This is internal.info, produced by makeinfo version 4.13 from
internal.texi.

This manual (31 May 2014) is for the internals of Libmarpa 6.1.0.

   Copyright (C) 2014 Jeffrey Kegler.

     Permission is granted to copy, distribute and/or modify this
     document under the terms of the GNU Free Documentation License,
     Version 1.3 or any later version published by the Free Software
     Foundation.  A copy of the license is included in the section
     entitled "GNU Free Documentation License."


File: internal.info,  Node: Top,  Next: Copying,  Prev: (dir),  Up: (dir)

Libmarpa internals
******************

This manual (31 May 2014) is for the internals of Libmarpa 6.1.0.

   Copyright (C) 2014 Jeffrey Kegler.

     Permission is granted to copy, distribute and/or modify this
     document under the terms of the GNU Free Documentation License,
     Version 1.3 or any later version published by the Free Software
     Foundation.  A copy of the license is included in the section
     entitled "GNU Free Documentation License."

* Menu:

* Copying::
* About this document::
* Internal Interface::
* GNU Free Documentation License::

 --- The Detailed Node Listing ---

Internal Interface

* Symbol internal methods::
* Rule internals::
* Grammar internals::
* Recognizer internals::
* Bocage internals::
* Ordering internals::
* Tree internals::
* Valuator internals::
* Debugging methods::


File: internal.info,  Node: Copying,  Next: About this document,  Prev: Top,  Up: Top

GNU LESSER GENERAL PUBLIC LICENSE
*********************************

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  0. Additional Definitions.

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File: internal.info,  Node: About this document,  Next: Internal Interface,  Prev: Copying,  Up: Top

1 About this document
*********************

This manual is a tool for is those working on the Libmarpa internals.
Unless you are thoroughly familiar with Libmarpa already, it is not of
interest to you.


File: internal.info,  Node: Internal Interface,  Next: GNU Free Documentation License,  Prev: About this document,  Up: Top

2 Internal Interface
********************

Internal methods are only for testing and development of libmarpa.
They are listed here (and sometimes described) for the convenience of
those working on libmarpa's internals.

   Internal methods are subject to change.  Applications should not use
internal methods.  If a description exists and might be helpful, it may
be included below, but all applications should treat these methods as
"undocumented".

* Menu:

* Symbol internal methods::
* Rule internals::
* Grammar internals::
* Recognizer internals::
* Bocage internals::
* Ordering internals::
* Tree internals::
* Valuator internals::
* Debugging methods::


File: internal.info,  Node: Symbol internal methods,  Next: Rule internals,  Prev: Internal Interface,  Up: Internal Interface

2.1 Symbol internal methods
===========================

 -- Function: int _marpa_g_nsy_is_start ( Marpa_Grammar G, Marpa_NSY_ID
          NSY_ID)

 -- Function: int _marpa_g_nsy_is_nulling ( Marpa_Grammar G,
          Marpa_NSY_ID NSY_ID)

 -- Function: int _marpa_g_nsy_is_lhs ( Marpa_Grammar G, Marpa_NSY_ID
          NSY_ID)

 -- Function: Marpa_NSY_ID _marpa_g_xsy_nulling_nsy ( Marpa_Grammar G,
          Marpa_Symbol_ID SYMID)

 -- Function: Marpa_NSY_ID _marpa_g_xsy_nsy ( Marpa_Grammar G,
          Marpa_Symbol_ID SYMID)

 -- Function: int _marpa_g_nsy_is_semantic ( Marpa_Grammar G,
          Marpa_NSY_ID NSY_ID)

 -- Function: Marpa_Rule_ID _marpa_g_source_xsy ( Marpa_Grammar G,
          Marpa_NSY_ID NSY_ID)

 -- Function: Marpa_Rule_ID _marpa_g_nsy_lhs_xrl ( Marpa_Grammar G,
          Marpa_NSY_ID NSY_ID)

 -- Function: int _marpa_g_nsy_xrl_offset ( Marpa_Grammar G,
          Marpa_NSY_ID NSY_ID )


File: internal.info,  Node: Rule internals,  Next: Grammar internals,  Prev: Symbol internal methods,  Up: Internal Interface

2.2 Rule internals
==================

 -- Function: int _marpa_g_rule_is_keep_separation ( Marpa_Grammar G,
          Marpa_Rule_ID RULE_ID)
     This function does nothing but return an undocumented flag.  At
     some point, I may optimize cases where separators are discarded,
     in which case this flag will be used.  I may also remove this call
     entirely.  Return value: Returns 1 if the keep separation flag is
     set, 0 if not.  Returns 0 if RULE_ID is not a sequence rule.  On
     failure, returns -2.

 -- Function: int _marpa_g_nsy_count ( Marpa_Grammar G)

 -- Function: int _marpa_g_irl_count ( Marpa_Grammar G)

 -- Function: Marpa_Symbol_ID _marpa_g_irl_lhs ( Marpa_Grammar G,
          Marpa_IRL_ID IRL_ID)
     Return value: On success, the LHS symbol of the IRL.  On failure,
     -2.

 -- Function: int _marpa_g_irl_length ( Marpa_Grammar G, Marpa_IRL_ID
          IRL_ID)
     The length of a IRL is the number of symbols on its RHS.

     Return value: On success, the IRL length.  On failure, -2.

 -- Function: Marpa_Symbol_ID _marpa_g_irl_rhs ( Marpa_Grammar G,
          Marpa_IRL_ID IRL_ID, int IX)
     The position in the IRL, IX, is zero-based.  If IX is greater than
     or equal the length of the IRL, it is a soft failure.  This can be
     used in loops, to avoid having to determine the IRL's length
     explicitly.

     Return value: On success, the symbol in position IX on the IRL's
     RHS.  If IX is greater than or equal to the length of the IRL, -1.
     On other failures, -2.

 -- Function: int _marpa_g_rule_is_used (Marpa_Grammar G, Marpa_Rule_ID
          RULE_ID)

 -- Function: int _marpa_g_irl_is_virtual_lhs (Marpa_Grammar G,
          Marpa_IRL_ID IRL_ID)

 -- Function: int _marpa_g_irl_is_virtual_rhs (Marpa_Grammar G,
          Marpa_IRL_ID IRL_ID)

 -- Function: `int' _marpa_g_virtual_start (Marpa_Grammar G,
          Marpa_IRL_ID IRL_ID)

 -- Function: `int' _marpa_g_virtual_end (Marpa_Grammar G, Marpa_IRL_ID
          IRL_ID)

 -- Function: Marpa_Rule_ID _marpa_g_source_xrl (Marpa_Grammar G,
          Marpa_IRL_ID IRL_ID)

 -- Function: int _marpa_g_real_symbol_count (Marpa_Grammar G,
          Marpa_IRL_ID IRL_ID)

 -- Function: Marpa_Rule_ID _marpa_g_irl_semantic_equivalent
          (Marpa_Grammar G, Marpa_IRL_ID IRL_ID)

 -- Function: Marpa_Rank _marpa_g_irl_rank ( Marpa_Grammar G,
          Marpa_IRL_ID IRL_ID)

 -- Function: Marpa_Rank _marpa_g_nsy_rank ( Marpa_Grammar G,
          Marpa_IRL_ID NSY_ID)


File: internal.info,  Node: Grammar internals,  Next: Recognizer internals,  Prev: Rule internals,  Up: Internal Interface

2.3 Grammar internal methods
============================

The methods in this section are accessors for Libmarpa's AHMs.  Their
use requires familiarity with Marpa's internals, as described in
`Marpa: The Program'.

 -- Function: int _marpa_g_ahm_count (Marpa_Grammar G)

 -- Function: Marpa_Rule_ID _marpa_g_ahm_irl (Marpa_Grammar G,
          Marpa_AHM_ID ITEM_ID)

 -- Function: int _marpa_g_ahm_position (Marpa_Grammar G, Marpa_AHM_ID
          ITEM_ID)

 -- Function: Marpa_Symbol_ID _marpa_g_ahm_postdot (Marpa_Grammar G,
          Marpa_AHM_ID ITEM_ID)


File: internal.info,  Node: Recognizer internals,  Next: Bocage internals,  Prev: Grammar internals,  Up: Internal Interface

2.4 Recognizer internals
========================

 -- Function: int _marpa_r_is_use_leo (Marpa_Recognizer R)
 -- Function: int _marpa_r_is_use_leo_set ( Marpa_Recognizer R, int
          VALUE)
     Reports and sets, respectively, the "use Leo" flag.  This flag
     controls whether Joop Leo's method for fast parsing of right
     recursion is used.  By default, this value is 1 and Leo parsing is
     in use.  This default should be used except for testing, debugging
     and development.

 -- Function: Marpa_Earley_Set_ID _marpa_r_trace_earley_set
          (Marpa_Recognizer R)

 -- Function: int _marpa_r_earley_set_size (Marpa_Recognizer r,
          Marpa_Earley_Set_ID SET_ID)

 -- Function: Marpa_Earleme _marpa_r_earley_set_trace (Marpa_Recognizer
          r, Marpa_Earley_Set_ID SET_ID)

 -- Function: Marpa_AHM_ID _marpa_r_earley_item_trace (Marpa_Recognizer
          r, Marpa_Earley_Item_ID ITEM_ID)

 -- Function: Marpa_Earley_Set_ID _marpa_r_earley_item_origin
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_leo_predecessor_symbol
          (Marpa_Recognizer R)

 -- Function: Marpa_Earley_Set_ID _marpa_r_leo_base_origin
          (Marpa_Recognizer R)

 -- Function: Marpa_AHM_ID _marpa_r_leo_base_state (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_postdot_symbol_trace
          (Marpa_Recognizer r, Marpa_Symbol_ID SYMID)

 -- Function: Marpa_Symbol_ID _marpa_r_first_postdot_item_trace
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_next_postdot_item_trace
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_postdot_item_symbol
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_first_token_link_trace
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_next_token_link_trace
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_first_completion_link_trace
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_next_completion_link_trace
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_first_leo_link_trace
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_next_leo_link_trace
          (Marpa_Recognizer R)

 -- Function: Marpa_AHM_ID _marpa_r_source_predecessor_state
          (Marpa_Recognizer R)

 -- Function: Marpa_Symbol_ID _marpa_r_source_token (Marpa_Recognizer
          r, int *VALUE_P)

 -- Function: Marpa_Symbol_ID _marpa_r_source_leo_transition_symbol
          (Marpa_Recognizer R)

 -- Function: Marpa_Earley_Set_ID _marpa_r_source_middle
          (Marpa_Recognizer R)


File: internal.info,  Node: Bocage internals,  Next: Ordering internals,  Prev: Recognizer internals,  Up: Internal Interface

2.5 Bocage internals
====================

 -- Function: int _marpa_b_and_node_count ( Marpa_Bocage B)

 -- Function: Marpa_Earley_Set_ID _marpa_b_and_node_middle (
          Marpa_Bocage B, Marpa_And_Node_ID AND_NODE_ID)

 -- Function: int _marpa_b_and_node_parent ( Marpa_Bocage B,
          Marpa_And_Node_ID AND_NODE_ID)

 -- Function: int _marpa_b_and_node_predecessor ( Marpa_Bocage B,
          Marpa_And_Node_ID AND_NODE_ID)

 -- Function: int _marpa_b_and_node_cause ( Marpa_Bocage B,
          Marpa_And_Node_ID AND_NODE_ID)

 -- Function: int _marpa_b_and_node_symbol ( Marpa_Bocage B,
          Marpa_And_Node_ID AND_NODE_ID)

 -- Function: Marpa_Symbol_ID _marpa_b_and_node_token ( Marpa_Bocage B,
          Marpa_And_Node_ID AND_NODE_ID, int* VALUE_P)
     Returns the data for the token of the and-node.  The symbol id is
     the return value, and the token value is placed in the location
     pointed to by VALUE_P, if that is non-null.  If AND_NODE_ID is not
     the ID of an and-node whose cause is a token, returns -1, without
     changing VALUE_P.  On failure, returns -2 without changing VALUE_P.

     There is no function to simply return the token value - because of
     the need to indicate errors, it is just as easy to return the
     symbol ID as well.

 -- Function: Marpa_Or_Node_ID _marpa_b_top_or_node ( Marpa_Bocage B)
     Return the ID of the top or-node.

 -- Function: int _marpa_b_or_node_set ( Marpa_Bocage B,
          Marpa_Or_Node_ID OR_NODE_ID)
     Return the ordinal of the current (final) Earley set of the
     or-node.

 -- Function: int _marpa_b_or_node_origin ( Marpa_Bocage B,
          Marpa_Or_Node_ID OR_NODE_ID)

 -- Function: Marpa_IRL_ID _marpa_b_or_node_irl ( Marpa_Bocage B,
          Marpa_Or_Node_ID OR_NODE_ID)

 -- Function: int _marpa_b_or_node_position ( Marpa_Bocage B,
          Marpa_Or_Node_ID OR_NODE_ID)

 -- Function: int _marpa_b_or_node_is_whole ( Marpa_Bocage B,
          Marpa_Or_Node_ID OR_NODE_ID)

 -- Function: int _marpa_b_or_node_is_semantic ( Marpa_Bocage B,
          Marpa_Or_Node_ID OR_NODE_ID)

 -- Function: int _marpa_b_or_node_first_and ( Marpa_Bocage B,
          Marpa_Or_Node_ID OR_NODE_ID)

 -- Function: int _marpa_b_or_node_last_and ( Marpa_Bocage B,
          Marpa_Or_Node_ID OR_NODE_ID)

 -- Function: int _marpa_b_or_node_and_count ( Marpa_Bocage B,
          Marpa_Or_Node_ID OR_NODE_ID)


File: internal.info,  Node: Ordering internals,  Next: Tree internals,  Prev: Bocage internals,  Up: Internal Interface

2.6 Ordering internals
======================

 -- Function: Marpa_And_Node_ID _marpa_o_and_order_get ( Marpa_Order O,
          Marpa_Or_Node_ID OR_NODE_ID, int IX)

 -- Function: int _marpa_o_or_node_and_node_count ( Marpa_Order O,
          Marpa_Or_Node_ID OR_NODE_ID)

 -- Function: int _marpa_o_or_node_and_node_id_by_ix ( Marpa_Order O,
          Marpa_Or_Node_ID OR_NODE_ID, int IX)


File: internal.info,  Node: Tree internals,  Next: Valuator internals,  Prev: Ordering internals,  Up: Internal Interface

2.7 Tree internals
==================

In Marpa, a nook is any node of a parse tree.  The usual term is "node",
but within Marpa, the word "node" is already heavily overloaded.  So
what most texts call "tree nodes" are here called "nooks".  "Nook" can
be thought of as a pun on both "node" and "fork".

 -- Function: int _marpa_t_size ( Marpa_Tree T)
     Return the size of the parse tree.  This is the number of nooks in
     its stack.  If there is a serious error, or if the tree is
     uninitialized, return -2.  If the tree is exhausted, return -1.

 -- Function: Marpa_Or_Node_ID _marpa_t_nook_or_node ( Marpa_Tree T,
          Marpa_Nook_ID NOOK_ID)
     Return the ID of the or-node for NOOK_ID.

 -- Function: int _marpa_t_nook_choice ( Marpa_Tree T, Marpa_Nook_ID
          NOOK_ID )
     Return the current choice for NOOK_ID.

 -- Function: int _marpa_t_nook_parent ( Marpa_Tree T, Marpa_Nook_ID
          NOOK_ID )
     Return the parent nook's ID for NOOK_ID.  As with the other nook
     trace functions, -1 is returned if NOOK_ID is not the ID of a nook
     on the stack, but -1 can also be a valid value.  If that's an
     issue, the NOOK_ID needs to be checked with one of the trace
     functions where -1 is never a valid value -- for example,
     `_marpa_t_nook_or_node'.

 -- Function: int _marpa_t_nook_cause_is_ready ( Marpa_Tree T,
          Marpa_Nook_ID NOOK_ID )
     Return the cause-is-ready bit for NOOK_ID.

 -- Function: int _marpa_t_nook_predecessor_is_ready ( Marpa_Tree T,
          Marpa_Nook_ID NOOK_ID )
     Return the predecessor-is-ready bit for NOOK_ID.

 -- Function: int _marpa_t_nook_is_cause ( Marpa_Tree T, Marpa_Nook_ID
          NOOK_ID )
     Return the is-cause bit for NOOK_ID.

 -- Function: int _marpa_t_nook_is_predecessor ( Marpa_Tree T,
          Marpa_Nook_ID NOOK_ID )
     Return the is-predecessor bit for NOOK_ID.


File: internal.info,  Node: Valuator internals,  Next: Debugging methods,  Prev: Tree internals,  Up: Internal Interface

2.8 Valuator internals
======================

 -- Function: int _marpa_v_trace ( Marpa_Value V, int FLAG)

 -- Function: Marpa_Nook_ID _marpa_v_nook ( Marpa_Value V)


File: internal.info,  Node: Debugging methods,  Prev: Valuator internals,  Up: Internal Interface

2.9 Debugging methods
=====================

 -- Function: const char* _marpa_tag(void)
     Returns a "tag" value.  This is to allow tagging the libraries
     with an completely arbitrary string identifier.  independent even
     of the versioning mechanism.  This allows debugging, for example,
     to determine which of two otherwise exactly identical libraries is
     in use.

 -- Function: int marpa_debug_level_set ( int LEVEL )

 -- Function: void marpa_debug_handler_set ( int (*DEBUG_HANDLER)(const
          char*, ...) )


File: internal.info,  Node: GNU Free Documentation License,  Prev: Internal Interface,  Up: Top

Appendix A GNU Free Documentation License
*****************************************

                     Version 1.3, 3 November 2008

     Copyright (C) 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.
     `http://fsf.org/'

     Everyone is permitted to copy and distribute verbatim copies
     of this license document, but changing it is not allowed.

  0. PREAMBLE

     The purpose of this License is to make a manual, textbook, or other
     functional and useful document "free" in the sense of freedom: to
     assure everyone the effective freedom to copy and redistribute it,
     with or without modifying it, either commercially or
     noncommercially.  Secondarily, this License preserves for the
     author and publisher a way to get credit for their work, while not
     being considered responsible for modifications made by others.

     This License is a kind of "copyleft", which means that derivative
     works of the document must themselves be free in the same sense.
     It complements the GNU General Public License, which is a copyleft
     license designed for free software.

     We have designed this License in order to use it for manuals for
     free software, because free software needs free documentation: a
     free program should come with manuals providing the same freedoms
     that the software does.  But this License is not limited to
     software manuals; it can be used for any textual work, regardless
     of subject matter or whether it is published as a printed book.
     We recommend this License principally for works whose purpose is
     instruction or reference.

  1. APPLICABILITY AND DEFINITIONS

     This License applies to any manual or other work, in any medium,
     that contains a notice placed by the copyright holder saying it
     can be distributed under the terms of this License.  Such a notice
     grants a world-wide, royalty-free license, unlimited in duration,
     to use that work under the conditions stated herein.  The
     "Document", below, refers to any such manual or work.  Any member
     of the public is a licensee, and is addressed as "you".  You
     accept the license if you copy, modify or distribute the work in a
     way requiring permission under copyright law.

     A "Modified Version" of the Document means any work containing the
     Document or a portion of it, either copied verbatim, or with
     modifications and/or translated into another language.

     A "Secondary Section" is a named appendix or a front-matter section
     of the Document that deals exclusively with the relationship of the
     publishers or authors of the Document to the Document's overall
     subject (or to related matters) and contains nothing that could
     fall directly within that overall subject.  (Thus, if the Document
     is in part a textbook of mathematics, a Secondary Section may not
     explain any mathematics.)  The relationship could be a matter of
     historical connection with the subject or with related matters, or
     of legal, commercial, philosophical, ethical or political position
     regarding them.

     The "Invariant Sections" are certain Secondary Sections whose
     titles are designated, as being those of Invariant Sections, in
     the notice that says that the Document is released under this
     License.  If a section does not fit the above definition of
     Secondary then it is not allowed to be designated as Invariant.
     The Document may contain zero Invariant Sections.  If the Document
     does not identify any Invariant Sections then there are none.

     The "Cover Texts" are certain short passages of text that are
     listed, as Front-Cover Texts or Back-Cover Texts, in the notice
     that says that the Document is released under this License.  A
     Front-Cover Text may be at most 5 words, and a Back-Cover Text may
     be at most 25 words.

     A "Transparent" copy of the Document means a machine-readable copy,
     represented in a format whose specification is available to the
     general public, that is suitable for revising the document
     straightforwardly with generic text editors or (for images
     composed of pixels) generic paint programs or (for drawings) some
     widely available drawing editor, and that is suitable for input to
     text formatters or for automatic translation to a variety of
     formats suitable for input to text formatters.  A copy made in an
     otherwise Transparent file format whose markup, or absence of
     markup, has been arranged to thwart or discourage subsequent
     modification by readers is not Transparent.  An image format is
     not Transparent if used for any substantial amount of text.  A
     copy that is not "Transparent" is called "Opaque".

     Examples of suitable formats for Transparent copies include plain
     ASCII without markup, Texinfo input format, LaTeX input format,
     SGML or XML using a publicly available DTD, and
     standard-conforming simple HTML, PostScript or PDF designed for
     human modification.  Examples of transparent image formats include
     PNG, XCF and JPG.  Opaque formats include proprietary formats that
     can be read and edited only by proprietary word processors, SGML or
     XML for which the DTD and/or processing tools are not generally
     available, and the machine-generated HTML, PostScript or PDF
     produced by some word processors for output purposes only.

     The "Title Page" means, for a printed book, the title page itself,
     plus such following pages as are needed to hold, legibly, the
     material this License requires to appear in the title page.  For
     works in formats which do not have any title page as such, "Title
     Page" means the text near the most prominent appearance of the
     work's title, preceding the beginning of the body of the text.

     The "publisher" means any person or entity that distributes copies
     of the Document to the public.

     A section "Entitled XYZ" means a named subunit of the Document
     whose title either is precisely XYZ or contains XYZ in parentheses
     following text that translates XYZ in another language.  (Here XYZ
     stands for a specific section name mentioned below, such as
     "Acknowledgements", "Dedications", "Endorsements", or "History".)
     To "Preserve the Title" of such a section when you modify the
     Document means that it remains a section "Entitled XYZ" according
     to this definition.

     The Document may include Warranty Disclaimers next to the notice
     which states that this License applies to the Document.  These
     Warranty Disclaimers are considered to be included by reference in
     this License, but only as regards disclaiming warranties: any other
     implication that these Warranty Disclaimers may have is void and
     has no effect on the meaning of this License.

  2. VERBATIM COPYING

     You may copy and distribute the Document in any medium, either
     commercially or noncommercially, provided that this License, the
     copyright notices, and the license notice saying this License
     applies to the Document are reproduced in all copies, and that you
     add no other conditions whatsoever to those of this License.  You
     may not use technical measures to obstruct or control the reading
     or further copying of the copies you make or distribute.  However,
     you may accept compensation in exchange for copies.  If you
     distribute a large enough number of copies you must also follow
     the conditions in section 3.

     You may also lend copies, under the same conditions stated above,
     and you may publicly display copies.

  3. COPYING IN QUANTITY

     If you publish printed copies (or copies in media that commonly
     have printed covers) of the Document, numbering more than 100, and
     the Document's license notice requires Cover Texts, you must
     enclose the copies in covers that carry, clearly and legibly, all
     these Cover Texts: Front-Cover Texts on the front cover, and
     Back-Cover Texts on the back cover.  Both covers must also clearly
     and legibly identify you as the publisher of these copies.  The
     front cover must present the full title with all words of the
     title equally prominent and visible.  You may add other material
     on the covers in addition.  Copying with changes limited to the
     covers, as long as they preserve the title of the Document and
     satisfy these conditions, can be treated as verbatim copying in
     other respects.

     If the required texts for either cover are too voluminous to fit
     legibly, you should put the first ones listed (as many as fit
     reasonably) on the actual cover, and continue the rest onto
     adjacent pages.

     If you publish or distribute Opaque copies of the Document
     numbering more than 100, you must either include a
     machine-readable Transparent copy along with each Opaque copy, or
     state in or with each Opaque copy a computer-network location from
     which the general network-using public has access to download
     using public-standard network protocols a complete Transparent
     copy of the Document, free of added material.  If you use the
     latter option, you must take reasonably prudent steps, when you
     begin distribution of Opaque copies in quantity, to ensure that
     this Transparent copy will remain thus accessible at the stated
     location until at least one year after the last time you
     distribute an Opaque copy (directly or through your agents or
     retailers) of that edition to the public.

     It is requested, but not required, that you contact the authors of
     the Document well before redistributing any large number of
     copies, to give them a chance to provide you with an updated
     version of the Document.

  4. MODIFICATIONS

     You may copy and distribute a Modified Version of the Document
     under the conditions of sections 2 and 3 above, provided that you
     release the Modified Version under precisely this License, with
     the Modified Version filling the role of the Document, thus
     licensing distribution and modification of the Modified Version to
     whoever possesses a copy of it.  In addition, you must do these
     things in the Modified Version:

       A. Use in the Title Page (and on the covers, if any) a title
          distinct from that of the Document, and from those of
          previous versions (which should, if there were any, be listed
          in the History section of the Document).  You may use the
          same title as a previous version if the original publisher of
          that version gives permission.

       B. List on the Title Page, as authors, one or more persons or
          entities responsible for authorship of the modifications in
          the Modified Version, together with at least five of the
          principal authors of the Document (all of its principal
          authors, if it has fewer than five), unless they release you
          from this requirement.

       C. State on the Title page the name of the publisher of the
          Modified Version, as the publisher.

       D. Preserve all the copyright notices of the Document.

       E. Add an appropriate copyright notice for your modifications
          adjacent to the other copyright notices.

       F. Include, immediately after the copyright notices, a license
          notice giving the public permission to use the Modified
          Version under the terms of this License, in the form shown in
          the Addendum below.

       G. Preserve in that license notice the full lists of Invariant
          Sections and required Cover Texts given in the Document's
          license notice.

       H. Include an unaltered copy of this License.

       I. Preserve the section Entitled "History", Preserve its Title,
          and add to it an item stating at least the title, year, new
          authors, and publisher of the Modified Version as given on
          the Title Page.  If there is no section Entitled "History" in
          the Document, create one stating the title, year, authors,
          and publisher of the Document as given on its Title Page,
          then add an item describing the Modified Version as stated in
          the previous sentence.

       J. Preserve the network location, if any, given in the Document
          for public access to a Transparent copy of the Document, and
          likewise the network locations given in the Document for
          previous versions it was based on.  These may be placed in
          the "History" section.  You may omit a network location for a
          work that was published at least four years before the
          Document itself, or if the original publisher of the version
          it refers to gives permission.

       K. For any section Entitled "Acknowledgements" or "Dedications",
          Preserve the Title of the section, and preserve in the
          section all the substance and tone of each of the contributor
          acknowledgements and/or dedications given therein.

       L. Preserve all the Invariant Sections of the Document,
          unaltered in their text and in their titles.  Section numbers
          or the equivalent are not considered part of the section
          titles.

       M. Delete any section Entitled "Endorsements".  Such a section
          may not be included in the Modified Version.

       N. Do not retitle any existing section to be Entitled
          "Endorsements" or to conflict in title with any Invariant
          Section.

       O. Preserve any Warranty Disclaimers.

     If the Modified Version includes new front-matter sections or
     appendices that qualify as Secondary Sections and contain no
     material copied from the Document, you may at your option
     designate some or all of these sections as invariant.  To do this,
     add their titles to the list of Invariant Sections in the Modified
     Version's license notice.  These titles must be distinct from any
     other section titles.

     You may add a section Entitled "Endorsements", provided it contains
     nothing but endorsements of your Modified Version by various
     parties--for example, statements of peer review or that the text
     has been approved by an organization as the authoritative
     definition of a standard.

     You may add a passage of up to five words as a Front-Cover Text,
     and a passage of up to 25 words as a Back-Cover Text, to the end
     of the list of Cover Texts in the Modified Version.  Only one
     passage of Front-Cover Text and one of Back-Cover Text may be
     added by (or through arrangements made by) any one entity.  If the
     Document already includes a cover text for the same cover,
     previously added by you or by arrangement made by the same entity
     you are acting on behalf of, you may not add another; but you may
     replace the old one, on explicit permission from the previous
     publisher that added the old one.

     The author(s) and publisher(s) of the Document do not by this
     License give permission to use their names for publicity for or to
     assert or imply endorsement of any Modified Version.

  5. COMBINING DOCUMENTS

     You may combine the Document with other documents released under
     this License, under the terms defined in section 4 above for
     modified versions, provided that you include in the combination
     all of the Invariant Sections of all of the original documents,
     unmodified, and list them all as Invariant Sections of your
     combined work in its license notice, and that you preserve all
     their Warranty Disclaimers.

     The combined work need only contain one copy of this License, and
     multiple identical Invariant Sections may be replaced with a single
     copy.  If there are multiple Invariant Sections with the same name
     but different contents, make the title of each such section unique
     by adding at the end of it, in parentheses, the name of the
     original author or publisher of that section if known, or else a
     unique number.  Make the same adjustment to the section titles in
     the list of Invariant Sections in the license notice of the
     combined work.

     In the combination, you must combine any sections Entitled
     "History" in the various original documents, forming one section
     Entitled "History"; likewise combine any sections Entitled
     "Acknowledgements", and any sections Entitled "Dedications".  You
     must delete all sections Entitled "Endorsements."

  6. COLLECTIONS OF DOCUMENTS

     You may make a collection consisting of the Document and other
     documents released under this License, and replace the individual
     copies of this License in the various documents with a single copy
     that is included in the collection, provided that you follow the
     rules of this License for verbatim copying of each of the
     documents in all other respects.

     You may extract a single document from such a collection, and
     distribute it individually under this License, provided you insert
     a copy of this License into the extracted document, and follow
     this License in all other respects regarding verbatim copying of
     that document.

  7. AGGREGATION WITH INDEPENDENT WORKS

     A compilation of the Document or its derivatives with other
     separate and independent documents or works, in or on a volume of
     a storage or distribution medium, is called an "aggregate" if the
     copyright resulting from the compilation is not used to limit the
     legal rights of the compilation's users beyond what the individual
     works permit.  When the Document is included in an aggregate, this
     License does not apply to the other works in the aggregate which
     are not themselves derivative works of the Document.

     If the Cover Text requirement of section 3 is applicable to these
     copies of the Document, then if the Document is less than one half
     of the entire aggregate, the Document's Cover Texts may be placed
     on covers that bracket the Document within the aggregate, or the
     electronic equivalent of covers if the Document is in electronic
     form.  Otherwise they must appear on printed covers that bracket
     the whole aggregate.

  8. TRANSLATION

     Translation is considered a kind of modification, so you may
     distribute translations of the Document under the terms of section
     4.  Replacing Invariant Sections with translations requires special
     permission from their copyright holders, but you may include
     translations of some or all Invariant Sections in addition to the
     original versions of these Invariant Sections.  You may include a
     translation of this License, and all the license notices in the
     Document, and any Warranty Disclaimers, provided that you also
     include the original English version of this License and the
     original versions of those notices and disclaimers.  In case of a
     disagreement between the translation and the original version of
     this License or a notice or disclaimer, the original version will
     prevail.

     If a section in the Document is Entitled "Acknowledgements",
     "Dedications", or "History", the requirement (section 4) to
     Preserve its Title (section 1) will typically require changing the
     actual title.

  9. TERMINATION

     You may not copy, modify, sublicense, or distribute the Document
     except as expressly provided under this License.  Any attempt
     otherwise to copy, modify, sublicense, or distribute it is void,
     and will automatically terminate your rights under this License.

     However, if you cease all violation of this License, then your
     license from a particular copyright holder is reinstated (a)
     provisionally, unless and until the copyright holder explicitly
     and finally terminates your license, and (b) permanently, if the
     copyright holder fails to notify you of the violation by some
     reasonable means prior to 60 days after the cessation.

     Moreover, your license from a particular copyright holder is
     reinstated permanently if the copyright holder notifies you of the
     violation by some reasonable means, this is the first time you have
     received notice of violation of this License (for any work) from
     that copyright holder, and you cure the violation prior to 30 days
     after your receipt of the notice.

     Termination of your rights under this section does not terminate
     the licenses of parties who have received copies or rights from
     you under this License.  If your rights have been terminated and
     not permanently reinstated, receipt of a copy of some or all of
     the same material does not give you any rights to use it.

 10. FUTURE REVISIONS OF THIS LICENSE

     The Free Software Foundation may publish new, revised versions of
     the GNU Free Documentation License from time to time.  Such new
     versions will be similar in spirit to the present version, but may
     differ in detail to address new problems or concerns.  See
     `http://www.gnu.org/copyleft/'.

     Each version of the License is given a distinguishing version
     number.  If the Document specifies that a particular numbered
     version of this License "or any later version" applies to it, you
     have the option of following the terms and conditions either of
     that specified version or of any later version that has been
     published (not as a draft) by the Free Software Foundation.  If
     the Document does not specify a version number of this License,
     you may choose any version ever published (not as a draft) by the
     Free Software Foundation.  If the Document specifies that a proxy
     can decide which future versions of this License can be used, that
     proxy's public statement of acceptance of a version permanently
     authorizes you to choose that version for the Document.

 11. RELICENSING

     "Massive Multiauthor Collaboration Site" (or "MMC Site") means any
     World Wide Web server that publishes copyrightable works and also
     provides prominent facilities for anybody to edit those works.  A
     public wiki that anybody can edit is an example of such a server.
     A "Massive Multiauthor Collaboration" (or "MMC") contained in the
     site means any set of copyrightable works thus published on the MMC
     site.

     "CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0
     license published by Creative Commons Corporation, a not-for-profit
     corporation with a principal place of business in San Francisco,
     California, as well as future copyleft versions of that license
     published by that same organization.

     "Incorporate" means to publish or republish a Document, in whole or
     in part, as part of another Document.

     An MMC is "eligible for relicensing" if it is licensed under this
     License, and if all works that were first published under this
     License somewhere other than this MMC, and subsequently
     incorporated in whole or in part into the MMC, (1) had no cover
     texts or invariant sections, and (2) were thus incorporated prior
     to November 1, 2008.

     The operator of an MMC Site may republish an MMC contained in the
     site under CC-BY-SA on the same site at any time before August 1,
     2009, provided the MMC is eligible for relicensing.


ADDENDUM: How to use this License for your documents
====================================================

To use this License in a document you have written, include a copy of
the License in the document and put the following copyright and license
notices just after the title page:

       Copyright (C)  YEAR  YOUR NAME.
       Permission is granted to copy, distribute and/or modify this document
       under the terms of the GNU Free Documentation License, Version 1.3
       or any later version published by the Free Software Foundation;
       with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
       Texts.  A copy of the license is included in the section entitled ``GNU
       Free Documentation License''.

   If you have Invariant Sections, Front-Cover Texts and Back-Cover
Texts, replace the "with...Texts." line with this:

         with the Invariant Sections being LIST THEIR TITLES, with
         the Front-Cover Texts being LIST, and with the Back-Cover Texts
         being LIST.

   If you have Invariant Sections without Cover Texts, or some other
combination of the three, merge those two alternatives to suit the
situation.

   If your document contains nontrivial examples of program code, we
recommend releasing these examples in parallel under your choice of
free software license, such as the GNU General Public License, to
permit their use in free software.



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Node: Rule internals11992
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Node: Bocage internals18047
Node: Ordering internals20572
Node: Tree internals21087
Node: Valuator internals23095
Node: Debugging methods23387
Node: GNU Free Documentation License24024

End Tag Table
