NAME

       Marpa::R2::NAIF::Semantics::Order - How the NAIF ranks ambiguous parses

Description

       This document deals with Marpa's low-level NAIF interface.  If you are new to Marpa, or are not sure
       which interface you are interested in, or do not know what the Named Argment InterFace (NAIF) is, you
       probably want to look instead at the document on semantics for the SLIF interface.

       Marpa allows ambiguous parses.  While an unambiguous parse can produce at most one parse tree and one
       parse result, an ambiguous parse will produce a parse series.  A parse series is a sequence of parse
       trees, each of which will have its own parse result.

       This document describes ways of controlling the order in which the NAIF recognizer's "value" method
       evaluates the parse trees of an ambiguous parse; It also describes ways to exclude selected parse trees
       from the parse series.

       Almost all of what is said in this document also applies to the SLIF recognizer's "value" method.
       Certain named arguments which control the parse order are present in the NAIF, but are not present in the
       SLIF, and this accounts for the differences between the two.

   Duplicate parses are eliminated
       When evaluating the parse trees in a parse series, Marpa never evaluates the same parse tree twice.  What
       this means probably matches the programmer intuition of what it should mean.  Marpa considers two parse
       trees to be the same if they are semantic equivalents.

       Two parse trees are semantic equivalents if and only if a recursive, top-down evaluation of each applies
       the same rules in the same order at the same earleme locations.  This definition implies that, given any
       deterministic semantics, two parse trees which are semantic equivalents will always produce the same
       parse result -- hence the term.  When the Marpa documentation refers to duplicate parses, it will mean
       that the two are semantic equivalents, unless otherwise stated.

   Default parse order
       In this document, the term arbitrary parse order is used to mean an arbitrary choice among the strict
       total orders of the equivalence classes that contain the semantically equivalent parse trees.  This set
       of equivalence classes is finite.

       Traversal of the parse trees in arbitrary parse order will be always be well-behaved in the sense that no
       two parse trees will be semantic duplicates, and no unique (semantic non-duplicate) parse tree will be
       omitted in it, No other property of arbitrary parse order is guaranteed.  For example, the order may
       change each time the parse series is traversed.

       By calling the recognizer's "value" method repeatedly, Marpa can produce all the parse results in the
       current parse series.  The default is for the parse results to be returned in an arbitrary parse order.
       This corresponds to the ""none"" value of the recognizer's "ranking_method" named argument.

   Ranking methods
       Marpa recognizer objects have a "ranking_method" named argument, whose value can be the name of a ranking
       method, or ""none"", indicating that the default ranking method is to be used.

   The "rule" ranking method
       The rule method ranks alternative parses according to their rules.  Every rule has a rule rank.  A rule's
       rank can be specified using the the "rank" named argument for that rule.  Rule ranks must be integers.
       If no rule rank is specified, the rule rank is 0.

   The "high_rule_only" ranking method
       The "high_rule_only" ranking method is similar to the "rule" ranking method, except that, at every choice
       point, it discards all of the choices which have a rank lower than that of the highest ranked
       alternative.

       Since the "high_rule_only" ranking method eliminates some parse trees, it can reduce or eliminate the
       ambiguity of a parse, but it does not necessarily do either.  This is because, at each choice point among
       the parse trees, it is possible that several of the choices, or all of them, will have the same rank as
       the highest ranked alternative.

   Rule ranking
       A parse series is kept in a structure called a parse bocage.  The parse bocage is a tree-like structure,
       whose root node is the common root of all the parse trees of the parse series.  In an unambiguous parse,
       there will be only one parse tree, and the parse bocage will be equivalent to that parse tree.  In an
       ambiguous parse, there will be choice points in the parse bocage.  At the choice points, there will be
       two or more alternatives -- choices which result in different parse trees.

       When ranking, the logic traverses the parse bocage, looking for choice points.  From the point of view of
       the individual parse trees, this traversal will be top-down and left-to-right.  At the choice points, the
       alternatives are ranked (in the "rule" ranking method) or selected (in the "high_rule_only" ranking
       method), by comparing them as follows:

       •   Different ranks: If the two alternatives have different rule ranks, they must also have different
           rules.  The alternative with the higher rule rank will rank high.

       •   Same Rule: If the two alternatives have the same rule, they rank as described under "Null variant
           ranking".

       •   Same rank, different rules: Two different rules can have the same rank.  If the two alternatives are
           for different rules, but the two rules have the same rank, the relative order of the two alternatives
           is arbitrary.

   Null variant ranking
       Some rules have a RHS which contains proper nullables: symbols which may be nulled, but which are not
       nulling symbols.  (Nulling symbols are symbols which are always nulled.)

       When a rule contains proper nullables, each application of that rule to a section of input creates a
       nulling variant -- that rule with a specific pattern of null and non-null symbols.  In many cases, this
       creates an ambiguity -- different nulling variants could apply to the same substring of input.  In
       ambiguous parsings of this kind, some applications may want to rank nulling variants that start with non-
       null symbols higher.  Other applications may want to do the opposite -- to rank nulling variants that
       start with null symbols higher.

       The "null_ranking" named argument for rules specifies which nulling variants are ranked high or low.
       Ranking of nulling variants is done left-to-right, with the null preference as indicated by the
       "null_ranking" named argument.  Specifically, if the "null_ranking" is ""low"", then the closer a nulling
       variant places its visible (non-null) symbols to the start of the rule, the higher it ranks.  "low" null
       ranking is the default.  If the "null_ranking" is ""high"", then the closer a nulling variant places its
       null symbols to the start of the rule, the higher it ranks.

   A general approach to sorting parses
       The most general way to sort Marpa parses is for the application to take control.  The application can
       set up the Marpa semantic actions so that the parse result of every parse tree is a "<rank, true_value>"
       duple.  The duples can then be sorted by "rank".  Once the resuls are sorted, the "rank" element of the
       duple can be discarded.  (Those familiar with the Schwartzian transform may note a resemblance.  In Perl,
       duples can be implemented as references to arrays of 2 elements.)

       The user needs to be careful.  In theory, ambiguity can cause an exponential explosion in the number of
       results.  In practice, ambiguity tends to get out of hand very easily.  Producing and sorting all the
       parses can take a very long time.

Copyright and License

         Copyright 2014 Jeffrey Kegler
         This file is part of Marpa::R2.  Marpa::R2 is free software: you can
         redistribute it and/or modify it under the terms of the GNU Lesser
         General Public License as published by the Free Software Foundation,
         either version 3 of the License, or (at your option) any later version.

         Marpa::R2 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.  See the GNU
         Lesser General Public License for more details.

         You should have received a copy of the GNU Lesser
         General Public License along with Marpa::R2.  If not, see
         http://www.gnu.org/licenses/.