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Tree::DAG_Node(3)     User Contributed Perl Documentation    Tree::DAG_Node(3)




NAME

       Tree::DAG_Node - An N-ary tree


SYNOPSIS

   Using as a base class
               package Game::Tree::Node;

               use parent 'Tree::DAG_Node';

               # Now add your own methods overriding/extending the methods in C<Tree::DAG_Node>...

   Using as a class on its own
               use Tree::DAG_Node;

               my($root) = Tree::DAG_Node -> new({name => 'root', attributes => {uid => 0} });

               $root -> add_daughter(Tree::DAG_Node -> new({name => 'one', attributes => {uid => 1} }) );
               $root -> add_daughter(Tree::DAG_Node -> new({name => 'two', attributes => {} }) );
               $root -> add_daughter(Tree::DAG_Node -> new({name => 'three'}) ); # Attrs default to {}.

       Or:

               my($count) = 0;
               my($tree)  = Tree::DAG_Node -> new({name => 'Root', attributes => {'uid' => $count} });

       Or:

               my $root = Tree::DAG_Node -> new();

               $root -> name("I'm the tops");
               $root -> attributes({uid => 0});

               my $new_daughter = $root -> new_daughter;

               $new_daughter -> name('Another node');
               $new_daughter -> attributes({uid => 1});
               ...

       Lastly, for fancy wrappers - called _add_daughter() - around "new()",
       see these modules: Marpa::Demo::StringParser and GraphViz2::Marpa. Both
       of these modules use Moo.

       See scripts/*.pl for other samples.

   Using with utf-8 data
       read_tree($file_name) works with utf-8 data. See t/read.tree.t and
       t/tree.utf8.attributes.txt.  Such a file can be created by redirecting
       the output of tree2string() to a file of type utf-8.

       See the docs for Encode for the difference between utf8 and utf-8. In
       brief, use utf-8.

       See also scripts/write_tree.pl and scripts/read.tree.pl and
       scripts/read.tree.log.


DESCRIPTION

       This class encapsulates/makes/manipulates objects that represent nodes
       in a tree structure. The tree structure is not an object itself, but is
       emergent from the linkages you create between nodes.  This class
       provides the methods for making linkages that can be used to build up a
       tree, while preventing you from ever making any kinds of linkages which
       are not allowed in a tree (such as having a node be its own mother or
       ancestor, or having a node have two mothers).

       This is what I mean by a "tree structure", a bit redundantly stated:

       o A tree is a special case of an acyclic directed graph
       o A tree is a network of nodes where there's exactly one root node
           Also, the only primary relationship between nodes is the mother-
           daughter relationship.

       o No node can be its own mother, or its mother's mother, etc
       o Each node in the tree has exactly one parent
           Except for the root of course, which is parentless.

       o Each node can have any number (0 .. N) daughter nodes
           A given node's daughter nodes constitute an ordered list.

           However, you are free to consider this ordering irrelevant.  Some
           applications do need daughters to be ordered, so I chose to
           consider this the general case.

       o A node can appear in only one tree, and only once in that tree
           Notably (notable because it doesn't follow from the two above
           points), a node cannot appear twice in its mother's daughter list.

       o There's an idea of up versus down
           Up means towards to the root, and down means away from the root
           (and towards the leaves).

       o There's an idea of left versus right
           Left is toward the start (index 0) of a given node's daughter list,
           and right is toward the end of a given node's daughter list.

       Trees as described above have various applications, among them:
       representing syntactic constituency, in formal linguistics;
       representing contingencies in a game tree; representing abstract syntax
       in the parsing of any computer language -- whether in expression trees
       for programming languages, or constituency in the parse of a markup
       language document.  (Some of these might not use the fact that
       daughters are ordered.)

       (Note: B-Trees are a very special case of the above kinds of trees, and
       are best treated with their own class.  Check CPAN for modules
       encapsulating B-Trees; or if you actually want a database, and for some
       reason ended up looking here, go look at AnyDBM_File.)

       Many base classes are not usable except as such -- but "Tree::DAG_Node"
       can be used as a normal class.  You can go ahead and say:

               use Tree::DAG_Node;
               my $root = Tree::DAG_Node->new();
               $root->name("I'm the tops");
               $new_daughter = Tree::DAG_Node->new();
               $new_daughter->name("More");
               $root->add_daughter($new_daughter);

       and so on, constructing and linking objects from "Tree::DAG_Node" and
       making useful tree structures out of them.


A NOTE TO THE READER

       This class is big and provides lots of methods.  If your problem is
       simple (say, just representing a simple parse tree), this class might
       seem like using an atomic sledgehammer to swat a fly.  But the
       complexity of this module's bells and whistles shouldn't detract from
       the efficiency of using this class for a simple purpose.  In fact, I'd
       be very surprised if any one user ever had use for more that even a
       third of the methods in this class.  And remember: an atomic
       sledgehammer will kill that fly.


OBJECT CONTENTS

       Implementationally, each node in a tree is an object, in the sense of
       being an arbitrarily complex data structure that belongs to a class
       (presumably "Tree::DAG_Node", or ones derived from it) that provides
       methods.

       The attributes of a node-object are:

       o mother -- this node's mother.  undef if this is a root
       o daughters -- the (possibly empty) list of daughters of this node
       o name -- the name for this node
           Need not be unique, or even printable.  This is printed in some of
           the various dumper methods, but it's up to you if you don't put
           anything meaningful or printable here.

       o attributes -- whatever the user wants to use it for
           Presumably a hashref to whatever other attributes the user wants to
           store without risk of colliding with the object's real attributes.
           (Example usage: attributes to an SGML tag -- you definitely
           wouldn't want the existence of a "mother=foo" pair in such a tag to
           collide with a node object's 'mother' attribute.)

           Aside from (by default) initializing it to {}, and having the
           access method called "attributes" (described a ways below), I don't
           do anything with the "attributes" in this module.  I basically
           intended this so that users who don't want/need to bother deriving
           a class from "Tree::DAG_Node", could still attach whatever data
           they wanted in a node.

       "mother" and "daughters" are attributes that relate to linkage -- they
       are never written to directly, but are changed as appropriate by the
       "linkage methods", discussed below.

       The other two (and whatever others you may add in derived classes) are
       simply accessed thru the same-named methods, discussed further below.

   About The Documented Interface
       Stick to the documented interface (and comments in the source --
       especially ones saying "undocumented!" and/or "disfavored!" -- do not
       count as documentation!), and don't rely on any behavior that's not in
       the documented interface.

       Specifically, unless the documentation for a particular method says
       "this method returns thus-and-such a value", then you should not rely
       on it returning anything meaningful.

       A passing acquaintance with at least the broader details of the source
       code for this class is assumed for anyone using this class as a base
       class -- especially if you're overriding existing methods, and
       definitely if you're overriding linkage methods.


MAIN CONSTRUCTOR, AND INITIALIZER

       the constructor CLASS->new() or CLASS->new($options)
           This creates a new node object, calls $object->_init($options) to
           provide it sane defaults (like: undef name, undef mother, no
           daughters, 'attributes' setting of a new empty hashref), and
           returns the object created.  (If you just said "CLASS->new()" or
           "CLASS->new", then it pretends you called "CLASS->new({})".)

           See also the comments under "new($hashref)" for options supported
           in the call to new().

           If you use "Tree::DAG_Node" as a superclass, and you add attributes
           that need to be initialized, what you need to do is provide an
           _init method that calls $this->SUPER::_init($options) to use its
           superclass's _init method, and then initializes the new attributes:

             sub _init {
               my($this, $options) = @_[0,1];
               $this->SUPER::_init($options); # call my superclass's _init to
                 # init all the attributes I'm inheriting

               # Now init /my/ new attributes:
               $this->{'amigos'} = []; # for example
             }

       the constructor $obj->new() or $obj->new($options)
           Just another way to get at the "new($hashref)" method. This does
           not copy $obj, but merely constructs a new object of the same class
           as it.  Saves you the bother of going $class = ref $obj; $obj2 =
           $class->new;

       the method $node->_init($options)
           Initialize the object's attribute values.  See the discussion
           above.  Presumably this should be called only by the guts of the
           "new($hashref)" constructor -- never by the end user.

           Currently there are no documented options for putting in the
           $options hashref, but (in case you want to disregard the above
           rant) the option exists for you to use $options for something
           useful in a derived class.

           Please see the source for more information.

       see also (below) the constructors "new_daughter" and
       "new_daughter_left"


METHODS

   add_daughter(LIST)
       An exact synonym for "add_daughters(LIST)".

   add_daughters(LIST)
       This method adds the node objects in LIST to the (right) end of
       $mother's daughter list.  Making a node N1 the daughter of another node
       N2 also means that N1's mother attribute is "automatically" set to N2;
       it also means that N1 stops being anything else's daughter as it
       becomes N2's daughter.

       If you try to make a node its own mother, a fatal error results.  If
       you try to take one of a node N1's ancestors and make it also a
       daughter of N1, a fatal error results.  A fatal error results if
       anything in LIST isn't a node object.

       If you try to make N1 a daughter of N2, but it's already a daughter of
       N2, then this is a no-operation -- it won't move such nodes to the end
       of the list or anything; it just skips doing anything with them.

   add_daughter_left(LIST)
       An exact synonym for "add_daughters_left(LIST)".

   add_daughters_left(LIST)
       This method is just like "add_daughters(LIST)", except that it adds the
       node objects in LIST to the (left) beginning of $mother's daughter
       list, instead of the (right) end of it.

   add_left_sister(LIST)
       An exact synonym for "add_left_sisters(LIST)".

   add_left_sisters(LIST)
       This adds the elements in LIST (in that order) as immediate left
       sisters of $node.  In other words, given that B's mother's daughter-
       list is (A,B,C,D), calling B->add_left_sisters(X,Y) makes B's mother's
       daughter-list (A,X,Y,B,C,D).

       If LIST is empty, this is a no-op, and returns empty-list.

       This is basically implemented as a call to $node->replace_with(LIST,
       $node), and so all replace_with's limitations and caveats apply.

       The return value of $node->add_left_sisters(LIST) is the elements of
       LIST that got added, as returned by replace_with -- minus the copies of
       $node you'd get from a straight call to $node->replace_with(LIST,
       $node).

   add_right_sister(LIST)
       An exact synonym for "add_right_sisters(LIST)".

   add_right_sisters(LIST)
       Just like add_left_sisters (which see), except that the elements in
       LIST (in that order) as immediate right sisters of $node;

       In other words, given that B's mother's daughter-list is (A,B,C,D),
       calling B->add_right_sisters(X,Y) makes B's mother's daughter-list
       (A,B,X,Y,C,D).

   address()
   address(ADDRESS)
       With the first syntax, returns the address of $node within its tree,
       based on its position within the tree.  An address is formed by noting
       the path between the root and $node, and concatenating the daughter-
       indices of the nodes this passes thru (starting with 0 for the root,
       and ending with $node).

       For example, if to get from node ROOT to node $node, you pass thru
       ROOT, A, B, and $node, then the address is determined as:

       o ROOT's my_daughter_index is 0
       o A's my_daughter_index is, suppose, 2
           A is index 2 in ROOT's daughter list.

       o B's my_daughter_index is, suppose, 0
           B is index 0 in A's daughter list.

       o $node's my_daughter_index is, suppose, 4
           $node is index 4 in B's daughter list.

       The address of the above-described $node is, therefore, "0:2:0:4".

       (As a somewhat special case, the address of the root is always "0"; and
       since addresses start from the root, all addresses start with a "0".)

       The second syntax, where you provide an address, starts from the root
       of the tree $anynode belongs to, and returns the node corresponding to
       that address.  Returns undef if no node corresponds to that address.
       Note that this routine may be somewhat liberal in its interpretation of
       what can constitute an address; i.e., it accepts "0.2.0.4", besides
       "0:2:0:4".

       Also note that the address of a node in a tree is meaningful only in
       that tree as currently structured.

       (Consider how ($address1 cmp $address2) may be magically meaningful to
       you, if you meant to figure out what nodes are to the right of what
       other nodes.)

   ancestors()
       Returns the list of this node's ancestors, starting with its mother,
       then grandmother, and ending at the root.  It does this by simply
       following the 'mother' attributes up as far as it can.  So if $item IS
       the root, this returns an empty list.

       Consider that scalar($node->ancestors) returns the ply of this node
       within the tree -- 2 for a granddaughter of the root, etc., and 0 for
       root itself.

   attribute()
   attribute(SCALAR)
       Exact synonyms for "attributes()" and "attributes(SCALAR)".

   attributes()
   attributes(SCALAR)
       In the first form, returns the value of the node object's "attributes"
       attribute.  In the second form, sets it to the value of SCALAR.  I
       intend this to be used to store a reference to a (presumably anonymous)
       hash the user can use to store whatever attributes he doesn't want to
       have to store as object attributes.  In this case, you needn't ever set
       the value of this.  (_init has already initialized it to {}.)  Instead
       you can just do...

         $node->attributes->{'foo'} = 'bar';

       ...to write foo => bar.

   clear_daughters()
       This unlinks all $mother's daughters.  Returns the list of what used to
       be $mother's daughters.

       Not to be confused with "remove_daughters(LIST)".

   common(LIST)
       Returns the lowest node in the tree that is ancestor-or-self to the
       nodes $node and LIST.

       If the nodes are far enough apart in the tree, the answer is just the
       root.

       If the nodes aren't all in the same tree, the answer is undef.

       As a degenerate case, if LIST is empty, returns $node.

   common_ancestor(LIST)
       Returns the lowest node that is ancestor to all the nodes given (in
       nodes $node and LIST).  In other words, it answers the question: "What
       node in the tree, as low as possible, is ancestor to the nodes given
       ($node and LIST)?"

       If the nodes are far enough apart, the answer is just the root --
       except if any of the nodes are the root itself, in which case the
       answer is undef (since the root has no ancestor).

       If the nodes aren't all in the same tree, the answer is undef.

       As a degenerate case, if LIST is empty, returns $node's mother; that'll
       be undef if $node is root.

   copy($option)
       Returns a copy of the calling node (the invocant). E.g.: my($copy) =
       $node -> copy;

       $option is a hashref of options, with these (key => value) pairs:

       o no_attribute_copy => $Boolean
           If set to 1, do not copy the node's attributes.

           If not specified, defaults to 0, which copies attributes.

   copy_at_and_under()
   copy_at_and_under($options)
       This returns a copy of the subtree consisting of $node and everything
       under it.

       If you pass no options, copy_at_and_under pretends you've passed {}.

       This works by recursively building up the new tree from the leaves,
       duplicating nodes using $orig_node->copy($options_ref) and then linking
       them up into a new tree of the same shape.

       Options you specify are passed down to calls to $node->copy.

   copy_tree()
   copy_tree($options)
       This returns the root of a copy of the tree that $node is a member of.
       If you pass no options, copy_tree pretends you've passed {}.

       This method is currently implemented as just a call to
       $this->root->copy_at_and_under($options), but magic may be added in the
       future.

       Options you specify are passed down to calls to $node->copy.

   daughters()
       This returns the (possibly empty) list of daughters for $node.

   decode_lol($lol)
       Returns an arrayref having decoded the deeply nested structure $lol.

       $lol will be the output of either tree_to_lol() or
       tree_to_simple_lol().

       See scripts/read.tree.pl, and it's output file scripts/read.tree.log.

   delete_tree()
       Destroys the entire tree that $node is a member of (starting at the
       root), by nulling out each node-object's attributes (including, most
       importantly, its linkage attributes -- hopefully this is more than
       sufficient to eliminate all circularity in the data structure), and
       then moving it into the class DEADNODE.

       Use this when you're finished with the tree in question, and want to
       free up its memory.  (If you don't do this, it'll get freed up anyway
       when your program ends.)

       If you try calling any methods on any of the node objects in the tree
       you've destroyed, you'll get an error like:

         Can't locate object method "leaves_under"
           via package "DEADNODE".

       So if you see that, that's what you've done wrong.  (Actually, the
       class DEADNODE does provide one method: a no-op method "delete_tree".
       So if you want to delete a tree, but think you may have deleted it
       already, it's safe to call $node->delete_tree on it (again).)

       The "delete_tree()" method is needed because Perl's garbage collector
       would never (as currently implemented) see that it was time to de-
       allocate the memory the tree uses -- until either you call
       $node->delete_tree, or until the program stops (at "global destruction"
       time, when everything is unallocated).

       Incidentally, there are better ways to do garbage-collecting on a tree,
       ways which don't require the user to explicitly call a method like
       "delete_tree()" -- they involve dummy classes, as explained at
       <http://mox.perl.com/misc/circle-destroy.pod>

       However, introducing a dummy class concept into "Tree::DAG_Node" would
       be rather a distraction.  If you want to do this with your derived
       classes, via a DESTROY in a dummy class (or in a tree-metainformation
       class, maybe), then feel free to.

       The only case where I can imagine "delete_tree()" failing to totally
       void the tree, is if you use the hashref in the "attributes" attribute
       to store (presumably among other things) references to other nodes'
       "attributes" hashrefs -- which 1) is maybe a bit odd, and 2) is your
       problem, because it's your hash structure that's circular, not the
       tree's.  Anyway, consider:

             # null out all my "attributes" hashes
             $anywhere->root->walk_down({
               'callback' => sub {
                 $hr = $_[0]->attributes; %$hr = (); return 1;
               }
             });
             # And then:
             $anywhere->delete_tree;

       (I suppose "delete_tree()" is a "destructor", or as close as you can
       meaningfully come for a circularity-rich data structure in Perl.)

       See also "WHEN AND HOW TO DESTROY THE TREE".

   depth_under()
       Returns an integer representing the number of branches between this
       $node and the most distant leaf under it.  (In other words, this
       returns the ply of subtree starting of $node.  Consider
       scalar($it->ancestors) if you want the ply of a node within the whole
       tree.)

   descendants()
       Returns a list consisting of all the descendants of $node.  Returns
       empty-list if $node is a terminal_node.

       (Note that it's spelled "descendants", not "descendents".)

   draw_ascii_tree([$options])
       Here, the [] refer to an optional parameter.

       Returns an arrayref of lines suitable for printing.

       Draws a nice ASCII-art representation of the tree structure.

       The tree looks like:

                            |
                         <Root>
                  /-------+-----+---+---\
                  |       |     |   |   |
                 <I>     <H>   <D> <E> <B>
                /---\   /---\   |   |   |
                |   |   |   |  <F> <F> <C>
               <J> <J> <J> <J>  |   |
                |   |   |   |  <G> <G>
               <K> <L> <K> <L>
                    |       |
                   <M>     <M>
                    |       |
                   <N>     <N>
                    |       |
                   <O>     <O>

       See scripts/cut.and.paste.subtrees.pl.

       Example usage:

         print map("$_\n", @{$tree->draw_ascii_tree});

       draw_ascii_tree() takes parameters you set in the $options hashref:

       o h_compact
           Takes 0 or 1.  Sets the extent to which draw_ascii_tree() tries to
           save horizontal space.

           If I think of a better scrunching algorithm, there'll be a "2"
           setting for this.

           Default: 1.

       o h_spacing
           Takes a number 0 or greater.  Sets the number of spaces inserted
           horizontally between nodes (and groups of nodes) in a tree.

           Default: 1.

       o no_name
           If true, draw_ascii_tree() doesn't print the name of the node; it
           simply prints a "*".

           Default: 0 (i.e., print the node name.)

       o v_compact
           Takes a number 0, 1, or 2.  Sets the degree to which
           draw_ascii_tree() tries to save vertical space.  Defaults to 1.

       The code occasionally returns trees that are a bit cock-eyed in parts;
       if anyone can suggest a better drawing algorithm, I'd be appreciative.

       See also "tree2string($options, [$some_tree])".

   dump_names($options)
       Returns an array.

       Dumps, as an indented list, the names of the nodes starting at $node,
       and continuing under it.  Options are:

       o _depth -- A nonnegative number
           Indicating the depth to consider $node as being at (and so the
           generation under that is that plus one, etc.).  You may choose to
           use set _depth => scalar($node->ancestors).

           Default: 0.

       o tick -- a string to preface each entry with
           This string goes between the indenting-spacing and the node's name.
           You may prefer "*" or "-> " or something.

           Default: ''.

       o indent -- the string used to indent with
           Another sane value might be '. ' (period, space).  Setting it to
           empty-string suppresses indenting.

           Default: ' ' x 2.

       The output is not printed, but is returned as a list, where each item
       is a line, with a "\n" at the end.

   format_node($options, $node)
       Returns a string consisting of the node's name and, optionally, it's
       attributes.

       Possible keys in the $options hashref:

       o no_attributes => $Boolean
           If 1, the node's attributes are not included in the string
           returned.

           Default: 0 (include attributes).

       Calls "hashref2string($hashref)".

       Called by "node2string($options, $node, $vert_dashes)".

       You would not normally call this method.

       If you don't wish to supply options, use format_node({}, $node).

   generation()
       Returns a list of all nodes (going left-to-right) that are in $node's
       generation -- i.e., that are the some number of nodes down from the
       root.  $root->generation() is just $root.

       Of course, $node is always in its own generation.

   generation_under($node)
       Like "generation()", but returns only the nodes in $node's generation
       that are also descendants of $node -- in other words,

           @us = $node->generation_under( $node->mother->mother );

       is all $node's first cousins (to borrow yet more kinship terminology)
       -- assuming $node does indeed have a grandmother.  Actually "cousins"
       isn't quite an apt word, because @us ends up including $node's siblings
       and $node.

       Actually, "generation_under($node)" is just an alias to "generation()",
       but I figure that this:

          @us = $node->generation_under($way_upline);

       is a bit more readable than this:

          @us = $node->generation($way_upline);

       But it's up to you.

       $node->generation_under($node) returns just $node.

       If you call $node->generation_under($node) but NODE2 is not $node or an
       ancestor of $node, it behaves as if you called just
       $node->generation().

   hashref2string($hashref)
       Returns the given hashref as a string.

       Called by "format_node($options, $node)".

   is_daughter_of($node2)
       Returns true iff $node is a daughter of $node2.  Currently implemented
       as just a test of ($it->mother eq $node2).

   is_node()
       This always returns true.  More pertinently, $object->can('is_node') is
       true (regardless of what "is_node()" would do if called) for objects
       belonging to this class or for any class derived from it.

   is_root()
       Returns 1 if the caller is the root, and 0 if it is not.

   leaves_under()
       Returns a list (going left-to-right) of all the leaf nodes under $node.
       ("Leaf nodes" are also called "terminal nodes" -- i.e., nodes that have
       no daughters.)  Returns $node in the degenerate case of $node being a
       leaf itself.

   left_sister()
       Returns the node that's the immediate left sister of $node.  If $node
       is the leftmost (or only) daughter of its mother (or has no mother),
       then this returns undef.

       See also "add_left_sisters(LIST)" and "add_right_sisters(LIST)".

   left_sisters()
       Returns a list of nodes that're sisters to the left of $node.  If $node
       is the leftmost (or only) daughter of its mother (or has no mother),
       then this returns an empty list.

       See also "add_left_sisters(LIST)" and "add_right_sisters(LIST)".

   lol_to_tree($lol)
       This must be called as a class method.

       Converts something like bracket-notation for "Chomsky trees" (or
       rather, the closest you can come with Perl
       list-of-lists(-of-lists(-of-lists))) into a tree structure.  Returns
       the root of the tree converted.

       The conversion rules are that:  1) if the last (possibly the only) item
       in a given list is a scalar, then that is used as the "name" attribute
       for the node based on this list.  2) All other items in the list
       represent daughter nodes of the current node -- recursively so, if they
       are list references; otherwise, (non-terminal) scalars are considered
       to denote nodes with that name.  So ['Foo', 'Bar', 'N'] is an alternate
       way to represent [['Foo'], ['Bar'], 'N'].

       An example will illustrate:

         use Tree::DAG_Node;
         $lol =
           [
             [
               [ [ 'Det:The' ],
                 [ [ 'dog' ], 'N'], 'NP'],
               [ '/with rabies\\', 'PP'],
               'NP'
             ],
             [ 'died', 'VP'],
             'S'
           ];
          $tree = Tree::DAG_Node->lol_to_tree($lol);
          $diagram = $tree->draw_ascii_tree;
          print map "$_\n", @$diagram;

       ...returns this tree:

                          |
                         <S>
                          |
                       /------------------\
                       |                  |
                     <NP>                <VP>
                       |                  |
               /---------------\        <died>
               |               |
             <NP>            <PP>
               |               |
            /-------\   </with rabies\>
            |       |
        <Det:The>  <N>
                    |
                  <dog>

       By the way (and this rather follows from the above rules), when
       denoting a LoL tree consisting of just one node, this:

         $tree = Tree::DAG_Node->lol_to_tree( 'Lonely' );

       is okay, although it'd probably occur to you to denote it only as:

         $tree = Tree::DAG_Node->lol_to_tree( ['Lonely'] );

       which is of course fine, too.

   mother()
       This returns what node is $node's mother.  This is undef if $node has
       no mother -- i.e., if it is a root.

       See also "is_root()" and "root()".

   my_daughter_index()
       Returns what index this daughter is, in its mother's "daughter" list.
       In other words, if $node is ($node->mother->daughters)[3], then
       $node->my_daughter_index returns 3.

       As a special case, returns 0 if $node has no mother.

   name()
   name(SCALAR)
       In the first form, returns the value of the node object's "name"
       attribute.  In the second form, sets it to the value of SCALAR.

   new($hashref)
       These options are supported in $hashref:

       o attributes => A hashref of attributes
       o daughters => An arrayref of nodes
       o mother => A node
       o name => A string

       See also "MAIN CONSTRUCTOR, AND INITIALIZER" for a long discussion on
       object creation.

   new_daughter()
   new_daughter($options)
       This constructs a new node (of the same class as $mother), and adds it
       to the (right) end of the daughter list of $mother. This is essentially
       the same as going

             $daughter = $mother->new;
             $mother->add_daughter($daughter);

       but is rather more efficient because (since $daughter is guaranteed new
       and isn't linked to/from anything), it doesn't have to check that
       $daughter isn't an ancestor of $mother, isn't already daughter to a
       mother it needs to be unlinked from, isn't already in $mother's
       daughter list, etc.

       As you'd expect for a constructor, it returns the node-object created.

       Note that if you radically change 'mother'/'daughters' bookkeeping, you
       may have to change this routine, since it's one of the places that
       directly writes to 'daughters' and 'mother'.

   new_daughter_left()
   new_daughter_left($options)
       This is just like $mother->new_daughter, but adds the new daughter to
       the left (start) of $mother's daughter list.

       Note that if you radically change 'mother'/'daughters' bookkeeping, you
       may have to change this routine, since it's one of the places that
       directly writes to 'daughters' and 'mother'.

   node2string($options, $node, $vert_dashes)
       Returns a string of the node's name and attributes, with a leading
       indent, suitable for printing.

       Possible keys in the $options hashref:

       o no_attributes => $Boolean
           If 1, the node's attributes are not included in the string
           returned.

           Default: 0 (include attributes).

       Ignore the parameter $vert_dashes. The code uses it as temporary
       storage.

       Calls "format_node($options, $node)".

       Called by "tree2string($options, [$some_tree])".

   quote_name($name)
       Returns the string "'$name'", which is used in various methods for
       outputting node names.

   random_network($options)
       This method can be called as a class method or as an object method.

       In the first case, constructs a randomly arranged network under a new
       node, and returns the root node of that tree.  In the latter case,
       constructs the network under $node.

       Currently, this is implemented a bit half-heartedly, and half-wittedly.
       I basically needed to make up random-looking networks to stress-test
       the various tree-dumper methods, and so wrote this.  If you actually
       want to rely on this for any application more serious than that, I
       suggest examining the source code and seeing if this does really what
       you need (say, in reliability of randomness); and feel totally free to
       suggest changes to me (especially in the form of "I rewrote
       "random_network($options)", here's the code...")

       It takes four options:

       o max_node_count -- maximum number of nodes this tree will be allowed
       to have (counting the root)
           Default: 25.

       o min_depth -- minimum depth for the tree
           Leaves can be generated only after this depth is reached, so the
           tree will be at least this deep -- unless max_node_count is hit
           first.

           Default: 2.

       o max_depth -- maximum depth for the tree
           The tree will not be deeper than this.

           Default: 3 plus min_depth.

       o max_children -- maximum number of children any mother in the tree can
       have.
           Default: 4.

   read_attributes($s)
       Parses the string $s and extracts the name and attributes, assuming the
       format is as generated by "tree2string($options, [$some_tree])".

       This bascially means the attribute string was generated by
       "hashref2string($hashref)".

       Attributes may be absent, in which case they default to {}.

       Returns a new node with this name and these attributes.

       This method is for use by "read_tree($file_name)".

       See t/tree.without.attributes.txt and t/tree.with.attributes.txt for
       sample data.

   read_tree($file_name)
       Returns the root of the tree read from $file_name.

       The file must have been written by re-directing the output of
       "tree2string($options, [$some_tree])" to a file, since it makes
       assumptions about the format of the stringified attributes.

       read_tree() works with utf-8 data. See t/read.tree.t and
       t/tree.utf8.attributes.txt.

       Note: To call this method you need a caller. It'll be a tree of 1 node.
       The reason is that inside this method it calls various other methods,
       and for these calls it needs $self. That way, those methods can be
       called from anywhere, and not just from within read_tree().

       For reading and writing trees to databases, see
       Tree::DAG_Node::Persist.

       Calls "string2hashref($s)".

   remove_daughter(LIST)
       An exact synonym for "remove_daughters(LIST)".

   remove_daughters(LIST)
       This removes the nodes listed in LIST from $mother's daughter list.
       This is a no-operation if LIST is empty.  If there are things in LIST
       that aren't a current daughter of $mother, they are ignored.

       Not to be confused with "clear_daughters()".

   replace_with(LIST)
       This replaces $node in its mother's daughter list, by unlinking $node
       and replacing it with the items in LIST.  This returns a list
       consisting of $node followed by LIST, i.e., the nodes that replaced it.

       LIST can include $node itself (presumably at most once).  LIST can also
       be the empty list.  However, if any items in LIST are sisters to $node,
       they are ignored, and are not in the copy of LIST passed as the return
       value.

       As you might expect for any linking operation, the items in LIST cannot
       be $node's mother, or any ancestor to it; and items in LIST are, of
       course, unlinked from their mothers (if they have any) as they're
       linked to $node's mother.

       (In the special (and bizarre) case where $node is root, this simply
       calls $this->unlink_from_mother on all the items in LIST, making them
       roots of their own trees.)

       Note that the daughter-list of $node is not necessarily affected; nor
       are the daughter-lists of the items in LIST.  I mention this in case
       you think replace_with switches one node for another, with respect to
       its mother list and its daughter list, leaving the rest of the tree
       unchanged. If that's what you want, replacing $Old with $New, then you
       want:

         $New->set_daughters($Old->clear_daughters);
         $Old->replace_with($New);

       (I can't say $node's and LIST-items' daughter lists are never affected
       my replace_with -- they can be affected in this case:

         $N1 = ($node->daughters)[0]; # first daughter of $node
         $N2 = ($N1->daughters)[0];   # first daughter of $N1;
         $N3 = Tree::DAG_Node->random_network; # or whatever
         $node->replace_with($N1, $N2, $N3);

       As a side affect of attaching $N1 and $N2 to $node's mother, they're
       unlinked from their parents ($node, and $N1, respectively).  But N3's
       daughter list is unaffected.

       In other words, this method does what it has to, as you'd expect it to.

   replace_with_daughters()
       This replaces $node in its mother's daughter list, by unlinking $node
       and replacing it with its daughters.  In other words, $node becomes
       motherless and daughterless as its daughters move up and take its
       place.  This returns a list consisting of $node followed by the nodes
       that were its daughters.

       In the special (and bizarre) case where $node is root, this simply
       unlinks its daughters from it, making them roots of their own trees.

       Effectively the same as $node->replace_with($node->daughters), but more
       efficient, since less checking has to be done.  (And I also think
       $node->replace_with_daughters is a more common operation in tree-
       wrangling than $node->replace_with(LIST), so deserves a named method of
       its own, but that's just me.)

       Note that if you radically change 'mother'/'daughters' bookkeeping, you
       may have to change this routine, since it's one of the places that
       directly writes to 'daughters' and 'mother'.

   right_sister()
       Returns the node that's the immediate right sister of $node.  If $node
       is the rightmost (or only) daughter of its mother (or has no mother),
       then this returns undef.

       See also "add_left_sisters(LIST)" and "add_right_sisters(LIST)".

   right_sisters()
       Returns a list of nodes that're sisters to the right of $node. If $node
       is the rightmost (or only) daughter of its mother (or has no mother),
       then this returns an empty list.

       See also "add_left_sisters(LIST)" and "add_right_sisters(LIST)".

   root()
       Returns the root of whatever tree $node is a member of.  If $node is
       the root, then the result is $node itself.

       Not to be confused with "is_root()".

   self_and_descendants()
       Returns a list consisting of itself (as element 0) and all the
       descendants of $node.  Returns just itself if $node is a terminal_node.

       (Note that it's spelled "descendants", not "descendents".)

   self_and_sisters()
       Returns a list of all nodes (going left-to-right) that have the same
       mother as $node -- including $node itself. This is just like
       $node->mother->daughters, except that that fails where $node is root,
       whereas $root->self_and_siblings, as a special case, returns $root.

       (Contrary to how you may interpret how this method is named, "self" is
       not (necessarily) the first element of what's returned.)

   set_daughters(LIST)
       This unlinks all $mother's daughters, and replaces them with the
       daughters in LIST.

       Currently implemented as just $mother->clear_daughters followed by
       $mother->add_daughters(LIST).

   simple_lol_to_tree($simple_lol)
       This must be called as a class method.

       This is like lol_to_tree, except that rule 1 doesn't apply -- i.e., all
       scalars (or really, anything not a listref) in the LoL-structure end up
       as named terminal nodes, and only terminal nodes get names (and, of
       course, that name comes from that scalar value).  This method is useful
       for making things like expression trees, or at least starting them off.
       Consider that this:

           $tree = Tree::DAG_Node->simple_lol_to_tree(
             [ 'foo', ['bar', ['baz'], 'quux'], 'zaz', 'pati' ]
           );

       converts from something like a Lispish or Iconish tree, if you pretend
       the brackets are parentheses.

       Note that there is a (possibly surprising) degenerate case of what I'm
       calling a "simple-LoL", and it's like this:

         $tree = Tree::DAG_Node->simple_lol_to_tree('Lonely');

       This is the (only) way you can specify a tree consisting of only a
       single node, which here gets the name 'Lonely'.

   sisters()
       Returns a list of all nodes (going left-to-right) that have the same
       mother as $node -- not including $node itself.  If $node is root, this
       returns empty-list.

   string2hashref($s)
       Returns the hashref built from the string.

       The string is expected to be something like '{AutoCommit => '1',
       PrintError => "0", ReportError => 1}'.

       The empty string is returned as {}.

       Called by "read_tree($file_name)".

   tree_to_lol()
       Returns that tree (starting at $node) represented as a LoL, like what
       $lol, above, holds.  (This is as opposed to
       "tree_to_lol_notation($options)", which returns the viewable code like
       what gets evaluated and stored in $lol, above.)

       Undefined node names are returned as the string 'undef'.

       See also "decode_lol($lol)".

       Lord only knows what you use this for -- maybe for feeding to
       Data::Dumper, in case "tree_to_lol_notation($options)" doesn't do just
       what you want?

   tree_to_lol_notation($options)
       Dumps a tree (starting at $node) as the sort of LoL-like bracket
       notation you see in the above example code.  Returns just one big block
       of text.  The only option is "multiline" -- if true, it dumps the text
       as the sort of indented structure as seen above; if false (and it
       defaults to false), dumps it all on one line (with no indenting, of
       course).

       For example, starting with the tree from the above example, this:

         print $tree->tree_to_lol_notation, "\n";

       prints the following (which I've broken over two lines for sake of
       printability of documentation):

         [[[['Det:The'], [['dog'], 'N'], 'NP'], [["/with rabies\x5c"],
         'PP'], 'NP'], [['died'], 'VP'], 'S'],

       Doing this:

         print $tree->tree_to_lol_notation({ multiline => 1 });

       prints the same content, just spread over many lines, and prettily
       indented.

       Undefined node names are returned as the string 'undef'.

   tree_to_simple_lol()
       Returns that tree (starting at $node) represented as a simple-LoL --
       i.e., one where non-terminal nodes are represented as listrefs, and
       terminal nodes are gotten from the contents of those nodes' "name'
       attributes.

       Note that in the case of $node being terminal, what you get back is the
       same as $node->name.

       Compare to tree_to_simple_lol_notation.

       Undefined node names are returned as the string 'undef'.

       See also "decode_lol($lol)".

   tree_to_simple_lol_notation($options)
       A simple-LoL version of tree_to_lol_notation (which see); takes the
       same options.

       Undefined node names are returned as the string 'undef'.

   tree2string($options, [$some_tree])
       Here, the [] represent an optional parameter.

       Returns an arrayref of lines, suitable for printing.

       Draws a nice ASCII-art representation of the tree structure.

       The tree looks like:

               Root. Attributes: {}
                   |--- A. Attributes: {# => "AA"}
                   |    |--- Ac. Attributes: {# => "AcAc"}
                   |    |    |--- A. Attributes: {# => "AA"}
                   |    |--- Ax. Attributes: {# => "AxAx"}
                   |    |--- A(C). Attributes: {# => "A(C)A(C)"}
                   |         |--- A. Attributes: {# => "AA"}
                   |              |--- A+-. Attributes: {# => "A+-A+-"}
                   |                   |--- A. Attributes: {# => "AA"}
                   |                        |--- A'. Attributes: {# => "A'A'"}
                   |                        |--- A'. Attributes: {# => "A'A'"}
                   |--- A. Attributes: {# => "AA"}
                        |--- A(R). Attributes: {# => "A(R)A(R)"}
                        |    |--- A(C). Attributes: {# => "A(C)A(C)"}
                        |--- AL. Attributes: {# => "ALAL"}
                        |--- a~. Attributes: {# => "a~a~"}
                        |--- a. Attributes: {# => "aa"}
                        |--- AxX. Attributes: {# => "AxXAxX"}
                             |--- A. Attributes: {# => "AA"}
                             |--- Ao. Attributes: {# => "AoAo"}
                             |--- A<<. Attributes: {# => "A<<A<<"}
                             |--- A>>. Attributes: {# => "A>>A>>"}

       Or, without attributes:

               Root
                   |--- A
                   |    |--- Ac
                   |    |    |--- A
                   |    |--- Ax
                   |    |--- A(C)
                   |         |--- A
                   |              |--- A+-
                   |                   |--- A
                   |                        |--- A'
                   |                        |--- A'
                   |--- A
                        |--- A(R)
                        |    |--- A(C)
                        |--- AL
                        |--- a~
                        |--- a
                        |--- AxX
                             |--- A
                             |--- Ao
                             |--- A<<
                             |--- A>>

       See scripts/cut.and.paste.subtrees.pl.

       Example usage:

         print map("$_\n", @{$tree->tree2string});

       Can be called with $some_tree set to any $node, and will print the tree
       assuming $node is the root.

       If you don't wish to supply options, use tree2string({}, $node).

       Possible keys in the $options hashref (which defaults to {}):

       o no_attributes => $Boolean
           If 1, the node's attributes are not included in the string
           returned.

           Default: 0 (include attributes).

       Calls "node2string($options, $node, $vert_dashes)".

       See also "draw_ascii_tree([$options])".

   unlink_from_mother()
       This removes node from the daughter list of its mother.  If it has no
       mother, this is a no-operation.

       Returns the mother unlinked from (if any).

   walk_down($options)
       Performs a depth-first traversal of the structure at and under $node.
       What it does at each node depends on the value of the options hashref,
       which you must provide.  There are three options, "callback" and
       "callbackback" (at least one of which must be defined, as a sub
       reference), and "_depth".

       This is what walk_down() does, in pseudocode form:

       o Starting point
           Start at the $node given.

       o Callback
           If there's a callback, call it with $node as the first argument,
           and the options hashref as the second argument (which contains the
           potentially useful _depth, remember).  This function must return
           true or false -- if false, it will block the next step:

       o Daughters
           If $node has any daughter nodes, increment _depth, and call
           $daughter->walk_down($options) for each daughter (in order, of
           course), where options_hashref is the same hashref it was called
           with.  When this returns, decrements _depth.

       Callbackback
           If there's a callbackback, call just it as with callback (but
           tossing out the return value).  Note that callback returning false
           blocks traversal below $node, but doesn't block calling
           callbackback for $node.  (Incidentally, in the unlikely case that
           $node has stopped being a node object, callbackback won't get
           called.)

       o Return

       $node->walk_down($options) is the way to recursively do things to a
       tree (if you start at the root) or part of a tree; if what you're doing
       is best done via pre-pre order traversal, use callback; if what you're
       doing is best done with post-order traversal, use callbackback.
       walk_down() is even the basis for plenty of the methods in this class.
       See the source code for examples both simple and horrific.

       Note that if you don't specify _depth, it effectively defaults to 0.
       You should set it to scalar($node->ancestors) if you want _depth to
       reflect the true depth-in-the-tree for the nodes called, instead of
       just the depth below $node.  (If $node is the root, there's no
       difference, of course.)

       And by the way, it's a bad idea to modify the tree from the callback.
       Unpredictable things may happen.  I instead suggest having your
       callback add to a stack of things that need changing, and then, once
       walk_down() is all finished, changing those nodes from that stack.

       Note that the existence of walk_down() doesn't mean you can't write you
       own special-use traversers.


WHEN AND HOW TO DESTROY THE TREE

       It should be clear to you that if you've built a big parse tree or
       something, and then you're finished with it, you should call
       $some_node->delete_tree on it if you want the memory back.

       But consider this case:  you've got this tree:

             A
           / | \
          B  C  D
          |     | \
          E     X  Y

       Let's say you decide you don't want D or any of its descendants in the
       tree, so you call D->unlink_from_mother.  This does NOT automagically
       destroy the tree D-X-Y.  Instead it merely splits the tree into two:

            A                        D
           / \                      / \
          B   C                    X   Y
          |
          E

       To destroy D and its little tree, you have to explicitly call
       delete_tree on it.

       Note, however, that if you call C->unlink_from_mother, and if you don't
       have a link to C anywhere, then it does magically go away.  This is
       because nothing links to C -- whereas with the D-X-Y tree, D links to X
       and Y, and X and Y each link back to D. Note that calling
       C->delete_tree is harmless -- after all, a tree of only one node is
       still a tree.

       So, this is a surefire way of getting rid of all $node's children and
       freeing up the memory associated with them and their descendants:

         foreach my $it ($node->clear_daughters) { $it->delete_tree }

       Just be sure not to do this:

         foreach my $it ($node->daughters) { $it->delete_tree }
         $node->clear_daughters;

       That's bad; the first call to $_->delete_tree will climb to the root of
       $node's tree, and nuke the whole tree, not just the bits under $node.
       You might as well have just called $node->delete_tree.  (Moreavor, once
       $node is dead, you can't call clear_daughters on it, so you'll get an
       error there.)


BUG REPORTS

       If you find a bug in this library, report it to me as soon as possible,
       at the address listed in the MAINTAINER section, below.  Please try to
       be as specific as possible about how you got the bug to occur.


HELP!

       If you develop a given routine for dealing with trees in some way, and
       use it a lot, then if you think it'd be of use to anyone else, do email
       me about it; it might be helpful to others to include that routine, or
       something based on it, in a later version of this module.

       It's occurred to me that you might like to (and might yourself develop
       routines to) draw trees in something other than ASCII art.  If you do
       so -- say, for PostScript output, or for output interpretable by some
       external plotting program --  I'd be most interested in the results.


RAMBLINGS

       This module uses "strict", but I never wrote it with -w warnings in
       mind -- so if you use -w, do not be surprised if you see complaints
       from the guts of DAG_Node.  As long as there is no way to turn off -w
       for a given module (instead of having to do it in every single
       subroutine with a "local $^W"), I'm not going to change this. However,
       I do, at points, get bursts of ambition, and I try to fix code in
       DAG_Node that generates warnings, as I come across them -- which is
       only occasionally.  Feel free to email me any patches for any such
       fixes you come up with, tho.

       Currently I don't assume (or enforce) anything about the class
       membership of nodes being manipulated, other than by testing whether
       each one provides a method "is_node()", a la:

         die "Not a node!!!" unless UNIVERSAL::can($node, "is_node");

       So, as far as I'm concerned, a given tree's nodes are free to belong to
       different classes, just so long as they provide/inherit "is_node()",
       the few methods that this class relies on to navigate the tree, and
       have the same internal object structure, or a superset of it.
       Presumably this would be the case for any object belonging to a class
       derived from "Tree::DAG_Node", or belonging to "Tree::DAG_Node" itself.

       When routines in this class access a node's "mother" attribute, or its
       "daughters" attribute, they (generally) do so directly (via
       $node->{'mother'}, etc.), for sake of efficiency.  But classes derived
       from this class should probably do this instead thru a method (via
       $node->mother, etc.), for sake of portability, abstraction, and general
       goodness.

       However, no routines in this class (aside from, necessarily, _init(),
       _init_name(), and "name()") access the "name" attribute directly;
       routines (like the various tree draw/dump methods) get the "name" value
       thru a call to $obj->name().  So if you want the object's name to not
       be a real attribute, but instead have it derived dynamically from some
       feature of the object (say, based on some of its other attributes, or
       based on its address), you can to override the "name()" method, without
       causing problems.  (Be sure to consider the case of $obj->name as a
       write method, as it's used in /lol_to_tree($lol) and
       "random_network($options)".)


FAQ

   Which is the best tree processing module?
       "Tree::DAG_Node", as it happens. More details: "SEE ALSO".

   How to process every node in tree?
       See "walk_down($options)". $options normally looks like this, assuming
       we wish to pass in an arrayref as a stack:

               my(@stack);

               $tree -> walk_down
               ({
                       callback =>
                       sub
                       {
                               my(@node, $options) = @_;

                               # Process $node, using $options...

                               push @{$$options{stack} }, $node -> name;

                               return 1; # Keep walking.
                       },
                       _depth => 0,
                       stack  => \@stack,
               });

               # Process @stack...

   How do I switch from Tree to Tree::DAG_Node?
       o The node's name
           In "Tree" you use $node -> value and in "Tree::DAG_Node" it's $node
           -> name.

       o The node's attributes
           In "Tree" you use $node -> meta and in "Tree::DAG_Node" it's $node
           -> attributes.

   Are there techniques for processing lists of nodes?
       o Copy the daughter list, and change it
                   @them    = $mother->daughters;
                   @removed = splice(@them, 0, 2, @new_nodes);

                   $mother->set_daughters(@them);

       o Select a sub-set of nodes
                   $mother->set_daughters
                   (
                           grep($_->name =~ /wanted/, $mother->daughters)
                   );

   Why did you break up the sections of methods in the POD?
       Because I want to list the methods in alphabetical order.

   Why did you move the POD to the end?
       Because the apostrophes in the text confused the syntax hightlighter in
       my editor UltraEdit.


SEE ALSO

       o HTML::Element(3), HTML::Tree(3) and HTML::TreeBuilder(3)
           Sean is also the author of these modules.

       o Tree(3)
           Lightweight.

       o Tree::Binary(3)
           Lightweight.

       o Tree::DAG_Node::Persist(3)
           Lightweight.

       o Tree::Persist(3)
           Lightweight.

       o Forest(3)
           Uses Moose.

       "Tree::DAG_Node" itself is also lightweight.


REFERENCES

       Wirth, Niklaus.  1976.  Algorithms + Data Structures = Programs
       Prentice-Hall, Englewood Cliffs, NJ.

       Knuth, Donald Ervin.  1997.  Art of Computer Programming, Volume 1,
       Third Edition: Fundamental Algorithms.  Addison-Wesley,  Reading, MA.

       Wirth's classic, currently and lamentably out of print, has a good
       section on trees.  I find it clearer than Knuth's (if not quite as
       encyclopedic), probably because Wirth's example code is in a block-
       structured high-level language (basically Pascal), instead of in
       assembler (MIX).

       Until some kind publisher brings out a new printing of Wirth's book,
       try poking around used bookstores (or "www.abebooks.com") for a copy.
       I think it was also republished in the 1980s under the title Algorithms
       and Data Structures, and in a German edition called Algorithmen und
       Datenstrukturen.  (That is, I'm sure books by Knuth were published
       under those titles, but I'm assuming that they're just later
       printings/editions of Algorithms + Data Structures = Programs.)


MACHINE-READABLE CHANGE LOG

       The file Changes was converted into Changelog.ini by
       Module::Metadata::Changes.


REPOSITORY

       <https://github.com/ronsavage/Tree-DAG_Node>


SUPPORT

       Email the author, or log a bug on RT:

       <https://rt.cpan.org/Public/Dist/Display.html?Name=Tree-DAG_Node>.


ACKNOWLEDGEMENTS

       The code to print the tree, in tree2string(), was adapted from
       Forest::Tree::Writer::ASCIIWithBranches by the dread Stevan Little.


MAINTAINER

       David Hand, "<cogent@cpan.org>" up to V 1.06.

       Ron Savage "<rsavage@cpan.org>" from V 1.07.

       In this POD, usage of 'I' refers to Sean, up until V 1.07.


AUTHOR

       Sean M. Burke, "<sburke@cpan.org>"


COPYRIGHT, LICENSE, AND DISCLAIMER

       Copyright 1998-2001, 2004, 2007 by Sean M. Burke and David Hand.

       This program is free software. It is released under the Artistic
       License 2.0.  See <http://opensource.org/licenses/Artistic-2.0>.

       This program is distributed in the hope that it will be useful, but
       without any warranty; without even the implied warranty of
       merchantability or fitness for a particular purpose.



perl v5.22.1                      2016-02-29                 Tree::DAG_Node(3)

tree-dag_node 1.290.0 - Generated Fri Apr 8 07:18:48 CDT 2016
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