURSOR_TREE)

    	depth: INTEGER_32
    			-- Depth of the tree
    			-- (from CURSOR_TREE)

    	level: INTEGER_32
    			-- Level of current node in tree
    			-- (Root is on level 1)
    			-- (from CURSOR_TREE)

    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
    			-- Is `other' attached to an object considered
    			-- equal to current object?
    			-- (from ANY)
    		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

    	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

    	above: BOOLEAN
    			-- Is there no valid cursor position above cursor?
    			-- (from RECURSIVE_CURSOR_TREE)

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

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

    	below: BOOLEAN
    			-- Is there no valid cursor position below cursor?
    			-- (from CURSOR_TREE)

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

    	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: off implies Result

    	extendible: BOOLEAN
    			-- May new items be added on current level?
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from  COLLECTION
    			True

    	full: BOOLEAN is False
    			-- Is tree filled to capacity? (Answer: no.)

    	is_empty: BOOLEAN
    			-- Is the tree empty?
    			-- (from RECURSIVE_CURSOR_TREE)

    	is_inserted (v: G): BOOLEAN
    			-- Has `v' been inserted by the most recent insertion?
    			-- (By default, the value returned is equivalent to calling
    			-- `has (v)'. However, descendants might be able to provide more
    			-- efficient implementations.)
    			-- (from COLLECTION)

    	is_leaf: BOOLEAN

    	is_root: BOOLEAN
    			-- Is cursor on tree root?
    			-- (from RECURSIVE_CURSOR_TREE)

    	isfirst: BOOLEAN
    			-- Is cursor on first sibling?
    			-- (from RECURSIVE_CURSOR_TREE)

    	islast: BOOLEAN
    			-- Is cursor on last sibling?
    			-- (from RECURSIVE_CURSOR_TREE)

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

    	off: BOOLEAN
    			-- Is there no current item?
    			-- (True if is_empty)
    			-- (from CURSOR_TREE)
    		require -- from  TRAVERSABLE
    			True

    	prunable: BOOLEAN is True

    	readable: BOOLEAN
    			-- Is there a current item that may be read?
    			-- (from CURSOR_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 RECURSIVE_CURSOR_TREE)

    	valid_cursor_index (i: INTEGER_32): BOOLEAN
    			-- Can cursor be moved to `i'-th child?
    			-- 0 is before and arity + 1 is after.
    			-- (from CURSOR_TREE)

    	writable: BOOLEAN
    			-- Is there a current item that may be modified?
    			-- (from CURSOR_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

    	back
    			-- Move cursor one position backward.
    			-- (from RECURSIVE_CURSOR_TREE)

    	breadth_forth
    			-- Move cursor to next position in breadth-first order.
    			-- If the active node is the last in
    			-- breadth-first order, the cursor ends up off.
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			not_off: not off

    	down (i: INTEGER_32)
    			-- Move cursor one level downward:
    			-- to `i'-th child if there is one,
    			-- or after if `i' = arity + 1,
    			-- or before if `i' = 0.
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from HIERARCHICAL
    			not_off: not off
    			argument_within_bounds: i >= 1 and i <= arity
    		require else -- from CURSOR_TREE
    			not_before: not before
    			not_after: not after
    			not_below: not below
    			valid_cursor_index: (above and i = 0) or else valid_cursor_index (i)
    		ensure then -- from CURSOR_TREE
    			gone_before: (i = 0) implies before

    	forth
    			-- Move cursor one position forward.
    			-- (from RECURSIVE_CURSOR_TREE)

    	go_last_child
    			-- Go to the last child of current parent.
    			-- No effect if below
    			-- (from CURSOR_TREE)
    		require -- from  LINEAR
    			True
    		require else -- from CURSOR_TREE
    			not_above: not above

    	go_to (p: CURSOR)
    			-- Move cursor to position `p'.
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from CURSOR_STRUCTURE
    			cursor_position_valid: valid_cursor (p)

    	level_back
    			-- Move cursor to previous position of current level.
    			-- (from CURSOR_TREE)

    	level_forth
    			-- Move cursor to next position of current level.
    			-- (from CURSOR_TREE)

    	postorder_forth
    			-- Move cursor to next position in postorder.
    			-- If the active node is the last in
    			-- postorder, the cursor ends up off.
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			not_off: not off

    	postorder_start
    			-- Move cursor to first position in postorder.
    			-- Leave cursor off if tree is empty.
    			-- (from CURSOR_TREE)

    	preorder_forth
    			-- Move cursor to next position in preorder.
    			-- If the active node is the last in
    			-- preorder, the cursor ends up off.
    			-- (from CURSOR_TREE)
    		require -- from LINEAR
    			not_after: not after

    	start
    			-- Move cursor to root.
    			-- Leave cursor off if is_empty.
    			-- (from CURSOR_TREE)
    		require -- from  TRAVERSABLE
    			True
    		ensure then -- from CURSOR_TREE
    			on_root_unless_empty: not is_empty implies is_root

    	start_on_level (l: INTEGER_32)
    			-- Move the cursor to the first position
    			-- of the `l'-th level counting from root.
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			argument_within_bounds: l >= 1 and then depth >= l
    		ensure -- from CURSOR_TREE
    			level_expected: level = l
    			is_first: isfirst

    	up
    			-- Move cursor one level upward to parent,
    			-- or above if is_root holds.
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from HIERARCHICAL
    			not_off: not off
    		require else -- from CURSOR_TREE
    			not_above: not above
    		ensure then -- from CURSOR_TREE
    			not_before: not before
    			not_after: not after
    			not_below: not below
    			coherency: (not old off and above) = (old is_root)

    feature -- Element change

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

    	container_fill (other: CONTAINER [G])
    			-- Fill with as many items of `other' as possible.
    			-- The representations of `other' and current structure
    			-- need not be the same.
    			-- (from COLLECTION)
    		require -- from COLLECTION
    			other_not_void: other /= Void
    			extendible: extendible

    	fill_from_active (other: CURSOR_TREE [G])
    			-- Copy subtree of `other''s active node
    			-- onto active node of current tree.
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			cursor_on_leaf: is_leaf

    	merge_left (other: CURSOR_TREE [G])
    			-- Merge the items of `other' into current structure to
    			-- the left of cursor position.
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			other_exists: other /= Void
    			not_before: not before
    			not_above: not above
    			only_one_root: (level = 1) implies is_empty

    	merge_right (other: CURSOR_TREE [G])
    			-- Merge the items of `other' into current structure to
    			-- the right of cursor position.
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			other_exists: other /= Void
    			not_after: not after
    			not_above: not above
    			only_one_root: (level = 1) implies is_empty

    	put (v: G)
    			-- Put `v' at cursor position.
    			-- (Synonym for replace)
    			-- (from CURSOR_TREE)
    		require -- from COLLECTION
    			extendible: extendible
    		ensure -- from COLLECTION
    			item_inserted: is_inserted (v)

    	put_child (v: G)
    			-- Put `v' as child of a leaf.
    		require
    			is_leaf: is_leaf

    	put_left (v: G)
    			-- Add `v' to the left of cursor position.
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			not_before: not before
    			not_above: not above
    			only_one_root: (level = 1) implies is_empty

    	put_right (v: G)
    			-- Add `v' to the right of cursor position.
    		require -- from CURSOR_TREE
    			not_after: not after
    			not_above: not above
    			only_one_root: (level = 1) implies is_empty

    	put_root (v: G)
    			-- Put `v' as root of an empty tree.
    		require
    			is_empty: is_empty
    		ensure
    			is_root: is_root
    			count = 1

    	replace (v: G)
    			-- Replace current item by `v'.
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from ACTIVE
    			writable: writable
    		ensure -- from ACTIVE
    			item_replaced: item = v

    feature -- Removal

    	remove
    			-- Remove node at cursor position
    			-- (and consequently the corresponding
    			-- subtree). Cursor moved up one level.
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from ACTIVE
    			prunable: prunable
    			writable: writable
    		ensure then -- from RECURSIVE_CURSOR_TREE
    			not_off_unless_empty: is_empty or else not off

    	wipe_out
    			-- Remove all items.
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from COLLECTION
    			prunable: prunable
    		ensure -- from COLLECTION
    			wiped_out: is_empty
    		ensure then -- from RECURSIVE_CURSOR_TREE
    			cursor_above: above

    feature -- Conversion

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

    feature -- Duplication

    	child_tree (i: INTEGER_32): like Current
    			-- Subtree rooted at `i'-th child
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			argument_within_bounds: i >= 1 and then i <= arity
    			not_off: not off

    	copy (other: like Current)
    			-- Update current object using fields of object attached
    			-- to `other', so as to yield equal objects.
    			-- (from ANY)
    		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)

    	parent_tree: like Current
    			-- Subtree rooted at parent
    			-- (from CURSOR_TREE)
    		require -- from CURSOR_TREE
    			not_on_root: not is_root
    			not_off: not off

    	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)

    	subtree: like Current
    			-- Subtree rooted at current node.
    		require -- from CURSOR_TREE
    			not_off: not off

    	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 -- Insert element

    	extend (v: G)
    			-- Add `v' after last child.
    			-- Make `v' the `first_child' if below and place
    			-- cursor before.
    			-- (from RECURSIVE_CURSOR_TREE)
    		require -- from COLLECTION
    			extendible: extendible
    		ensure -- from COLLECTION
    			item_inserted: is_inserted (v)
    		ensure then -- from BAG
    			one_more_occurrence: occurrences (v) = old (occurrences (v)) + 1

    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 TRAVERSABLE)
    		require -- from TRAVERSABLE
    			action_exists: action /= Void

    	linear_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 TRAVERSABLE)
    		require -- from TRAVERSABLE
    			action_exists: action /= Void
    			test_exits: test /= Void

    	linear_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

    	linear_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_empty implies Result

    	for_all (test: FUNCTION [ANY, TUPLE [G], BOOLEAN]): BOOLEAN
    			-- Is `test' true for all items?
    			-- (from TRAVERSABLE)
    		require -- from TRAVERSABLE
    			test_exits: test /= Void

    	there_exists (test: FUNCTION [ANY, TUPLE [G], BOOLEAN]): BOOLEAN
    			-- Is `test' true for at least one item?
    			-- (from TRAVERSABLE)
    		require -- from TRAVERSABLE
    			test_exits: test /= Void

    	linear_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)

    feature {ANY} -- Retrieval

    	frozen internal_correct_mismatch
    			-- Called from runtime to perform a proper dynamic dispatch on `correct_mismatch'
    			-- from MISMATCH_CORRECTOR.
    			-- (from ANY)

    invariant
    		-- from RECURSIVE_CURSOR_TREE
    	coherency: not above implies active_parent.child = active

    		-- from CURSOR_TREE
    	non_negative_depth: depth >= 0
    	non_negative_breadth: breadth >= 0
    	is_leaf_definition: not off implies is_leaf = (arity = 0)
    	above_property: above implies (arity <= 1)
    	on_tree: (isfirst or islast or is_leaf or is_root) implies not off
    	off_definition: off = after or before or above or below
    	below_constraint: below implies ((after or before) and not above)
    	above_constraint: above implies not (before or after or below)
    	after_constraint: after implies not (before or above)
    	before_constaint: before implies not (after or above)
    	empty_below_constraint: (is_empty and (after or before)) implies below

    		-- from HIERARCHICAL
    	non_negative_successor_count: arity >= 0

    		-- from TRAVERSABLE
    	empty_constraint: is_empty implies off

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

    		-- from ACTIVE
    	writable_constraint: writable implies readable
    	empty_constraint: is_empty implies (not readable) and (not writable)

    		-- from LINEAR
    	after_constraint: after implies off

    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_CURSOR_TREE